author | Dan |
Mon, 12 May 2008 00:59:46 -0400 | |
changeset 554 | e87390b1f9b0 |
parent 436 | 242353360e37 |
permissions | -rw-r--r-- |
436
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1 |
//////////////////////////////////////////////////////////////////////////////////////// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
2 |
// Big Integer Library v. 5.1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
3 |
// Created 2000, last modified 2007 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
4 |
// Leemon Baird |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
5 |
// www.leemon.com |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
6 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
7 |
// Version history: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
8 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
9 |
// v 5.1 8 Oct 2007 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
10 |
// - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
11 |
// - added functions GCD and randBigInt, which call GCD_ and randBigInt_ |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
12 |
// - fixed a bug found by Rob Visser (see comment with his name below) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
13 |
// - improved comments |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
14 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
15 |
// This file is public domain. You can use it for any purpose without restriction. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
16 |
// I do not guarantee that it is correct, so use it at your own risk. If you use |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
17 |
// it for something interesting, I'd appreciate hearing about it. If you find |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
18 |
// any bugs or make any improvements, I'd appreciate hearing about those too. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
19 |
// It would also be nice if my name and address were left in the comments. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
20 |
// But none of that is required. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
21 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
22 |
// This code defines a bigInt library for arbitrary-precision integers. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
23 |
// A bigInt is an array of integers storing the value in chunks of bpe bits, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
24 |
// little endian (buff[0] is the least significant word). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
25 |
// Negative bigInts are stored two's complement. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
26 |
// Some functions assume their parameters have at least one leading zero element. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
27 |
// Functions with an underscore at the end of the name have unpredictable behavior in case of overflow, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
28 |
// so the caller must make sure the arrays must be big enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
29 |
// For each function where a parameter is modified, that same |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
30 |
// variable must not be used as another argument too. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
31 |
// So, you cannot square x by doing multMod_(x,x,n). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
32 |
// You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
33 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
34 |
// These functions are designed to avoid frequent dynamic memory allocation in the inner loop. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
35 |
// For most functions, if it needs a BigInt as a local variable it will actually use |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
36 |
// a global, and will only allocate to it only when it's not the right size. This ensures |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
37 |
// that when a function is called repeatedly with same-sized parameters, it only allocates |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
38 |
// memory on the first call. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
39 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
40 |
// Note that for cryptographic purposes, the calls to Math.random() must |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
41 |
// be replaced with calls to a better pseudorandom number generator. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
42 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
43 |
// In the following, "bigInt" means a bigInt with at least one leading zero element, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
44 |
// and "integer" means a nonnegative integer less than radix. In some cases, integer |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
45 |
// can be negative. Negative bigInts are 2s complement. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
46 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
47 |
// The following functions do not modify their inputs. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
48 |
// Those returning a bigInt, string, or Array will dynamically allocate memory for that value. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
49 |
// Those returning a boolean will return the integer 0 (false) or 1 (true). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
50 |
// Those returning boolean or int will not allocate memory except possibly on the first time they're called with a given parameter size. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
51 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
52 |
// bigInt add(x,y) //return (x+y) for bigInts x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
53 |
// bigInt addInt(x,n) //return (x+n) where x is a bigInt and n is an integer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
54 |
// string bigInt2str(x,base) //return a string form of bigInt x in a given base, with 2 <= base <= 95 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
55 |
// int bitSize(x) //return how many bits long the bigInt x is, not counting leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
56 |
// bigInt dup(x) //return a copy of bigInt x |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
57 |
// boolean equals(x,y) //is the bigInt x equal to the bigint y? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
58 |
// boolean equalsInt(x,y) //is bigint x equal to integer y? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
59 |
// bigInt expand(x,n) //return a copy of x with at least n elements, adding leading zeros if needed |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
60 |
// Array findPrimes(n) //return array of all primes less than integer n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
61 |
// bigInt GCD(x,y) //return greatest common divisor of bigInts x and y (each with same number of elements). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
62 |
// boolean greater(x,y) //is x>y? (x and y are nonnegative bigInts) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
63 |
// boolean greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
64 |
// bigInt int2bigInt(t,n,m) //return a bigInt equal to integer t, with at least n bits and m array elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
65 |
// bigInt inverseMod(x,n) //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
66 |
// int inverseModInt(x,n) //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
67 |
// boolean isZero(x) //is the bigInt x equal to zero? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
68 |
// boolean millerRabin(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime (as opposed to definitely composite)? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
69 |
// bigInt mod(x,n) //return a new bigInt equal to (x mod n) for bigInts x and n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
70 |
// int modInt(x,n) //return x mod n for bigInt x and integer n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
71 |
// bigInt mult(x,y) //return x*y for bigInts x and y. This is faster when y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
72 |
// bigInt multMod(x,y,n) //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
73 |
// boolean negative(x) //is bigInt x negative? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
74 |
// bigInt powMod(x,y,n) //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
75 |
// bigInt randBigInt(n,s) //return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
76 |
// bigInt randTruePrime(k) //return a new, random, k-bit, true prime bigInt using Maurer's algorithm. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
77 |
// bigInt str2bigInt(s,b,n,m) //return a bigInt for number represented in string s in base b with at least n bits and m array elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
78 |
// bigInt sub(x,y) //return (x-y) for bigInts x and y. Negative answers will be 2s complement |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
79 |
// bigInt bigint_trim(x,k) //return a copy of x with exactly k leading zero elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
80 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
81 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
82 |
// The following functions each have a non-underscored version, which most users should call instead. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
83 |
// These functions each write to a single parameter, and the caller is responsible for ensuring the array |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
84 |
// passed in is large enough to hold the result. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
85 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
86 |
// void addInt_(x,n) //do x=x+n where x is a bigInt and n is an integer |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
87 |
// void add_(x,y) //do x=x+y for bigInts x and y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
88 |
// void copy_(x,y) //do x=y on bigInts x and y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
89 |
// void copyInt_(x,n) //do x=n on bigInt x and integer n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
90 |
// void GCD_(x,y) //set x to the greatest common divisor of bigInts x and y, (y is destroyed). (This never overflows its array). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
91 |
// boolean inverseMod_(x,n) //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
92 |
// void mod_(x,n) //do x=x mod n for bigInts x and n. (This never overflows its array). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
93 |
// void mult_(x,y) //do x=x*y for bigInts x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
94 |
// void multMod_(x,y,n) //do x=x*y mod n for bigInts x,y,n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
95 |
// void powMod_(x,y,n) //do x=x**y mod n, where x,y,n are bigInts (n is odd) and ** is exponentiation. 0**0=1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
96 |
// void randBigInt_(b,n,s) //do b = an n-bit random BigInt. if s=1, then nth bit (most significant bit) is set to 1. n>=1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
97 |
// void randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
98 |
// void sub_(x,y) //do x=x-y for bigInts x and y. Negative answers will be 2s complement. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
99 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
100 |
// The following functions do NOT have a non-underscored version. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
101 |
// They each write a bigInt result to one or more parameters. The caller is responsible for |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
102 |
// ensuring the arrays passed in are large enough to hold the results. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
103 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
104 |
// void addShift_(x,y,ys) //do x=x+(y<<(ys*bpe)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
105 |
// void carry_(x) //do carries and borrows so each element of the bigInt x fits in bpe bits. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
106 |
// void divide_(x,y,q,r) //divide x by y giving quotient q and remainder r |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
107 |
// int divInt_(x,n) //do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
108 |
// int eGCD_(x,y,d,a,b) //sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
109 |
// void halve_(x) //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement. (This never overflows its array). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
110 |
// void leftShift_(x,n) //left shift bigInt x by n bits. n<bpe. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
111 |
// void linComb_(x,y,a,b) //do x=a*x+b*y for bigInts x and y and integers a and b |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
112 |
// void linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
113 |
// void mont_(x,y,n,np) //Montgomery multiplication (see comments where the function is defined) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
114 |
// void multInt_(x,n) //do x=x*n where x is a bigInt and n is an integer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
115 |
// void rightShift_(x,n) //right shift bigInt x by n bits. 0 <= n < bpe. (This never overflows its array). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
116 |
// void squareMod_(x,n) //do x=x*x mod n for bigInts x,n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
117 |
// void subShift_(x,y,ys) //do x=x-(y<<(ys*bpe)). Negative answers will be 2s complement. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
118 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
119 |
// The following functions are based on algorithms from the _Handbook of Applied Cryptography_ |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
120 |
// powMod_() = algorithm 14.94, Montgomery exponentiation |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
121 |
// eGCD_,inverseMod_() = algorithm 14.61, Binary extended GCD_ |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
122 |
// GCD_() = algorothm 14.57, Lehmer's algorithm |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
123 |
// mont_() = algorithm 14.36, Montgomery multiplication |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
124 |
// divide_() = algorithm 14.20 Multiple-precision division |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
125 |
// squareMod_() = algorithm 14.16 Multiple-precision squaring |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
126 |
// randTruePrime_() = algorithm 4.62, Maurer's algorithm |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
127 |
// millerRabin() = algorithm 4.24, Miller-Rabin algorithm |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
128 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
129 |
// Profiling shows: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
130 |
// randTruePrime_() spends: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
131 |
// 10% of its time in calls to powMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
132 |
// 85% of its time in calls to millerRabin() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
133 |
// millerRabin() spends: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
134 |
// 99% of its time in calls to powMod_() (always with a base of 2) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
135 |
// powMod_() spends: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
136 |
// 94% of its time in calls to mont_() (almost always with x==y) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
137 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
138 |
// This suggests there are several ways to speed up this library slightly: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
139 |
// - convert powMod_ to use a Montgomery form of k-ary window (or maybe a Montgomery form of sliding window) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
140 |
// -- this should especially focus on being fast when raising 2 to a power mod n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
141 |
// - convert randTruePrime_() to use a minimum r of 1/3 instead of 1/2 with the appropriate change to the test |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
142 |
// - tune the parameters in randTruePrime_(), including c, m, and recLimit |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
143 |
// - speed up the single loop in mont_() that takes 95% of the runtime, perhaps by reducing checking |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
144 |
// within the loop when all the parameters are the same length. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
145 |
// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
146 |
// There are several ideas that look like they wouldn't help much at all: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
147 |
// - replacing trial division in randTruePrime_() with a sieve (that speeds up something taking almost no time anyway) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
148 |
// - increase bpe from 15 to 30 (that would help if we had a 32*32->64 multiplier, but not with JavaScript's 32*32->32) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
149 |
// - speeding up mont_(x,y,n,np) when x==y by doing a non-modular, non-Montgomery square |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
150 |
// followed by a Montgomery reduction. The intermediate answer will be twice as long as x, so that |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
151 |
// method would be slower. This is unfortunate because the code currently spends almost all of its time |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
152 |
// doing mont_(x,x,...), both for randTruePrime_() and powMod_(). A faster method for Montgomery squaring |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
153 |
// would have a large impact on the speed of randTruePrime_() and powMod_(). HAC has a couple of poorly-worded |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
154 |
// sentences that seem to imply it's faster to do a non-modular square followed by a single |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
155 |
// Montgomery reduction, but that's obviously wrong. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
156 |
//////////////////////////////////////////////////////////////////////////////////////// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
157 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
158 |
//globals |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
159 |
bpe=0; //bits stored per array element |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
160 |
mask=0; //AND this with an array element to chop it down to bpe bits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
161 |
radix=mask+1; //equals 2^bpe. A single 1 bit to the left of the last bit of mask. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
162 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
163 |
//the digits for converting to different bases |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
164 |
digitsStr='0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-'; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
165 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
166 |
//initialize the global variables |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
167 |
for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++); //bpe=number of bits in the mantissa on this platform |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
168 |
bpe>>=1; //bpe=number of bits in one element of the array representing the bigInt |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
169 |
mask=(1<<bpe)-1; //AND the mask with an integer to get its bpe least significant bits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
170 |
radix=mask+1; //2^bpe. a single 1 bit to the left of the first bit of mask |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
171 |
one=int2bigInt(1,1,1); //constant used in powMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
172 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
173 |
//the following global variables are scratchpad memory to |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
174 |
//reduce dynamic memory allocation in the inner loop |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
175 |
t=new Array(0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
176 |
ss=t; //used in mult_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
177 |
s0=t; //used in multMod_(), squareMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
178 |
s1=t; //used in powMod_(), multMod_(), squareMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
179 |
s2=t; //used in powMod_(), multMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
180 |
s3=t; //used in powMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
181 |
s4=t; s5=t; //used in mod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
182 |
s6=t; //used in bigInt2str() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
183 |
s7=t; //used in powMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
184 |
T=t; //used in GCD_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
185 |
sa=t; //used in mont_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
186 |
mr_x1=t; mr_r=t; mr_a=t; //used in millerRabin() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
187 |
eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t; //used in eGCD_(), inverseMod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
188 |
md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
189 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
190 |
primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
191 |
s_a=t; s_r2=t; s_n=t; s_b=t; s_d=t; s_x1=t; s_x2=t, s_aa=t; //used in randTruePrime_() |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
192 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
193 |
//////////////////////////////////////////////////////////////////////////////////////// |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
194 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
195 |
//return array of all primes less than integer n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
196 |
function findPrimes(n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
197 |
var i,s,p,ans; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
198 |
s=new Array(n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
199 |
for (i=0;i<n;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
200 |
s[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
201 |
s[0]=2; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
202 |
p=0; //first p elements of s are primes, the rest are a sieve |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
203 |
for(;s[p]<n;) { //s[p] is the pth prime |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
204 |
for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
205 |
s[i]=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
206 |
p++; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
207 |
s[p]=s[p-1]+1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
208 |
for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
209 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
210 |
ans=new Array(p); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
211 |
for(i=0;i<p;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
212 |
ans[i]=s[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
213 |
return ans; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
214 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
215 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
216 |
//does a single round of Miller-Rabin base b consider x to be a possible prime? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
217 |
//x is a bigInt, and b is an integer |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
218 |
function millerRabin(x,b) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
219 |
var i,j,k,s; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
220 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
221 |
if (mr_x1.length!=x.length) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
222 |
mr_x1=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
223 |
mr_r=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
224 |
mr_a=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
225 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
226 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
227 |
copyInt_(mr_a,b); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
228 |
copy_(mr_r,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
229 |
copy_(mr_x1,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
230 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
231 |
addInt_(mr_r,-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
232 |
addInt_(mr_x1,-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
233 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
234 |
//s=the highest power of two that divides mr_r |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
235 |
k=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
236 |
for (i=0;i<mr_r.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
237 |
for (j=1;j<mask;j<<=1) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
238 |
if (x[i] & j) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
239 |
s=(k<mr_r.length+bpe ? k : 0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
240 |
i=mr_r.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
241 |
j=mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
242 |
} else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
243 |
k++; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
244 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
245 |
if (s) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
246 |
rightShift_(mr_r,s); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
247 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
248 |
powMod_(mr_a,mr_r,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
249 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
250 |
if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
251 |
j=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
252 |
while (j<=s-1 && !equals(mr_a,mr_x1)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
253 |
squareMod_(mr_a,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
254 |
if (equalsInt(mr_a,1)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
255 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
256 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
257 |
j++; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
258 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
259 |
if (!equals(mr_a,mr_x1)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
260 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
261 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
262 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
263 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
264 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
265 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
266 |
//returns how many bits long the bigInt is, not counting leading zeros. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
267 |
function bitSize(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
268 |
var j,z,w; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
269 |
for (j=x.length-1; (x[j]==0) && (j>0); j--); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
270 |
for (z=0,w=x[j]; w; (w>>=1),z++); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
271 |
z+=bpe*j; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
272 |
return z; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
273 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
274 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
275 |
//return a copy of x with at least n elements, adding leading zeros if needed |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
276 |
function expand(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
277 |
var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
278 |
copy_(ans,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
279 |
return ans; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
280 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
281 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
282 |
//return a k-bit true random prime using Maurer's algorithm. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
283 |
function randTruePrime(k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
284 |
var ans=int2bigInt(0,k,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
285 |
randTruePrime_(ans,k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
286 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
287 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
288 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
289 |
//return a new bigInt equal to (x mod n) for bigInts x and n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
290 |
function mod(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
291 |
var ans=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
292 |
mod_(ans,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
293 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
294 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
295 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
296 |
//return (x+n) where x is a bigInt and n is an integer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
297 |
function addInt(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
298 |
var ans=expand(x,x.length+1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
299 |
addInt_(ans,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
300 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
301 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
302 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
303 |
//return x*y for bigInts x and y. This is faster when y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
304 |
function mult(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
305 |
var ans=expand(x,x.length+y.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
306 |
mult_(ans,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
307 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
308 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
309 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
310 |
//return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
311 |
function powMod(x,y,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
312 |
var ans=expand(x,n.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
313 |
powMod_(ans,bigint_trim(y,2),bigint_trim(n,2),0); //this should work without the trim, but doesn't |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
314 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
315 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
316 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
317 |
//return (x-y) for bigInts x and y. Negative answers will be 2s complement |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
318 |
function sub(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
319 |
var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
320 |
sub_(ans,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
321 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
322 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
323 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
324 |
//return (x+y) for bigInts x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
325 |
function add(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
326 |
var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
327 |
add_(ans,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
328 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
329 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
330 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
331 |
//return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
332 |
function inverseMod(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
333 |
var ans=expand(x,n.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
334 |
var s; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
335 |
s=inverseMod_(ans,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
336 |
return s ? bigint_trim(ans,1) : null; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
337 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
338 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
339 |
//return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
340 |
function multMod(x,y,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
341 |
var ans=expand(x,n.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
342 |
multMod_(ans,y,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
343 |
return bigint_trim(ans,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
344 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
345 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
346 |
//generate a k-bit true random prime using Maurer's algorithm, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
347 |
//and put it into ans. The bigInt ans must be large enough to hold it. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
348 |
function randTruePrime_(ans,k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
349 |
var c,m,pm,dd,j,r,B,divisible,z,zz,recSize; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
350 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
351 |
if (primes.length==0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
352 |
primes=findPrimes(30000); //check for divisibility by primes <=30000 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
353 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
354 |
if (pows.length==0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
355 |
pows=new Array(512); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
356 |
for (j=0;j<512;j++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
357 |
pows[j]=Math.pow(2,j/511.-1.); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
358 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
359 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
360 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
361 |
//c and m should be tuned for a particular machine and value of k, to maximize speed |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
362 |
c=0.1; //c=0.1 in HAC |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
363 |
m=20; //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
364 |
recLimit=20; //stop recursion when k <=recLimit. Must have recLimit >= 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
365 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
366 |
if (s_i2.length!=ans.length) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
367 |
s_i2=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
368 |
s_R =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
369 |
s_n1=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
370 |
s_r2=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
371 |
s_d =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
372 |
s_x1=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
373 |
s_x2=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
374 |
s_b =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
375 |
s_n =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
376 |
s_i =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
377 |
s_rm=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
378 |
s_q =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
379 |
s_a =dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
380 |
s_aa=dup(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
381 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
382 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
383 |
if (k <= recLimit) { //generate small random primes by trial division up to its square root |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
384 |
pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
385 |
copyInt_(ans,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
386 |
for (dd=1;dd;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
387 |
dd=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
388 |
ans[0]= 1 | (1<<(k-1)) | Math.floor(Math.random()*(1<<k)); //random, k-bit, odd integer, with msb 1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
389 |
for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
390 |
if (0==(ans[0]%primes[j])) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
391 |
dd=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
392 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
393 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
394 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
395 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
396 |
carry_(ans); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
397 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
398 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
399 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
400 |
B=c*k*k; //try small primes up to B (or all the primes[] array if the largest is less than B). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
401 |
if (k>2*m) //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
402 |
for (r=1; k-k*r<=m; ) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
403 |
r=pows[Math.floor(Math.random()*512)]; //r=Math.pow(2,Math.random()-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
404 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
405 |
r=.5; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
406 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
407 |
//simulation suggests the more complex algorithm using r=.333 is only slightly faster. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
408 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
409 |
recSize=Math.floor(r*k)+1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
410 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
411 |
randTruePrime_(s_q,recSize); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
412 |
copyInt_(s_i2,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
413 |
s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe)); //s_i2=2^(k-2) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
414 |
divide_(s_i2,s_q,s_i,s_rm); //s_i=floor((2^(k-1))/(2q)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
415 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
416 |
z=bitSize(s_i); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
417 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
418 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
419 |
for (;;) { //generate z-bit numbers until one falls in the range [0,s_i-1] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
420 |
randBigInt_(s_R,z,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
421 |
if (greater(s_i,s_R)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
422 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
423 |
} //now s_R is in the range [0,s_i-1] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
424 |
addInt_(s_R,1); //now s_R is in the range [1,s_i] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
425 |
add_(s_R,s_i); //now s_R is in the range [s_i+1,2*s_i] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
426 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
427 |
copy_(s_n,s_q); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
428 |
mult_(s_n,s_R); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
429 |
multInt_(s_n,2); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
430 |
addInt_(s_n,1); //s_n=2*s_R*s_q+1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
431 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
432 |
copy_(s_r2,s_R); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
433 |
multInt_(s_r2,2); //s_r2=2*s_R |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
434 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
435 |
//check s_n for divisibility by small primes up to B |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
436 |
for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
437 |
if (modInt(s_n,primes[j])==0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
438 |
divisible=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
439 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
440 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
441 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
442 |
if (!divisible) //if it passes small primes check, then try a single Miller-Rabin base 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
443 |
if (!millerRabin(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
444 |
divisible=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
445 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
446 |
if (!divisible) { //if it passes that test, continue checking s_n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
447 |
addInt_(s_n,-3); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
448 |
for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--); //strip leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
449 |
for (zz=0,w=s_n[j]; w; (w>>=1),zz++); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
450 |
zz+=bpe*j; //zz=number of bits in s_n, ignoring leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
451 |
for (;;) { //generate z-bit numbers until one falls in the range [0,s_n-1] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
452 |
randBigInt_(s_a,zz,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
453 |
if (greater(s_n,s_a)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
454 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
455 |
} //now s_a is in the range [0,s_n-1] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
456 |
addInt_(s_n,3); //now s_a is in the range [0,s_n-4] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
457 |
addInt_(s_a,2); //now s_a is in the range [2,s_n-2] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
458 |
copy_(s_b,s_a); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
459 |
copy_(s_n1,s_n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
460 |
addInt_(s_n1,-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
461 |
powMod_(s_b,s_n1,s_n); //s_b=s_a^(s_n-1) modulo s_n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
462 |
addInt_(s_b,-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
463 |
if (isZero(s_b)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
464 |
copy_(s_b,s_a); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
465 |
powMod_(s_b,s_r2,s_n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
466 |
addInt_(s_b,-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
467 |
copy_(s_aa,s_n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
468 |
copy_(s_d,s_b); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
469 |
GCD_(s_d,s_n); //if s_b and s_n are relatively prime, then s_n is a prime |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
470 |
if (equalsInt(s_d,1)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
471 |
copy_(ans,s_aa); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
472 |
return; //if we've made it this far, then s_n is absolutely guaranteed to be prime |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
473 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
474 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
475 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
476 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
477 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
478 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
479 |
//Return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
480 |
function randBigInt(n,s) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
481 |
var a,b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
482 |
a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
483 |
b=int2bigInt(0,0,a); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
484 |
randBigInt_(b,n,s); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
485 |
return b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
486 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
487 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
488 |
//Set b to an n-bit random BigInt. If s=1, then the most significant of those n bits is set to 1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
489 |
//Array b must be big enough to hold the result. Must have n>=1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
490 |
function randBigInt_(b,n,s) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
491 |
var i,a; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
492 |
for (i=0;i<b.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
493 |
b[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
494 |
a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
495 |
for (i=0;i<a;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
496 |
b[i]=Math.floor(Math.random()*(1<<(bpe-1))); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
497 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
498 |
b[a-1] &= (2<<((n-1)%bpe))-1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
499 |
if (s==1) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
500 |
b[a-1] |= (1<<((n-1)%bpe)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
501 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
502 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
503 |
//Return the greatest common divisor of bigInts x and y (each with same number of elements). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
504 |
function GCD(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
505 |
var xc,yc; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
506 |
xc=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
507 |
yc=dup(y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
508 |
GCD_(xc,yc); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
509 |
return xc; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
510 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
511 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
512 |
//set x to the greatest common divisor of bigInts x and y (each with same number of elements). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
513 |
//y is destroyed. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
514 |
function GCD_(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
515 |
var i,xp,yp,A,B,C,D,q,sing; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
516 |
if (T.length!=x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
517 |
T=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
518 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
519 |
sing=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
520 |
while (sing) { //while y has nonzero elements other than y[0] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
521 |
sing=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
522 |
for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
523 |
if (y[i]) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
524 |
sing=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
525 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
526 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
527 |
if (!sing) break; //quit when y all zero elements except possibly y[0] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
528 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
529 |
for (i=x.length;!x[i] && i>=0;i--); //find most significant element of x |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
530 |
xp=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
531 |
yp=y[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
532 |
A=1; B=0; C=0; D=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
533 |
while ((yp+C) && (yp+D)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
534 |
q =Math.floor((xp+A)/(yp+C)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
535 |
qp=Math.floor((xp+B)/(yp+D)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
536 |
if (q!=qp) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
537 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
538 |
t= A-q*C; A=C; C=t; // do (A,B,xp, C,D,yp) = (C,D,yp, A,B,xp) - q*(0,0,0, C,D,yp) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
539 |
t= B-q*D; B=D; D=t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
540 |
t=xp-q*yp; xp=yp; yp=t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
541 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
542 |
if (B) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
543 |
copy_(T,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
544 |
linComb_(x,y,A,B); //x=A*x+B*y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
545 |
linComb_(y,T,D,C); //y=D*y+C*T |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
546 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
547 |
mod_(x,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
548 |
copy_(T,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
549 |
copy_(x,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
550 |
copy_(y,T); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
551 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
552 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
553 |
if (y[0]==0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
554 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
555 |
t=modInt(x,y[0]); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
556 |
copyInt_(x,y[0]); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
557 |
y[0]=t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
558 |
while (y[0]) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
559 |
x[0]%=y[0]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
560 |
t=x[0]; x[0]=y[0]; y[0]=t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
561 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
562 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
563 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
564 |
//do x=x**(-1) mod n, for bigInts x and n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
565 |
//If no inverse exists, it sets x to zero and returns 0, else it returns 1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
566 |
//The x array must be at least as large as the n array. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
567 |
function inverseMod_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
568 |
var k=1+2*Math.max(x.length,n.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
569 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
570 |
if(!(x[0]&1) && !(n[0]&1)) { //if both inputs are even, then inverse doesn't exist |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
571 |
copyInt_(x,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
572 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
573 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
574 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
575 |
if (eg_u.length!=k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
576 |
eg_u=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
577 |
eg_v=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
578 |
eg_A=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
579 |
eg_B=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
580 |
eg_C=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
581 |
eg_D=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
582 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
583 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
584 |
copy_(eg_u,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
585 |
copy_(eg_v,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
586 |
copyInt_(eg_A,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
587 |
copyInt_(eg_B,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
588 |
copyInt_(eg_C,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
589 |
copyInt_(eg_D,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
590 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
591 |
while(!(eg_u[0]&1)) { //while eg_u is even |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
592 |
halve_(eg_u); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
593 |
if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
594 |
halve_(eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
595 |
halve_(eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
596 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
597 |
add_(eg_A,n); halve_(eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
598 |
sub_(eg_B,x); halve_(eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
599 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
600 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
601 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
602 |
while (!(eg_v[0]&1)) { //while eg_v is even |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
603 |
halve_(eg_v); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
604 |
if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
605 |
halve_(eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
606 |
halve_(eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
607 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
608 |
add_(eg_C,n); halve_(eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
609 |
sub_(eg_D,x); halve_(eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
610 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
611 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
612 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
613 |
if (!greater(eg_v,eg_u)) { //eg_v <= eg_u |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
614 |
sub_(eg_u,eg_v); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
615 |
sub_(eg_A,eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
616 |
sub_(eg_B,eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
617 |
} else { //eg_v > eg_u |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
618 |
sub_(eg_v,eg_u); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
619 |
sub_(eg_C,eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
620 |
sub_(eg_D,eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
621 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
622 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
623 |
if (equalsInt(eg_u,0)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
624 |
if (negative(eg_C)) //make sure answer is nonnegative |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
625 |
add_(eg_C,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
626 |
copy_(x,eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
627 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
628 |
if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
629 |
copyInt_(x,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
630 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
631 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
632 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
633 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
634 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
635 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
636 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
637 |
//return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
638 |
function inverseModInt(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
639 |
var a=1,b=0,t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
640 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
641 |
if (x==1) return a; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
642 |
if (x==0) return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
643 |
b-=a*Math.floor(n/x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
644 |
n%=x; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
645 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
646 |
if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to += |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
647 |
if (n==0) return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
648 |
a-=b*Math.floor(x/n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
649 |
x%=n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
650 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
651 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
652 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
653 |
//this deprecated function is for backward compatibility only. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
654 |
function inverseModInt_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
655 |
return inverseModInt(x,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
656 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
657 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
658 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
659 |
//Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
660 |
// v = GCD_(x,y) = a*x-b*y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
661 |
//The bigInts v, a, b, must have exactly as many elements as the larger of x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
662 |
function eGCD_(x,y,v,a,b) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
663 |
var g=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
664 |
var k=Math.max(x.length,y.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
665 |
if (eg_u.length!=k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
666 |
eg_u=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
667 |
eg_A=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
668 |
eg_B=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
669 |
eg_C=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
670 |
eg_D=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
671 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
672 |
while(!(x[0]&1) && !(y[0]&1)) { //while x and y both even |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
673 |
halve_(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
674 |
halve_(y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
675 |
g++; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
676 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
677 |
copy_(eg_u,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
678 |
copy_(v,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
679 |
copyInt_(eg_A,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
680 |
copyInt_(eg_B,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
681 |
copyInt_(eg_C,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
682 |
copyInt_(eg_D,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
683 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
684 |
while(!(eg_u[0]&1)) { //while u is even |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
685 |
halve_(eg_u); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
686 |
if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
687 |
halve_(eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
688 |
halve_(eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
689 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
690 |
add_(eg_A,y); halve_(eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
691 |
sub_(eg_B,x); halve_(eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
692 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
693 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
694 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
695 |
while (!(v[0]&1)) { //while v is even |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
696 |
halve_(v); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
697 |
if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
698 |
halve_(eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
699 |
halve_(eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
700 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
701 |
add_(eg_C,y); halve_(eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
702 |
sub_(eg_D,x); halve_(eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
703 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
704 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
705 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
706 |
if (!greater(v,eg_u)) { //v<=u |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
707 |
sub_(eg_u,v); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
708 |
sub_(eg_A,eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
709 |
sub_(eg_B,eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
710 |
} else { //v>u |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
711 |
sub_(v,eg_u); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
712 |
sub_(eg_C,eg_A); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
713 |
sub_(eg_D,eg_B); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
714 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
715 |
if (equalsInt(eg_u,0)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
716 |
if (negative(eg_C)) { //make sure a (C)is nonnegative |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
717 |
add_(eg_C,y); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
718 |
sub_(eg_D,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
719 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
720 |
multInt_(eg_D,-1); ///make sure b (D) is nonnegative |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
721 |
copy_(a,eg_C); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
722 |
copy_(b,eg_D); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
723 |
leftShift_(v,g); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
724 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
725 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
726 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
727 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
728 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
729 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
730 |
//is bigInt x negative? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
731 |
function negative(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
732 |
return ((x[x.length-1]>>(bpe-1))&1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
733 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
734 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
735 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
736 |
//is (x << (shift*bpe)) > y? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
737 |
//x and y are nonnegative bigInts |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
738 |
//shift is a nonnegative integer |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
739 |
function greaterShift(x,y,shift) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
740 |
var kx=x.length, ky=y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
741 |
k=((kx+shift)<ky) ? (kx+shift) : ky; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
742 |
for (i=ky-1-shift; i<kx && i>=0; i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
743 |
if (x[i]>0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
744 |
return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
745 |
for (i=kx-1+shift; i<ky; i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
746 |
if (y[i]>0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
747 |
return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
748 |
for (i=k-1; i>=shift; i--) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
749 |
if (x[i-shift]>y[i]) return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
750 |
else if (x[i-shift]<y[i]) return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
751 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
752 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
753 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
754 |
//is x > y? (x and y both nonnegative) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
755 |
function greater(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
756 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
757 |
var k=(x.length<y.length) ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
758 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
759 |
for (i=x.length;i<y.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
760 |
if (y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
761 |
return 0; //y has more digits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
762 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
763 |
for (i=y.length;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
764 |
if (x[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
765 |
return 1; //x has more digits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
766 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
767 |
for (i=k-1;i>=0;i--) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
768 |
if (x[i]>y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
769 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
770 |
else if (x[i]<y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
771 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
772 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
773 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
774 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
775 |
//divide x by y giving quotient q and remainder r. (q=floor(x/y), r=x mod y). All 4 are bigints. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
776 |
//x must have at least one leading zero element. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
777 |
//y must be nonzero. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
778 |
//q and r must be arrays that are exactly the same length as x. (Or q can have more). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
779 |
//Must have x.length >= y.length >= 2. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
780 |
function divide_(x,y,q,r) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
781 |
var kx, ky; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
782 |
var i,j,y1,y2,c,a,b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
783 |
copy_(r,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
784 |
for (ky=y.length;y[ky-1]==0;ky--); //ky is number of elements in y, not including leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
785 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
786 |
//normalize: ensure the most significant element of y has its highest bit set |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
787 |
b=y[ky-1]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
788 |
for (a=0; b; a++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
789 |
b>>=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
790 |
a=bpe-a; //a is how many bits to shift so that the high order bit of y is leftmost in its array element |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
791 |
leftShift_(y,a); //multiply both by 1<<a now, then divide both by that at the end |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
792 |
leftShift_(r,a); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
793 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
794 |
//Rob Visser discovered a bug: the following line was originally just before the normalization. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
795 |
for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
796 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
797 |
copyInt_(q,0); // q=0 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
798 |
while (!greaterShift(y,r,kx-ky)) { // while (leftShift_(y,kx-ky) <= r) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
799 |
subShift_(r,y,kx-ky); // r=r-leftShift_(y,kx-ky) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
800 |
q[kx-ky]++; // q[kx-ky]++; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
801 |
} // } |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
802 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
803 |
for (i=kx-1; i>=ky; i--) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
804 |
if (r[i]==y[ky-1]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
805 |
q[i-ky]=mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
806 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
807 |
q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
808 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
809 |
//The following for(;;) loop is equivalent to the commented while loop, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
810 |
//except that the uncommented version avoids overflow. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
811 |
//The commented loop comes from HAC, which assumes r[-1]==y[-1]==0 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
812 |
// while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
813 |
// q[i-ky]--; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
814 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
815 |
y2=(ky>1 ? y[ky-2] : 0)*q[i-ky]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
816 |
c=y2>>bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
817 |
y2=y2 & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
818 |
y1=c+q[i-ky]*y[ky-1]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
819 |
c=y1>>bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
820 |
y1=y1 & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
821 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
822 |
if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
823 |
q[i-ky]--; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
824 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
825 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
826 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
827 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
828 |
linCombShift_(r,y,-q[i-ky],i-ky); //r=r-q[i-ky]*leftShift_(y,i-ky) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
829 |
if (negative(r)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
830 |
addShift_(r,y,i-ky); //r=r+leftShift_(y,i-ky) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
831 |
q[i-ky]--; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
832 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
833 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
834 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
835 |
rightShift_(y,a); //undo the normalization step |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
836 |
rightShift_(r,a); //undo the normalization step |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
837 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
838 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
839 |
//do carries and borrows so each element of the bigInt x fits in bpe bits. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
840 |
function carry_(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
841 |
var i,k,c,b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
842 |
k=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
843 |
c=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
844 |
for (i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
845 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
846 |
b=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
847 |
if (c<0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
848 |
b=-(c>>bpe); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
849 |
c+=b*radix; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
850 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
851 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
852 |
c=(c>>bpe)-b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
853 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
854 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
855 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
856 |
//return x mod n for bigInt x and integer n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
857 |
function modInt(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
858 |
var i,c=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
859 |
for (i=x.length-1; i>=0; i--) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
860 |
c=(c*radix+x[i])%n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
861 |
return c; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
862 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
863 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
864 |
//convert the integer t into a bigInt with at least the given number of bits. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
865 |
//the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
866 |
//Pad the array with leading zeros so that it has at least minSize elements. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
867 |
//There will always be at least one leading 0 element. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
868 |
function int2bigInt(t,bits,minSize) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
869 |
var i,k; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
870 |
k=Math.ceil(bits/bpe)+1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
871 |
k=minSize>k ? minSize : k; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
872 |
buff=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
873 |
copyInt_(buff,t); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
874 |
return buff; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
875 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
876 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
877 |
//return the bigInt given a string representation in a given base. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
878 |
//Pad the array with leading zeros so that it has at least minSize elements. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
879 |
//If base=-1, then it reads in a space-separated list of array elements in decimal. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
880 |
//The array will always have at least one leading zero, unless base=-1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
881 |
function str2bigInt(s,base,minSize) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
882 |
var d, i, j, x, y, kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
883 |
var k=s.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
884 |
if (base==-1) { //comma-separated list of array elements in decimal |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
885 |
x=new Array(0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
886 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
887 |
y=new Array(x.length+1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
888 |
for (i=0;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
889 |
y[i+1]=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
890 |
y[0]=parseInt(s,10); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
891 |
x=y; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
892 |
d=s.indexOf(',',0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
893 |
if (d<1) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
894 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
895 |
s=s.substring(d+1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
896 |
if (s.length==0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
897 |
break; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
898 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
899 |
if (x.length<minSize) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
900 |
y=new Array(minSize); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
901 |
copy_(y,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
902 |
return y; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
903 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
904 |
return x; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
905 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
906 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
907 |
x=int2bigInt(0,base*k,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
908 |
for (i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
909 |
d=digitsStr.indexOf(s.substring(i,i+1),0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
910 |
if (base<=36 && d>=36) //convert lowercase to uppercase if base<=36 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
911 |
d-=26; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
912 |
if (d<base && d>=0) { //ignore illegal characters |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
913 |
multInt_(x,base); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
914 |
addInt_(x,d); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
915 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
916 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
917 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
918 |
for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
919 |
k=minSize>k+1 ? minSize : k+1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
920 |
y=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
921 |
kk=k<x.length ? k : x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
922 |
for (i=0;i<kk;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
923 |
y[i]=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
924 |
for (;i<k;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
925 |
y[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
926 |
return y; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
927 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
928 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
929 |
//is bigint x equal to integer y? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
930 |
//y must have less than bpe bits |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
931 |
function equalsInt(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
932 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
933 |
if (x[0]!=y) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
934 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
935 |
for (i=1;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
936 |
if (x[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
937 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
938 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
939 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
940 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
941 |
//are bigints x and y equal? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
942 |
//this works even if x and y are different lengths and have arbitrarily many leading zeros |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
943 |
function equals(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
944 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
945 |
var k=x.length<y.length ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
946 |
for (i=0;i<k;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
947 |
if (x[i]!=y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
948 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
949 |
if (x.length>y.length) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
950 |
for (;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
951 |
if (x[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
952 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
953 |
} else { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
954 |
for (;i<y.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
955 |
if (y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
956 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
957 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
958 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
959 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
960 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
961 |
//is the bigInt x equal to zero? |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
962 |
function isZero(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
963 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
964 |
for (i=0;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
965 |
if (x[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
966 |
return 0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
967 |
return 1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
968 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
969 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
970 |
//convert a bigInt into a string in a given base, from base 2 up to base 95. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
971 |
//Base -1 prints the contents of the array representing the number. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
972 |
function bigInt2str(x,base) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
973 |
var i,t,s=""; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
974 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
975 |
if (s6.length!=x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
976 |
s6=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
977 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
978 |
copy_(s6,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
979 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
980 |
if (base==-1) { //return the list of array contents |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
981 |
for (i=x.length-1;i>0;i--) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
982 |
s+=x[i]+','; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
983 |
s+=x[0]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
984 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
985 |
else { //return it in the given base |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
986 |
while (!isZero(s6)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
987 |
t=divInt_(s6,base); //t=s6 % base; s6=floor(s6/base); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
988 |
s=digitsStr.substring(t,t+1)+s; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
989 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
990 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
991 |
if (s.length==0) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
992 |
s="0"; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
993 |
return s; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
994 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
995 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
996 |
//returns a duplicate of bigInt x |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
997 |
function dup(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
998 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
999 |
buff=new Array(x.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1000 |
copy_(buff,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1001 |
return buff; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1002 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1003 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1004 |
//do x=y on bigInts x and y. x must be an array at least as big as y (not counting the leading zeros in y). |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1005 |
function copy_(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1006 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1007 |
var k=x.length<y.length ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1008 |
for (i=0;i<k;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1009 |
x[i]=y[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1010 |
for (i=k;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1011 |
x[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1012 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1013 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1014 |
//do x=y on bigInt x and integer y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1015 |
function copyInt_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1016 |
var i,c; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1017 |
for (c=n,i=0;i<x.length;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1018 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1019 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1020 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1021 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1022 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1023 |
//do x=x+n where x is a bigInt and n is an integer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1024 |
//x must be large enough to hold the result. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1025 |
function addInt_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1026 |
var i,k,c,b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1027 |
x[0]+=n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1028 |
k=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1029 |
c=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1030 |
for (i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1031 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1032 |
b=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1033 |
if (c<0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1034 |
b=-(c>>bpe); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1035 |
c+=b*radix; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1036 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1037 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1038 |
c=(c>>bpe)-b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1039 |
if (!c) return; //stop carrying as soon as the carry_ is zero |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1040 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1041 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1042 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1043 |
//right shift bigInt x by n bits. 0 <= n < bpe. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1044 |
function rightShift_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1045 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1046 |
var k=Math.floor(n/bpe); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1047 |
if (k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1048 |
for (i=0;i<x.length-k;i++) //right shift x by k elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1049 |
x[i]=x[i+k]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1050 |
for (;i<x.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1051 |
x[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1052 |
n%=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1053 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1054 |
for (i=0;i<x.length-1;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1055 |
x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1056 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1057 |
x[i]>>=n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1058 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1059 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1060 |
//do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1061 |
function halve_(x) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1062 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1063 |
for (i=0;i<x.length-1;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1064 |
x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1)); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1065 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1066 |
x[i]=(x[i]>>1) | (x[i] & (radix>>1)); //most significant bit stays the same |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1067 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1068 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1069 |
//left shift bigInt x by n bits. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1070 |
function leftShift_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1071 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1072 |
var k=Math.floor(n/bpe); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1073 |
if (k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1074 |
for (i=x.length; i>=k; i--) //left shift x by k elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1075 |
x[i]=x[i-k]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1076 |
for (;i>=0;i--) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1077 |
x[i]=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1078 |
n%=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1079 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1080 |
if (!n) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1081 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1082 |
for (i=x.length-1;i>0;i--) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1083 |
x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n))); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1084 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1085 |
x[i]=mask & (x[i]<<n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1086 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1087 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1088 |
//do x=x*n where x is a bigInt and n is an integer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1089 |
//x must be large enough to hold the result. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1090 |
function multInt_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1091 |
var i,k,c,b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1092 |
if (!n) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1093 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1094 |
k=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1095 |
c=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1096 |
for (i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1097 |
c+=x[i]*n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1098 |
b=0; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1099 |
if (c<0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1100 |
b=-(c>>bpe); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1101 |
c+=b*radix; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1102 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1103 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1104 |
c=(c>>bpe)-b; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1105 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1106 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1107 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1108 |
//do x=floor(x/n) for bigInt x and integer n, and return the remainder |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1109 |
function divInt_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1110 |
var i,r=0,s; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1111 |
for (i=x.length-1;i>=0;i--) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1112 |
s=r*radix+x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1113 |
x[i]=Math.floor(s/n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1114 |
r=s%n; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1115 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1116 |
return r; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1117 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1118 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1119 |
//do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1120 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1121 |
function linComb_(x,y,a,b) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1122 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1123 |
k=x.length<y.length ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1124 |
kk=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1125 |
for (c=0,i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1126 |
c+=a*x[i]+b*y[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1127 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1128 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1129 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1130 |
for (i=k;i<kk;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1131 |
c+=a*x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1132 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1133 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1134 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1135 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1136 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1137 |
//do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1138 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1139 |
function linCombShift_(x,y,b,ys) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1140 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1141 |
k=x.length<ys+y.length ? x.length : ys+y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1142 |
kk=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1143 |
for (c=0,i=ys;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1144 |
c+=x[i]+b*y[i-ys]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1145 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1146 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1147 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1148 |
for (i=k;c && i<kk;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1149 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1150 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1151 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1152 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1153 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1154 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1155 |
//do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1156 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1157 |
function addShift_(x,y,ys) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1158 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1159 |
k=x.length<ys+y.length ? x.length : ys+y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1160 |
kk=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1161 |
for (c=0,i=ys;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1162 |
c+=x[i]+y[i-ys]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1163 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1164 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1165 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1166 |
for (i=k;c && i<kk;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1167 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1168 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1169 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1170 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1171 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1172 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1173 |
//do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1174 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1175 |
function subShift_(x,y,ys) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1176 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1177 |
k=x.length<ys+y.length ? x.length : ys+y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1178 |
kk=x.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1179 |
for (c=0,i=ys;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1180 |
c+=x[i]-y[i-ys]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1181 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1182 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1183 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1184 |
for (i=k;c && i<kk;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1185 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1186 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1187 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1188 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1189 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1190 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1191 |
//do x=x-y for bigInts x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1192 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1193 |
//negative answers will be 2s complement |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1194 |
function sub_(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1195 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1196 |
k=x.length<y.length ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1197 |
for (c=0,i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1198 |
c+=x[i]-y[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1199 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1200 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1201 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1202 |
for (i=k;c && i<x.length;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1203 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1204 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1205 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1206 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1207 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1208 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1209 |
//do x=x+y for bigInts x and y. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1210 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1211 |
function add_(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1212 |
var i,c,k,kk; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1213 |
k=x.length<y.length ? x.length : y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1214 |
for (c=0,i=0;i<k;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1215 |
c+=x[i]+y[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1216 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1217 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1218 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1219 |
for (i=k;c && i<x.length;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1220 |
c+=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1221 |
x[i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1222 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1223 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1224 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1225 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1226 |
//do x=x*y for bigInts x and y. This is faster when y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1227 |
function mult_(x,y) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1228 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1229 |
if (ss.length!=2*x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1230 |
ss=new Array(2*x.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1231 |
copyInt_(ss,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1232 |
for (i=0;i<y.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1233 |
if (y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1234 |
linCombShift_(ss,x,y[i],i); //ss=1*ss+y[i]*(x<<(i*bpe)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1235 |
copy_(x,ss); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1236 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1237 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1238 |
//do x=x mod n for bigInts x and n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1239 |
function mod_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1240 |
if (s4.length!=x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1241 |
s4=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1242 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1243 |
copy_(s4,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1244 |
if (s5.length!=x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1245 |
s5=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1246 |
divide_(s4,n,s5,x); //x = remainder of s4 / n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1247 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1248 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1249 |
//do x=x*y mod n for bigInts x,y,n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1250 |
//for greater speed, let y<x. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1251 |
function multMod_(x,y,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1252 |
var i; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1253 |
if (s0.length!=2*x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1254 |
s0=new Array(2*x.length); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1255 |
copyInt_(s0,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1256 |
for (i=0;i<y.length;i++) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1257 |
if (y[i]) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1258 |
linCombShift_(s0,x,y[i],i); //s0=1*s0+y[i]*(x<<(i*bpe)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1259 |
mod_(s0,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1260 |
copy_(x,s0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1261 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1262 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1263 |
//do x=x*x mod n for bigInts x,n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1264 |
function squareMod_(x,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1265 |
var i,j,d,c,kx,kn,k; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1266 |
for (kx=x.length; kx>0 && !x[kx-1]; kx--); //ignore leading zeros in x |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1267 |
k=kx>n.length ? 2*kx : 2*n.length; //k=# elements in the product, which is twice the elements in the larger of x and n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1268 |
if (s0.length!=k) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1269 |
s0=new Array(k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1270 |
copyInt_(s0,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1271 |
for (i=0;i<kx;i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1272 |
c=s0[2*i]+x[i]*x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1273 |
s0[2*i]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1274 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1275 |
for (j=i+1;j<kx;j++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1276 |
c=s0[i+j]+2*x[i]*x[j]+c; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1277 |
s0[i+j]=(c & mask); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1278 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1279 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1280 |
s0[i+kx]=c; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1281 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1282 |
mod_(s0,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1283 |
copy_(x,s0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1284 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1285 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1286 |
//return x with exactly k leading zero elements |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1287 |
function bigint_trim(x,k) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1288 |
var i,y; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1289 |
for (i=x.length; i>0 && !x[i-1]; i--); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1290 |
y=new Array(i+k); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1291 |
copy_(y,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1292 |
return y; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1293 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1294 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1295 |
//do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation. 0**0=1. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1296 |
//this is faster when n is odd. x usually needs to have as many elements as n. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1297 |
function powMod_(x,y,n) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1298 |
var k1,k2,kn,np; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1299 |
if(s7.length!=n.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1300 |
s7=dup(n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1301 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1302 |
//for even modulus, use a simple square-and-multiply algorithm, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1303 |
//rather than using the more complex Montgomery algorithm. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1304 |
if ((n[0]&1)==0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1305 |
copy_(s7,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1306 |
copyInt_(x,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1307 |
while(!equalsInt(y,0)) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1308 |
if (y[0]&1) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1309 |
multMod_(x,s7,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1310 |
divInt_(y,2); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1311 |
squareMod_(s7,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1312 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1313 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1314 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1315 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1316 |
//calculate np from n for the Montgomery multiplications |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1317 |
copyInt_(s7,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1318 |
for (kn=n.length;kn>0 && !n[kn-1];kn--); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1319 |
np=radix-inverseModInt(modInt(n,radix),radix); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1320 |
s7[kn]=1; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1321 |
multMod_(x ,s7,n); // x = x * 2**(kn*bp) mod n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1322 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1323 |
if (s3.length!=x.length) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1324 |
s3=dup(x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1325 |
else |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1326 |
copy_(s3,x); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1327 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1328 |
for (k1=y.length-1;k1>0 & !y[k1]; k1--); //k1=first nonzero element of y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1329 |
if (y[k1]==0) { //anything to the 0th power is 1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1330 |
copyInt_(x,1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1331 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1332 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1333 |
for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1); //k2=position of first 1 bit in y[k1] |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1334 |
for (;;) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1335 |
if (!(k2>>=1)) { //look at next bit of y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1336 |
k1--; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1337 |
if (k1<0) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1338 |
mont_(x,one,n,np); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1339 |
return; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1340 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1341 |
k2=1<<(bpe-1); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1342 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1343 |
mont_(x,x,n,np); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1344 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1345 |
if (k2 & y[k1]) //if next bit is a 1 |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1346 |
mont_(x,s3,n,np); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1347 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1348 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1349 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1350 |
//do x=x*y*Ri mod n for bigInts x,y,n, |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1351 |
// where Ri = 2**(-kn*bpe) mod n, and kn is the |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1352 |
// number of elements in the n array, not |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1353 |
// counting leading zeros. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1354 |
//x must be large enough to hold the answer. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1355 |
//It's OK if x and y are the same variable. |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1356 |
//must have: |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1357 |
// x,y < n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1358 |
// n is odd |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1359 |
// np = -(n^(-1)) mod radix |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1360 |
function mont_(x,y,n,np) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1361 |
var i,j,c,ui,t; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1362 |
var kn=n.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1363 |
var ky=y.length; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1364 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1365 |
if (sa.length!=kn) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1366 |
sa=new Array(kn); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1367 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1368 |
for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1369 |
//this function sometimes gives wrong answers when the next line is uncommented |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1370 |
//for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1371 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1372 |
copyInt_(sa,0); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1373 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1374 |
//the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large keys |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1375 |
for (i=0; i<kn; i++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1376 |
t=sa[0]+x[i]*y[0]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1377 |
ui=((t & mask) * np) & mask; //the inner "& mask" is needed on Macintosh MSIE, but not windows MSIE |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1378 |
c=(t+ui*n[0]) >> bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1379 |
t=x[i]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1380 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1381 |
//do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1382 |
for (j=1;j<ky;j++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1383 |
c+=sa[j]+t*y[j]+ui*n[j]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1384 |
sa[j-1]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1385 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1386 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1387 |
for (;j<kn;j++) { |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1388 |
c+=sa[j]+ui*n[j]; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1389 |
sa[j-1]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1390 |
c>>=bpe; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1391 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1392 |
sa[j-1]=c & mask; |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1393 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1394 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1395 |
if (!greater(n,sa)) |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1396 |
sub_(sa,n); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1397 |
copy_(x,sa); |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1398 |
} |
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1399 |
|
242353360e37
Added support for Diffie-Hellman key exchange during login. w00t!
Dan
parents:
diff
changeset
|
1400 |