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diff --git a/frontend/gamma/js/ClipperzCryptoLibrary/BigInt_scoped.js b/frontend/gamma/js/ClipperzCryptoLibrary/BigInt_scoped.js deleted file mode 100644 index bc60330..0000000 --- a/frontend/gamma/js/ClipperzCryptoLibrary/BigInt_scoped.js +++ b/dev/null @@ -1,1644 +0,0 @@ -/* - -Copyright 2008-2013 Clipperz Srl - -This file is part of Clipperz, the online password manager. -For further information about its features and functionalities please -refer to http://www.clipperz.com. - -* Clipperz is free software: you can redistribute it and/or modify it - under the terms of the GNU Affero General Public License as published - by the Free Software Foundation, either version 3 of the License, or - (at your option) any later version. - -* Clipperz is distributed in the hope that it will be useful, but - WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. - See the GNU Affero General Public License for more details. - -* You should have received a copy of the GNU Affero General Public - License along with Clipperz. If not, see http://www.gnu.org/licenses/. - -*/ - -if (typeof(Clipperz) == 'undefined') { Clipperz = {}; } -if (typeof(Clipperz.Crypto) == 'undefined') { Clipperz.Crypto = {}; } - -if (typeof(Leemon) == 'undefined') { Leemon = {}; } -if (typeof(Baird.Crypto) == 'undefined') { Baird.Crypto = {}; } -if (typeof(Baird.Crypto.BigInt) == 'undefined') { Baird.Crypto.BigInt = {}; } - - -//############################################################################# -// Downloaded on March 05, 2007 from http://www.leemon.com/crypto/BigInt.js -//############################################################################# - -//////////////////////////////////////////////////////////////////////////////////////// -// Big Integer Library v. 5.0 -// Created 2000, last modified 2006 -// Leemon Baird -// www.leemon.com -// -// This file is public domain. You can use it for any purpose without restriction. -// I do not guarantee that it is correct, so use it at your own risk. If you use -// it for something interesting, I'd appreciate hearing about it. If you find -// any bugs or make any improvements, I'd appreciate hearing about those too. -// It would also be nice if my name and address were left in the comments. -// But none of that is required. -// -// This code defines a bigInt library for arbitrary-precision integers. -// A bigInt is an array of integers storing the value in chunks of bpe bits, -// little endian (buff[0] is the least significant word). -// Negative bigInts are stored two's complement. -// Some functions assume their parameters have at least one leading zero element. -// Functions with an underscore at the end of the name have unpredictable behavior in case of overflow, -// so the caller must make sure overflow won't happen. -// For each function where a parameter is modified, that same -// variable must not be used as another argument too. -// So, you cannot square x by doing multMod_(x,x,n). -// You must use squareMod_(x,n) instead, or do y=dup(x); multMod_(x,y,n). -// -// These functions are designed to avoid frequent dynamic memory allocation in the inner loop. -// For most functions, if it needs a BigInt as a local variable it will actually use -// a global, and will only allocate to it when it's not the right size. This ensures -// that when a function is called repeatedly with same-sized parameters, it only allocates -// memory on the first call. -// -// Note that for cryptographic purposes, the calls to Math.random() must -// be replaced with calls to a better pseudorandom number generator. -// -// In the following, "bigInt" means a bigInt with at least one leading zero element, -// and "integer" means a nonnegative integer less than radix. In some cases, integer -// can be negative. Negative bigInts are 2s complement. -// -// The following functions do not modify their inputs, but dynamically allocate memory every time they are called: -// -// function bigInt2str(x,base) //convert a bigInt into a string in a given base, from base 2 up to base 95 -// function dup(x) //returns a copy of bigInt x -// function findPrimes(n) //return array of all primes less than integer n -// function int2bigInt(t,n,m) //convert integer t to a bigInt with at least n bits and m array elements -// function str2bigInt(s,b,n,m) //convert string s in base b to a bigInt with at least n bits and m array elements -// function trim(x,k) //return a copy of x with exactly k leading zero elements -// -// The following functions do not modify their inputs, so there is never a problem with the result being too big: -// -// function bitSize(x) //returns how many bits long the bigInt x is, not counting leading zeros -// function equals(x,y) //is the bigInt x equal to the bigint y? -// function equalsInt(x,y) //is bigint x equal to integer y? -// function greater(x,y) //is x>y? (x and y are nonnegative bigInts) -// function greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y? -// function isZero(x) //is the bigInt x equal to zero? -// function millerRabin(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime (as opposed to definitely composite)? -// function modInt(x,n) //return x mod n for bigInt x and integer n. -// function negative(x) //is bigInt x negative? -// -// The following functions do not modify their inputs, but allocate memory and call functions with underscores -// -// function add(x,y) //return (x+y) for bigInts x and y. -// function addInt(x,n) //return (x+n) where x is a bigInt and n is an integer. -// function expand(x,n) //return a copy of x with at least n elements, adding leading zeros if needed -// function inverseMod(x,n) //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null -// function mod(x,n) //return a new bigInt equal to (x mod n) for bigInts x and n. -// function mult(x,y) //return x*y for bigInts x and y. This is faster when y<x. -// function multMod(x,y,n) //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. -// function 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. -// function randTruePrime(k) //return a new, random, k-bit, true prime using Maurer's algorithm. -// function sub(x,y) //return (x-y) for bigInts x and y. Negative answers will be 2s complement -// -// The following functions write a bigInt result to one of the parameters, but -// the result is never bigger than the original, so there can't be overflow problems: -// -// function divInt_(x,n) //do x=floor(x/n) for bigInt x and integer n, and return the remainder -// function GCD_(x,y) //set x to the greatest common divisor of bigInts x and y, (y is destroyed). -// function halve_(x) //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement -// function mod_(x,n) //do x=x mod n for bigInts x and n. -// function rightShift_(x,n) //right shift bigInt x by n bits. 0 <= n < bpe. -// -// The following functions write a bigInt result to one of the parameters. The caller is responsible for -// ensuring it is large enough to hold the result. -// -// function addInt_(x,n) //do x=x+n where x is a bigInt and n is an integer -// function add_(x,y) //do x=x+y for bigInts x and y -// function addShift_(x,y,ys) //do x=x+(y<<(ys*bpe)) -// function copy_(x,y) //do x=y on bigInts x and y -// function copyInt_(x,n) //do x=n on bigInt x and integer n -// function carry_(x) //do carries and borrows so each element of the bigInt x fits in bpe bits. -// function divide_(x,y,q,r) //divide_ x by y giving quotient q and remainder r -// function eGCD_(x,y,d,a,b) //sets a,b,d to positive big integers such that d = GCD_(x,y) = a*x-b*y -// function inverseMod_(x,n) //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist -// function inverseModInt_(x,n) //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse -// function leftShift_(x,n) //left shift bigInt x by n bits. n<bpe. -// function linComb_(x,y,a,b) //do x=a*x+b*y for bigInts x and y and integers a and b -// function linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys -// function mont_(x,y,n,np) //Montgomery multiplication (see comments where the function is defined) -// function mult_(x,y) //do x=x*y for bigInts x and y. -// function multInt_(x,n) //do x=x*n where x is a bigInt and n is an integer. -// function multMod_(x,y,n) //do x=x*y mod n for bigInts x,y,n. -// function 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. -// function 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. -// function randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb. -// function squareMod_(x,n) //do x=x*x mod n for bigInts x,n -// function sub_(x,y) //do x=x-y for bigInts x and y. Negative answers will be 2s complement. -// function subShift_(x,y,ys) //do x=x-(y<<(ys*bpe)). Negative answers will be 2s complement. -// -// The following functions are based on algorithms from the _Handbook of Applied Cryptography_ -// powMod_() = algorithm 14.94, Montgomery exponentiation -// eGCD_,inverseMod_() = algorithm 14.61, Binary extended GCD_ -// GCD_() = algorothm 14.57, Lehmer's algorithm -// mont_() = algorithm 14.36, Montgomery multiplication -// divide_() = algorithm 14.20 Multiple-precision division -// squareMod_() = algorithm 14.16 Multiple-precision squaring -// randTruePrime_() = algorithm 4.62, Maurer's algorithm -// millerRabin() = algorithm 4.24, Miller-Rabin algorithm -// -// Profiling shows: -// randTruePrime_() spends: -// 10% of its time in calls to powMod_() -// 85% of its time in calls to millerRabin() -// millerRabin() spends: -// 99% of its time in calls to powMod_() (always with a base of 2) -// powMod_() spends: -// 94% of its time in calls to mont_() (almost always with x==y) -// -// This suggests there are several ways to speed up this library slightly: -// - convert powMod_ to use a Montgomery form of k-ary window (or maybe a Montgomery form of sliding window) -// -- this should especially focus on being fast when raising 2 to a power mod n -// - convert randTruePrime_() to use a minimum r of 1/3 instead of 1/2 with the appropriate change to the test -// - tune the parameters in randTruePrime_(), including c, m, and recLimit -// - speed up the single loop in mont_() that takes 95% of the runtime, perhaps by reducing checking -// within the loop when all the parameters are the same length. -// -// There are several ideas that look like they wouldn't help much at all: -// - replacing trial division in randTruePrime_() with a sieve (that speeds up something taking almost no time anyway) -// - 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) -// - speeding up mont_(x,y,n,np) when x==y by doing a non-modular, non-Montgomery square -// followed by a Montgomery reduction. The intermediate answer will be twice as long as x, so that -// method would be slower. This is unfortunate because the code currently spends almost all of its time -// doing mont_(x,x,...), both for randTruePrime_() and powMod_(). A faster method for Montgomery squaring -// would have a large impact on the speed of randTruePrime_() and powMod_(). HAC has a couple of poorly-worded -// sentences that seem to imply it's faster to do a non-modular square followed by a single -// Montgomery reduction, but that's obviously wrong. -//////////////////////////////////////////////////////////////////////////////////////// - -// -// The whole library has been moved into the Baird.Crypto.BigInt scope by Giulio Cesare Solaroli <giulio.cesare@clipperz.com> -// -Baird.Crypto.BigInt.VERSION = "5.0"; -Baird.Crypto.BigInt.NAME = "Baird.Crypto.BigInt"; - -MochiKit.Base.update(Baird.Crypto.BigInt, { - //globals - 'bpe': 0, //bits stored per array element - 'mask': 0, //AND this with an array element to chop it down to bpe bits - 'radix': Baird.Crypto.BigInt.mask + 1, //equals 2^bpe. A single 1 bit to the left of the last bit of mask. - - //the digits for converting to different bases - 'digitsStr': '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'\"+-', - -//initialize the global variables -for (bpe=0; (1<<(bpe+1)) > (1<<bpe); bpe++); //bpe=number of bits in the mantissa on this platform -bpe>>=1; //bpe=number of bits in one element of the array representing the bigInt -mask=(1<<bpe)-1; //AND the mask with an integer to get its bpe least significant bits -radix=mask+1; //2^bpe. a single 1 bit to the left of the first bit of mask -one=int2bigInt(1,1,1); //constant used in powMod_() - -//the following global variables are scratchpad memory to -//reduce dynamic memory allocation in the inner loop -t=new Array(0); -ss=t; //used in mult_() -s0=t; //used in multMod_(), squareMod_() -s1=t; //used in powMod_(), multMod_(), squareMod_() -s2=t; //used in powMod_(), multMod_() -s3=t; //used in powMod_() -s4=t; s5=t; //used in mod_() -s6=t; //used in bigInt2str() -s7=t; //used in powMod_() -T=t; //used in GCD_() -sa=t; //used in mont_() -mr_x1=t; mr_r=t; mr_a=t; //used in millerRabin() -eg_v=t; eg_u=t; eg_A=t; eg_B=t; eg_C=t; eg_D=t; //used in eGCD_(), inverseMod_() -md_q1=t; md_q2=t; md_q3=t; md_r=t; md_r1=t; md_r2=t; md_tt=t; //used in mod_() - -primes=t; pows=t; s_i=t; s_i2=t; s_R=t; s_rm=t; s_q=t; s_n1=t; - 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_() - -//////////////////////////////////////////////////////////////////////////////////////// - - //return array of all primes less than integer n - 'findPrimes': function(n) { - var i,s,p,ans; - s=new Array(n); - for (i=0;i<n;i++) - s[i]=0; - s[0]=2; - p=0; //first p elements of s are primes, the rest are a sieve - for(;s[p]<n;) { //s[p] is the pth prime - for(i=s[p]*s[p]; i<n; i+=s[p]) //mark multiples of s[p] - s[i]=1; - p++; - s[p]=s[p-1]+1; - for(; s[p]<n && s[s[p]]; s[p]++); //find next prime (where s[p]==0) - } - ans=new Array(p); - for(i=0;i<p;i++) - ans[i]=s[i]; - return ans; - }, - - //does a single round of Miller-Rabin base b consider x to be a possible prime? - //x is a bigInt, and b is an integer - 'millerRabin': function(x,b) { - var i,j,k,s; - - if (mr_x1.length!=x.length) { - mr_x1=dup(x); - mr_r=dup(x); - mr_a=dup(x); - } - - copyInt_(mr_a,b); - copy_(mr_r,x); - copy_(mr_x1,x); - - addInt_(mr_r,-1); - addInt_(mr_x1,-1); - - //s=the highest power of two that divides mr_r - k=0; - for (i=0;i<mr_r.length;i++) - for (j=1;j<mask;j<<=1) - if (x[i] & j) { - s=(k<mr_r.length+bpe ? k : 0); - i=mr_r.length; - j=mask; - } else - k++; - - if (s) - rightShift_(mr_r,s); - - powMod_(mr_a,mr_r,x); - - if (!equalsInt(mr_a,1) && !equals(mr_a,mr_x1)) { - j=1; - while (j<=s-1 && !equals(mr_a,mr_x1)) { - squareMod_(mr_a,x); - if (equalsInt(mr_a,1)) { - return 0; - } - j++; - } - if (!equals(mr_a,mr_x1)) { - return 0; - } - } - - return 1; - }, - - //returns how many bits long the bigInt is, not counting leading zeros. - 'bitSize': function(x) { - var j,z,w; - for (j=x.length-1; (x[j]==0) && (j>0); j--); - for (z=0,w=x[j]; w; (w>>=1),z++); - z+=bpe*j; - return z; - }, - - //return a copy of x with at least n elements, adding leading zeros if needed - 'expand': function(x,n) { - var ans=int2bigInt(0,(x.length>n ? x.length : n)*bpe,0); - copy_(ans,x); - return ans; - }, - - //return a k-bit true random prime using Maurer's algorithm. - 'randTruePrime': function(k) { - var ans=int2bigInt(0,k,0); - randTruePrime_(ans,k); - return trim(ans,1); - }, - - //return a new bigInt equal to (x mod n) for bigInts x and n. - 'mod': function(x,n) { - var ans=dup(x); - mod_(ans,n); - return trim(ans,1); - }, - - //return (x+n) where x is a bigInt and n is an integer. - 'addInt': function(x,n) { - var ans=expand(x,x.length+1); - addInt_(ans,n); - return trim(ans,1); - }, - - //return x*y for bigInts x and y. This is faster when y<x. - 'mult': function(x,y) { - var ans=expand(x,x.length+y.length); - mult_(ans,y); - return trim(ans,1); - }, - - //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n. - 'powMod': function(x,y,n) { - var ans=expand(x,n.length); - powMod_(ans,trim(y,2),trim(n,2),0); //this should work without the trim, but doesn't - return trim(ans,1); - }, - - //return (x-y) for bigInts x and y. Negative answers will be 2s complement - 'sub': function(x,y) { - var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); - sub_(ans,y); - return trim(ans,1); - }, - - //return (x+y) for bigInts x and y. - 'add': function(x,y) { - var ans=expand(x,(x.length>y.length ? x.length+1 : y.length+1)); - add_(ans,y); - return trim(ans,1); - }, - - //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null - 'inverseMod': function(x,n) { - var ans=expand(x,n.length); - var s; - s=inverseMod_(ans,n); - return s ? trim(ans,1) : null; - }, - - //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x. - 'multMod': function(x,y,n) { - var ans=expand(x,n.length); - multMod_(ans,y,n); - return trim(ans,1); - }, - - //generate a k-bit true random prime using Maurer's algorithm, - //and put it into ans. The bigInt ans must be large enough to hold it. - 'randTruePrime_': function(ans,k) { - var c,m,pm,dd,j,r,B,divisible,z,zz,recSize; - - if (primes.length==0) - primes=findPrimes(30000); //check for divisibility by primes <=30000 - - if (pows.length==0) { - pows=new Array(512); - for (j=0;j<512;j++) { - pows[j]=Math.pow(2,j/511.-1.); - } - } - - //c and m should be tuned for a particular machine and value of k, to maximize speed - //this was: c=primes[primes.length-1]/k/k; //check using all the small primes. (c=0.1 in HAC) - c=0.1; - m=20; //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits - recLimit=20; /*must be at least 2 (was 29)*/ //stop recursion when k <=recLimit - - if (s_i2.length!=ans.length) { - s_i2=dup(ans); - s_R =dup(ans); - s_n1=dup(ans); - s_r2=dup(ans); - s_d =dup(ans); - s_x1=dup(ans); - s_x2=dup(ans); - s_b =dup(ans); - s_n =dup(ans); - s_i =dup(ans); - s_rm=dup(ans); - s_q =dup(ans); - s_a =dup(ans); - s_aa=dup(ans); - } - - if (k <= recLimit) { //generate small random primes by trial division up to its square root - pm=(1<<((k+2)>>1))-1; //pm is binary number with all ones, just over sqrt(2^k) - copyInt_(ans,0); - for (dd=1;dd;) { - dd=0; - ans[0]= 1 | (1<<(k-1)) | Math.floor(Math.random()*(1<<k)); //random, k-bit, odd integer, with msb 1 - for (j=1;(j<primes.length) && ((primes[j]&pm)==primes[j]);j++) { //trial division by all primes 3...sqrt(2^k) - if (0==(ans[0]%primes[j])) { - dd=1; - break; - } - } - } - carry_(ans); - return; - } - - B=c*k*k; //try small primes up to B (or all the primes[] array if the largest is less than B). - if (k>2*m) //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits - for (r=1; k-k*r<=m; ) - r=pows[Math.floor(Math.random()*512)]; //r=Math.pow(2,Math.random()-1); - else - r=.5; - - //simulation suggests the more complex algorithm using r=.333 is only slightly faster. - - recSize=Math.floor(r*k)+1; - - randTruePrime_(s_q,recSize); - copyInt_(s_i2,0); - s_i2[Math.floor((k-2)/bpe)] |= (1<<((k-2)%bpe)); //s_i2=2^(k-2) - divide_(s_i2,s_q,s_i,s_rm); //s_i=floor((2^(k-1))/(2q)) - - z=bitSize(s_i); - - for (;;) { - for (;;) { //generate z-bit numbers until one falls in the range [0,s_i-1] - randBigInt_(s_R,z,0); - if (greater(s_i,s_R)) - break; - } //now s_R is in the range [0,s_i-1] - addInt_(s_R,1); //now s_R is in the range [1,s_i] - add_(s_R,s_i); //now s_R is in the range [s_i+1,2*s_i] - - copy_(s_n,s_q); - mult_(s_n,s_R); - multInt_(s_n,2); - addInt_(s_n,1); //s_n=2*s_R*s_q+1 - - copy_(s_r2,s_R); - multInt_(s_r2,2); //s_r2=2*s_R - - //check s_n for divisibility by small primes up to B - for (divisible=0,j=0; (j<primes.length) && (primes[j]<B); j++) - if (modInt(s_n,primes[j])==0) { - divisible=1; - break; - } - - if (!divisible) //if it passes small primes check, then try a single Miller-Rabin base 2 - if (!millerRabin(s_n,2)) //this line represents 75% of the total runtime for randTruePrime_ - divisible=1; - - if (!divisible) { //if it passes that test, continue checking s_n - addInt_(s_n,-3); - for (j=s_n.length-1;(s_n[j]==0) && (j>0); j--); //strip leading zeros - for (zz=0,w=s_n[j]; w; (w>>=1),zz++); - zz+=bpe*j; //zz=number of bits in s_n, ignoring leading zeros - for (;;) { //generate z-bit numbers until one falls in the range [0,s_n-1] - randBigInt_(s_a,zz,0); - if (greater(s_n,s_a)) - break; - } //now s_a is in the range [0,s_n-1] - addInt_(s_n,3); //now s_a is in the range [0,s_n-4] - addInt_(s_a,2); //now s_a is in the range [2,s_n-2] - copy_(s_b,s_a); - copy_(s_n1,s_n); - addInt_(s_n1,-1); - powMod_(s_b,s_n1,s_n); //s_b=s_a^(s_n-1) modulo s_n - addInt_(s_b,-1); - if (isZero(s_b)) { - copy_(s_b,s_a); - powMod_(s_b,s_r2,s_n); - addInt_(s_b,-1); - copy_(s_aa,s_n); - copy_(s_d,s_b); - GCD_(s_d,s_n); //if s_b and s_n are relatively prime, then s_n is a prime - if (equalsInt(s_d,1)) { - copy_(ans,s_aa); - return; //if we've made it this far, then s_n is absolutely guaranteed to be prime - } - } - } - } - }, - - //set b to an n-bit random BigInt. If s=1, then nth bit (most significant bit) is set to 1. - //array b must be big enough to hold the result. Must have n>=1 - 'randBigInt_': function(b,n,s) { - var i,a; - for (i=0;i<b.length;i++) - b[i]=0; - a=Math.floor((n-1)/bpe)+1; //# array elements to hold the BigInt - for (i=0;i<a;i++) { - b[i]=Math.floor(Math.random()*(1<<(bpe-1))); - } - b[a-1] &= (2<<((n-1)%bpe))-1; - if (s) - b[a-1] |= (1<<((n-1)%bpe)); - }, - - //set x to the greatest common divisor of x and y. - //x,y are bigInts with the same number of elements. y is destroyed. - 'GCD_': function(x,y) { - var i,xp,yp,A,B,C,D,q,sing; - if (T.length!=x.length) - T=dup(x); - - sing=1; - while (sing) { //while y has nonzero elements other than y[0] - sing=0; - for (i=1;i<y.length;i++) //check if y has nonzero elements other than 0 - if (y[i]) { - sing=1; - break; - } - if (!sing) break; //quit when y all zero elements except possibly y[0] - - for (i=x.length;!x[i] && i>=0;i--); //find most significant element of x - xp=x[i]; - yp=y[i]; - A=1; B=0; C=0; D=1; - while ((yp+C) && (yp+D)) { - q =Math.floor((xp+A)/(yp+C)); - qp=Math.floor((xp+B)/(yp+D)); - if (q!=qp) - break; - 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) - t= B-q*D; B=D; D=t; - t=xp-q*yp; xp=yp; yp=t; - } - if (B) { - copy_(T,x); - linComb_(x,y,A,B); //x=A*x+B*y - linComb_(y,T,D,C); //y=D*y+C*T - } else { - mod_(x,y); - copy_(T,x); - copy_(x,y); - copy_(y,T); - } - } - if (y[0]==0) - return; - t=modInt(x,y[0]); - copyInt_(x,y[0]); - y[0]=t; - while (y[0]) { - x[0]%=y[0]; - t=x[0]; x[0]=y[0]; y[0]=t; - } - }, - -//do x=x**(-1) mod n, for bigInts x and n. -//If no inverse exists, it sets x to zero and returns 0, else it returns 1. -//The x array must be at least as large as the n array. -function inverseMod_(x,n) { - var k=1+2*Math.max(x.length,n.length); - - if(!(x[0]&1) && !(n[0]&1)) { //if both inputs are even, then inverse doesn't exist - copyInt_(x,0); - return 0; - } - - if (eg_u.length!=k) { - eg_u=new Array(k); - eg_v=new Array(k); - eg_A=new Array(k); - eg_B=new Array(k); - eg_C=new Array(k); - eg_D=new Array(k); - } - - copy_(eg_u,x); - copy_(eg_v,n); - copyInt_(eg_A,1); - copyInt_(eg_B,0); - copyInt_(eg_C,0); - copyInt_(eg_D,1); - for (;;) { - while(!(eg_u[0]&1)) { //while eg_u is even - halve_(eg_u); - if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if eg_A==eg_B==0 mod 2 - halve_(eg_A); - halve_(eg_B); - } else { - add_(eg_A,n); halve_(eg_A); - sub_(eg_B,x); halve_(eg_B); - } - } - - while (!(eg_v[0]&1)) { //while eg_v is even - halve_(eg_v); - if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if eg_C==eg_D==0 mod 2 - halve_(eg_C); - halve_(eg_D); - } else { - add_(eg_C,n); halve_(eg_C); - sub_(eg_D,x); halve_(eg_D); - } - } - - if (!greater(eg_v,eg_u)) { //eg_v <= eg_u - sub_(eg_u,eg_v); - sub_(eg_A,eg_C); - sub_(eg_B,eg_D); - } else { //eg_v > eg_u - sub_(eg_v,eg_u); - sub_(eg_C,eg_A); - sub_(eg_D,eg_B); - } - - if (equalsInt(eg_u,0)) { - if (negative(eg_C)) //make sure answer is nonnegative - add_(eg_C,n); - copy_(x,eg_C); - - if (!equalsInt(eg_v,1)) { //if GCD_(x,n)!=1, then there is no inverse - copyInt_(x,0); - return 0; - } - return 1; - } - } -} - -//return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse -function inverseModInt_(x,n) { - var a=1,b=0,t; - for (;;) { - if (x==1) return a; - if (x==0) return 0; - b-=a*Math.floor(n/x); - n%=x; - - if (n==1) return b; //to avoid negatives, change this b to n-b, and each -= to += - if (n==0) return 0; - a-=b*Math.floor(x/n); - x%=n; - } -} - -//Given positive bigInts x and y, change the bigints v, a, and b to positive bigInts such that: -// v = GCD_(x,y) = a*x-b*y -//The bigInts v, a, b, must have exactly as many elements as the larger of x and y. -function eGCD_(x,y,v,a,b) { - var g=0; - var k=Math.max(x.length,y.length); - if (eg_u.length!=k) { - eg_u=new Array(k); - eg_A=new Array(k); - eg_B=new Array(k); - eg_C=new Array(k); - eg_D=new Array(k); - } - while(!(x[0]&1) && !(y[0]&1)) { //while x and y both even - halve_(x); - halve_(y); - g++; - } - copy_(eg_u,x); - copy_(v,y); - copyInt_(eg_A,1); - copyInt_(eg_B,0); - copyInt_(eg_C,0); - copyInt_(eg_D,1); - for (;;) { - while(!(eg_u[0]&1)) { //while u is even - halve_(eg_u); - if (!(eg_A[0]&1) && !(eg_B[0]&1)) { //if A==B==0 mod 2 - halve_(eg_A); - halve_(eg_B); - } else { - add_(eg_A,y); halve_(eg_A); - sub_(eg_B,x); halve_(eg_B); - } - } - - while (!(v[0]&1)) { //while v is even - halve_(v); - if (!(eg_C[0]&1) && !(eg_D[0]&1)) { //if C==D==0 mod 2 - halve_(eg_C); - halve_(eg_D); - } else { - add_(eg_C,y); halve_(eg_C); - sub_(eg_D,x); halve_(eg_D); - } - } - - if (!greater(v,eg_u)) { //v<=u - sub_(eg_u,v); - sub_(eg_A,eg_C); - sub_(eg_B,eg_D); - } else { //v>u - sub_(v,eg_u); - sub_(eg_C,eg_A); - sub_(eg_D,eg_B); - } - if (equalsInt(eg_u,0)) { - if (negative(eg_C)) { //make sure a (C)is nonnegative - add_(eg_C,y); - sub_(eg_D,x); - } - multInt_(eg_D,-1); ///make sure b (D) is nonnegative - copy_(a,eg_C); - copy_(b,eg_D); - leftShift_(v,g); - return; - } - } -} - - -//is bigInt x negative? -function negative(x) { - return ((x[x.length-1]>>(bpe-1))&1); -} - - -//is (x << (shift*bpe)) > y? -//x and y are nonnegative bigInts -//shift is a nonnegative integer -function greaterShift(x,y,shift) { - var kx=x.length, ky=y.length; - k=((kx+shift)<ky) ? (kx+shift) : ky; - for (i=ky-1-shift; i<kx && i>=0; i++) - if (x[i]>0) - return 1; //if there are nonzeros in x to the left of the first column of y, then x is bigger - for (i=kx-1+shift; i<ky; i++) - if (y[i]>0) - return 0; //if there are nonzeros in y to the left of the first column of x, then x is not bigger - for (i=k-1; i>=shift; i--) - if (x[i-shift]>y[i]) return 1; - else if (x[i-shift]<y[i]) return 0; - return 0; -} - -//is x > y? (x and y both nonnegative) -function greater(x,y) { - var i; - var k=(x.length<y.length) ? x.length : y.length; - - for (i=x.length;i<y.length;i++) - if (y[i]) - return 0; //y has more digits - - for (i=y.length;i<x.length;i++) - if (x[i]) - return 1; //x has more digits - - for (i=k-1;i>=0;i--) - if (x[i]>y[i]) - return 1; - else if (x[i]<y[i]) - return 0; - return 0; -} - -//divide_ x by y giving quotient q and remainder r. (q=floor(x/y), r=x mod y). All 4 are bigints. -//x must have at least one leading zero element. -//y must be nonzero. -//q and r must be arrays that are exactly the same length as x. -//the x array must have at least as many elements as y. -function divide_(x,y,q,r) { - var kx, ky; - var i,j,y1,y2,c,a,b; - copy_(r,x); - for (ky=y.length;y[ky-1]==0;ky--); //kx,ky is number of elements in x,y, not including leading zeros - for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); - - //normalize: ensure the most significant element of y has its highest bit set - b=y[ky-1]; - for (a=0; b; a++) - b>>=1; - a=bpe-a; //a is how many bits to shift so that the high order bit of y is leftmost in its array element - leftShift_(y,a); //multiply both by 1<<a now, then divide_ both by that at the end - leftShift_(r,a); - - copyInt_(q,0); // q=0 - while (!greaterShift(y,r,kx-ky)) { // while (leftShift_(y,kx-ky) <= r) { - subShift_(r,y,kx-ky); // r=r-leftShift_(y,kx-ky) - q[kx-ky]++; // q[kx-ky]++; - } // } - - for (i=kx-1; i>=ky; i--) { - if (r[i]==y[ky-1]) - q[i-ky]=mask; - else - q[i-ky]=Math.floor((r[i]*radix+r[i-1])/y[ky-1]); - - //The following for(;;) loop is equivalent to the commented while loop, - //except that the uncommented version avoids overflow. - //The commented loop comes from HAC, which assumes r[-1]==y[-1]==0 - // while (q[i-ky]*(y[ky-1]*radix+y[ky-2]) > r[i]*radix*radix+r[i-1]*radix+r[i-2]) - // q[i-ky]--; - for (;;) { - y2=(ky>1 ? y[ky-2] : 0)*q[i-ky]; - c=y2>>bpe; - y2=y2 & mask; - y1=c+q[i-ky]*y[ky-1]; - c=y1>>bpe; - y1=y1 & mask; - - if (c==r[i] ? y1==r[i-1] ? y2>(i>1 ? r[i-2] : 0) : y1>r[i-1] : c>r[i]) - q[i-ky]--; - else - break; - } - - linCombShift_(r,y,-q[i-ky],i-ky); //r=r-q[i-ky]*leftShift_(y,i-ky) - if (negative(r)) { - addShift_(r,y,i-ky); //r=r+leftShift_(y,i-ky) - q[i-ky]--; - } - } - - rightShift_(y,a); //undo the normalization step - rightShift_(r,a); //undo the normalization step -} - -//do carries and borrows so each element of the bigInt x fits in bpe bits. -function carry_(x) { - var i,k,c,b; - k=x.length; - c=0; - for (i=0;i<k;i++) { - c+=x[i]; - b=0; - if (c<0) { - b=-(c>>bpe); - c+=b*radix; - } - x[i]=c & mask; - c=(c>>bpe)-b; - } -} - -//return x mod n for bigInt x and integer n. -function modInt(x,n) { - var i,c=0; - for (i=x.length-1; i>=0; i--) - c=(c*radix+x[i])%n; - return c; -} - -//convert the integer t into a bigInt with at least the given number of bits. -//the returned array stores the bigInt in bpe-bit chunks, little endian (buff[0] is least significant word) -//Pad the array with leading zeros so that it has at least minSize elements. -//There will always be at least one leading 0 element. -function int2bigInt(t,bits,minSize) { - var i,k; - k=Math.ceil(bits/bpe)+1; - k=minSize>k ? minSize : k; - buff=new Array(k); - copyInt_(buff,t); - return buff; -} - -//return the bigInt given a string representation in a given base. -//Pad the array with leading zeros so that it has at least minSize elements. -//If base=-1, then it reads in a space-separated list of array elements in decimal. -//The array will always have at least one leading zero, unless base=-1. -function str2bigInt(s,base,minSize) { - var d, i, j, x, y, kk; - var k=s.length; - if (base==-1) { //comma-separated list of array elements in decimal - x=new Array(0); - for (;;) { - y=new Array(x.length+1); - for (i=0;i<x.length;i++) - y[i+1]=x[i]; - y[0]=parseInt(s,10); - x=y; - d=s.indexOf(',',0); - if (d<1) - break; - s=s.substring(d+1); - if (s.length==0) - break; - } - if (x.length<minSize) { - y=new Array(minSize); - copy_(y,x); - return y; - } - return x; - } - - x=int2bigInt(0,base*k,0); - for (i=0;i<k;i++) { - d=digitsStr.indexOf(s.substring(i,i+1),0); - if (base<=36 && d>=36) //convert lowercase to uppercase if base<=36 - d-=26; - if (d<base && d>=0) { //ignore illegal characters - multInt_(x,base); - addInt_(x,d); - } - } - - for (k=x.length;k>0 && !x[k-1];k--); //strip off leading zeros - k=minSize>k+1 ? minSize : k+1; - y=new Array(k); - kk=k<x.length ? k : x.length; - for (i=0;i<kk;i++) - y[i]=x[i]; - for (;i<k;i++) - y[i]=0; - return y; -} - -//is bigint x equal to integer y? -//y must have less than bpe bits -function equalsInt(x,y) { - var i; - if (x[0]!=y) - return 0; - for (i=1;i<x.length;i++) - if (x[i]) - return 0; - return 1; -} - -//are bigints x and y equal? -//this works even if x and y are different lengths and have arbitrarily many leading zeros -function equals(x,y) { - var i; - var k=x.length<y.length ? x.length : y.length; - for (i=0;i<k;i++) - if (x[i]!=y[i]) - return 0; - if (x.length>y.length) { - for (;i<x.length;i++) - if (x[i]) - return 0; - } else { - for (;i<y.length;i++) - if (y[i]) - return 0; - } - return 1; -} - -//is the bigInt x equal to zero? -function isZero(x) { - var i; - for (i=0;i<x.length;i++) - if (x[i]) - return 0; - return 1; -} - -//convert a bigInt into a string in a given base, from base 2 up to base 95. -//Base -1 prints the contents of the array representing the number. -function bigInt2str(x,base) { - var i,t,s=""; - - if (s6.length!=x.length) - s6=dup(x); - else - copy_(s6,x); - - if (base==-1) { //return the list of array contents - for (i=x.length-1;i>0;i--) - s+=x[i]+','; - s+=x[0]; - } - else { //return it in the given base - while (!isZero(s6)) { - t=divInt_(s6,base); //t=s6 % base; s6=floor(s6/base); - s=digitsStr.substring(t,t+1)+s; - } - } - if (s.length==0) - s="0"; - return s; -} - -//returns a duplicate of bigInt x -function dup(x) { - var i; - buff=new Array(x.length); - copy_(buff,x); - return buff; -} - -//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). -function copy_(x,y) { - var i; - var k=x.length<y.length ? x.length : y.length; - for (i=0;i<k;i++) - x[i]=y[i]; - for (i=k;i<x.length;i++) - x[i]=0; -} - -//do x=y on bigInt x and integer y. -function copyInt_(x,n) { - var i,c; - for (c=n,i=0;i<x.length;i++) { - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x+n where x is a bigInt and n is an integer. -//x must be large enough to hold the result. -function addInt_(x,n) { - var i,k,c,b; - x[0]+=n; - k=x.length; - c=0; - for (i=0;i<k;i++) { - c+=x[i]; - b=0; - if (c<0) { - b=-(c>>bpe); - c+=b*radix; - } - x[i]=c & mask; - c=(c>>bpe)-b; - if (!c) return; //stop carrying as soon as the carry_ is zero - } -} - -//right shift bigInt x by n bits. 0 <= n < bpe. -function rightShift_(x,n) { - var i; - var k=Math.floor(n/bpe); - if (k) { - for (i=0;i<x.length-k;i++) //right shift x by k elements - x[i]=x[i+k]; - for (;i<x.length;i++) - x[i]=0; - n%=bpe; - } - for (i=0;i<x.length-1;i++) { - x[i]=mask & ((x[i+1]<<(bpe-n)) | (x[i]>>n)); - } - x[i]>>=n; -} - -//do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement -function halve_(x) { - var i; - for (i=0;i<x.length-1;i++) { - x[i]=mask & ((x[i+1]<<(bpe-1)) | (x[i]>>1)); - } - x[i]=(x[i]>>1) | (x[i] & (radix>>1)); //most significant bit stays the same -} - -//left shift bigInt x by n bits. -function leftShift_(x,n) { - var i; - var k=Math.floor(n/bpe); - if (k) { - for (i=x.length; i>=k; i--) //left shift x by k elements - x[i]=x[i-k]; - for (;i>=0;i--) - x[i]=0; - n%=bpe; - } - if (!n) - return; - for (i=x.length-1;i>0;i--) { - x[i]=mask & ((x[i]<<n) | (x[i-1]>>(bpe-n))); - } - x[i]=mask & (x[i]<<n); -} - -//do x=x*n where x is a bigInt and n is an integer. -//x must be large enough to hold the result. -function multInt_(x,n) { - var i,k,c,b; - if (!n) - return; - k=x.length; - c=0; - for (i=0;i<k;i++) { - c+=x[i]*n; - b=0; - if (c<0) { - b=-(c>>bpe); - c+=b*radix; - } - x[i]=c & mask; - c=(c>>bpe)-b; - } -} - -//do x=floor(x/n) for bigInt x and integer n, and return the remainder -function divInt_(x,n) { - var i,r=0,s; - for (i=x.length-1;i>=0;i--) { - s=r*radix+x[i]; - x[i]=Math.floor(s/n); - r=s%n; - } - return r; -} - -//do the linear combination x=a*x+b*y for bigInts x and y, and integers a and b. -//x must be large enough to hold the answer. -function linComb_(x,y,a,b) { - var i,c,k,kk; - k=x.length<y.length ? x.length : y.length; - kk=x.length; - for (c=0,i=0;i<k;i++) { - c+=a*x[i]+b*y[i]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;i<kk;i++) { - c+=a*x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do the linear combination x=a*x+b*(y<<(ys*bpe)) for bigInts x and y, and integers a, b and ys. -//x must be large enough to hold the answer. -function linCombShift_(x,y,b,ys) { - var i,c,k,kk; - k=x.length<ys+y.length ? x.length : ys+y.length; - kk=x.length; - for (c=0,i=ys;i<k;i++) { - c+=x[i]+b*y[i-ys]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;c && i<kk;i++) { - c+=x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x+(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. -//x must be large enough to hold the answer. -function addShift_(x,y,ys) { - var i,c,k,kk; - k=x.length<ys+y.length ? x.length : ys+y.length; - kk=x.length; - for (c=0,i=ys;i<k;i++) { - c+=x[i]+y[i-ys]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;c && i<kk;i++) { - c+=x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x-(y<<(ys*bpe)) for bigInts x and y, and integers a,b and ys. -//x must be large enough to hold the answer. -function subShift_(x,y,ys) { - var i,c,k,kk; - k=x.length<ys+y.length ? x.length : ys+y.length; - kk=x.length; - for (c=0,i=ys;i<k;i++) { - c+=x[i]-y[i-ys]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;c && i<kk;i++) { - c+=x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x-y for bigInts x and y. -//x must be large enough to hold the answer. -//negative answers will be 2s complement -function sub_(x,y) { - var i,c,k,kk; - k=x.length<y.length ? x.length : y.length; - for (c=0,i=0;i<k;i++) { - c+=x[i]-y[i]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;c && i<x.length;i++) { - c+=x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x+y for bigInts x and y. -//x must be large enough to hold the answer. -function add_(x,y) { - var i,c,k,kk; - k=x.length<y.length ? x.length : y.length; - for (c=0,i=0;i<k;i++) { - c+=x[i]+y[i]; - x[i]=c & mask; - c>>=bpe; - } - for (i=k;c && i<x.length;i++) { - c+=x[i]; - x[i]=c & mask; - c>>=bpe; - } -} - -//do x=x*y for bigInts x and y. This is faster when y<x. -function mult_(x,y) { - var i; - if (ss.length!=2*x.length) - ss=new Array(2*x.length); - copyInt_(ss,0); - for (i=0;i<y.length;i++) - if (y[i]) - linCombShift_(ss,x,y[i],i); //ss=1*ss+y[i]*(x<<(i*bpe)) - copy_(x,ss); -} - -//do x=x mod n for bigInts x and n. -function mod_(x,n) { - if (s4.length!=x.length) - s4=dup(x); - else - copy_(s4,x); - if (s5.length!=x.length) - s5=dup(x); - divide_(s4,n,s5,x); //x = remainder of s4 / n -} - -//do x=x*y mod n for bigInts x,y,n. -//for greater speed, let y<x. -function multMod_(x,y,n) { - var i; - if (s0.length!=2*x.length) - s0=new Array(2*x.length); - copyInt_(s0,0); - for (i=0;i<y.length;i++) - if (y[i]) - linCombShift_(s0,x,y[i],i); //s0=1*s0+y[i]*(x<<(i*bpe)) - mod_(s0,n); - copy_(x,s0); -} - -//do x=x*x mod n for bigInts x,n. -function squareMod_(x,n) { - var i,j,d,c,kx,kn,k; - for (kx=x.length; kx>0 && !x[kx-1]; kx--); //ignore leading zeros in x - 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 - if (s0.length!=k) - s0=new Array(k); - copyInt_(s0,0); - for (i=0;i<kx;i++) { - c=s0[2*i]+x[i]*x[i]; - s0[2*i]=c & mask; - c>>=bpe; - for (j=i+1;j<kx;j++) { - c=s0[i+j]+2*x[i]*x[j]+c; - s0[i+j]=(c & mask); - c>>=bpe; - } - s0[i+kx]=c; - } - mod_(s0,n); - copy_(x,s0); -} - -//return x with exactly k leading zero elements -function trim(x,k) { - var i,y; - for (i=x.length; i>0 && !x[i-1]; i--); - y=new Array(i+k); - copy_(y,x); - return y; -} - -//do x=x**y mod n, where x,y,n are bigInts and ** is exponentiation. 0**0=1. -//this is faster when n is odd. x usually needs to have as many elements as n. -function powMod_(x,y,n) { - var k1,k2,kn,np; - if(s7.length!=n.length) - s7=dup(n); - - //for even modulus, use a simple square-and-multiply algorithm, - //rather than using the more complex Montgomery algorithm. - if ((n[0]&1)==0) { - copy_(s7,x); - copyInt_(x,1); - while(!equalsInt(y,0)) { - if (y[0]&1) - multMod_(x,s7,n); - divInt_(y,2); - squareMod_(s7,n); - } - return; - } - - //calculate np from n for the Montgomery multiplications - copyInt_(s7,0); - for (kn=n.length;kn>0 && !n[kn-1];kn--); - np=radix-inverseModInt_(modInt(n,radix),radix); - s7[kn]=1; - multMod_(x ,s7,n); // x = x * 2**(kn*bp) mod n - - if (s3.length!=x.length) - s3=dup(x); - else - copy_(s3,x); - - for (k1=y.length-1;k1>0 & !y[k1]; k1--); //k1=first nonzero element of y - if (y[k1]==0) { //anything to the 0th power is 1 - copyInt_(x,1); - return; - } - for (k2=1<<(bpe-1);k2 && !(y[k1] & k2); k2>>=1); //k2=position of first 1 bit in y[k1] - for (;;) { - if (!(k2>>=1)) { //look at next bit of y - k1--; - if (k1<0) { - mont_(x,one,n,np); - return; - } - k2=1<<(bpe-1); - } - mont_(x,x,n,np); - - if (k2 & y[k1]) //if next bit is a 1 - mont_(x,s3,n,np); - } -} - -//do x=x*y*Ri mod n for bigInts x,y,n, -// where Ri = 2**(-kn*bpe) mod n, and kn is the -// number of elements in the n array, not -// counting leading zeros. -//x must be large enough to hold the answer. -//It's OK if x and y are the same variable. -//must have: -// x,y < n -// n is odd -// np = -(n^(-1)) mod radix -function mont_(x,y,n,np) { - var i,j,c,ui,t; - var kn=n.length; - var ky=y.length; - - if (sa.length!=kn) - sa=new Array(kn); - - for (;kn>0 && n[kn-1]==0;kn--); //ignore leading zeros of n - //this function sometimes gives wrong answers when the next line is uncommented - //for (;ky>0 && y[ky-1]==0;ky--); //ignore leading zeros of y - - copyInt_(sa,0); - - //the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large keys - for (i=0; i<kn; i++) { - t=sa[0]+x[i]*y[0]; - ui=((t & mask) * np) & mask; //the inner "& mask" is needed on Macintosh MSIE, but not windows MSIE - c=(t+ui*n[0]) >> bpe; - t=x[i]; - - //do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe - for (j=1;j<ky;j++) { - c+=sa[j]+t*y[j]+ui*n[j]; - sa[j-1]=c & mask; - c>>=bpe; - } - for (;j<kn;j++) { - c+=sa[j]+ui*n[j]; - sa[j-1]=c & mask; - c>>=bpe; - } - sa[j-1]=c & mask; - } - - if (!greater(n,sa)) - sub_(sa,n); - copy_(x,sa); -} - - - - -//############################################################################# -//############################################################################# -//############################################################################# -//############################################################################# -//############################################################################# -//############################################################################# -//############################################################################# - - - - - -//############################################################################# - -Clipperz.Crypto.BigInt = function (aValue, aBase) { - var base; - var value; - - if (typeof(aValue) == 'object') { - this._internalValue = aValue; - } else { - if (typeof(aValue) == 'undefined') { - value = "0"; - } else { - value = aValue + ""; - } - - if (typeof(aBase) == 'undefined') { - base = 10; - } else { - base = aBase; - } - - this._internalValue = str2bigInt(value, base, 1, 1); - } - - return this; -} - -//============================================================================= - -MochiKit.Base.update(Clipperz.Crypto.BigInt.prototype, { - - //------------------------------------------------------------------------- - - 'internalValue': function () { - return this._internalValue; - }, - - //------------------------------------------------------------------------- - - 'isBigInt': true, - - //------------------------------------------------------------------------- - - 'toString': function(aBase) { - return this.asString(aBase); - }, - - //------------------------------------------------------------------------- - - 'asString': function (aBase) { - var base; - - if (typeof(aBase) == 'undefined') { - base = 10; - } else { - base = aBase; - } - - return bigInt2str(this.internalValue(), base).toLowerCase(); - }, - - //------------------------------------------------------------------------- - - 'equals': function (aValue) { - var result; - - if (aValue.isBigInt) { - result = equals(this.internalValue(), aValue.internalValue()); - } else if (typeof(aValue) == "number") { - result = equalsInt(this.internalValue(), aValue); - } else { - throw Clipperz.Crypt.BigInt.exception.UnknownType; - } - - return result; - }, - - //------------------------------------------------------------------------- - - 'add': function (aValue) { - var result; - - if (aValue.isBigInt) { - result = add(this.internalValue(), aValue.internalValue()); - } else { - result = addInt(this.internalValue(), aValue); - } - - return new Clipperz.Crypto.BigInt(result); - }, - - //------------------------------------------------------------------------- - - 'subtract': function (aValue) { - var result; - var value; - - if (aValue.isBigInt) { - value = aValue; - } else { - value = new Clipperz.Crypto.BigInt(aValue); - } - - result = sub(this.internalValue(), value.internalValue()); - - return new Clipperz.Crypto.BigInt(result); - }, - - //------------------------------------------------------------------------- - - 'multiply': function (aValue, aModule) { - var result; - var value; - - if (aValue.isBigInt) { - value = aValue; - } else { - value = new Clipperz.Crypto.BigInt(aValue); - } - - if (typeof(aModule) == 'undefined') { - result = mult(this.internalValue(), value.internalValue()); - } else { - result = multMod(this.internalValue(), value.internalValue(), aModule); - } - - return new Clipperz.Crypto.BigInt(result); - }, - - //------------------------------------------------------------------------- - - 'module': function (aModule) { - var result; - var module; - - if (aModule.isBigInt) { - module = aModule; - } else { - module = new Clipperz.Crypto.BigInt(aModule); - } - - result = mod(this.internalValue(), module.internalValue()); - - return new Clipperz.Crypto.BigInt(result); - }, - - //------------------------------------------------------------------------- - - 'powerModule': function(aValue, aModule) { - var result; - var value; - var module; - - if (aValue.isBigInt) { - value = aValue; - } else { - value = new Clipperz.Crypto.BigInt(aValue); - } - - if (aModule.isBigInt) { - module = aModule; - } else { - module = new Clipperz.Crypto.BigInt(aModule); - } - - if (aValue == -1) { - result = inverseMod(this.internalValue(), module.internalValue()); - } else { - result = powMod(this.internalValue(), value.internalValue(), module.internalValue()); - } - - return new Clipperz.Crypto.BigInt(result); - }, - - //------------------------------------------------------------------------- - - 'bitSize': function() { - return bitSize(this.internalValue()); - }, - - //------------------------------------------------------------------------- - __syntaxFix__: "syntax fix" - -}); - -//############################################################################# - -Clipperz.Crypto.BigInt.randomPrime = function(aBitSize) { - return new Clipperz.Crypto.BigInt(randTruePrime(aBitSize)); -} - -//############################################################################# -//############################################################################# -//############################################################################# - -Clipperz.Crypto.BigInt.equals = function(a, b) { - return a.equals(b); -} - -Clipperz.Crypto.BigInt.add = function(a, b) { - return a.add(b); -} - -Clipperz.Crypto.BigInt.subtract = function(a, b) { - return a.subtract(b); -} - -Clipperz.Crypto.BigInt.multiply = function(a, b, module) { - return a.multiply(b, module); -} - -Clipperz.Crypto.BigInt.module = function(a, module) { - return a.module(module); -} - -Clipperz.Crypto.BigInt.powerModule = function(a, b, module) { - return a.powerModule(b, module); -} - -Clipperz.Crypto.BigInt.exception = { - UnknownType: new MochiKit.Base.NamedError("Clipperz.Crypto.BigInt.exception.UnknownType") -} |