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diff --git a/frontend/delta/js/Clipperz/Crypto/BigInt.js b/frontend/delta/js/Clipperz/Crypto/BigInt.js new file mode 100644 index 0000000..031ed30 --- a/dev/null +++ b/frontend/delta/js/Clipperz/Crypto/BigInt.js @@ -0,0 +1,1754 @@ +/* + +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 = {}; } + +//############################################################################# +// 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 int2bigInt(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. +//////////////////////////////////////////////////////////////////////////////////////// + +//globals +bpe=0; //bits stored per array element +mask=0; //AND this with an array element to chop it down to bpe bits +radix=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 +function findPrimes(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 +function millerRabin(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. +function bitSize(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 +function expand(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. +function randTruePrime(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. +function mod(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. +function addInt(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. +function mult(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. +function powMod(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 +function sub(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. +function add(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 +function inverseMod(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. +function multMod(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. +function randTruePrime_(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 +function randBigInt_(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. +function GCD_(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, { + + 'clone': function() { + return new Clipperz.Crypto.BigInt(this.internalValue()); + }, + + //------------------------------------------------------------------------- + + 'internalValue': function () { + return this._internalValue; + }, + + //------------------------------------------------------------------------- + + 'isBigInt': true, + + //------------------------------------------------------------------------- + + 'toString': function(aBase) { + return this.asString(aBase); + }, + + //------------------------------------------------------------------------- + + 'asString': function (aBase, minimumLength) { + var result; + var base; + + if (typeof(aBase) == 'undefined') { + base = 10; + } else { + base = aBase; + } + + result = bigInt2str(this.internalValue(), base).toLowerCase(); + + if ((typeof(minimumLength) != 'undefined') && (result.length < minimumLength)) { + var i, c; + c = (minimumLength - result.length); + for (i=0; i<c; i++) { + result = '0' + result; + } + } + + return result; + }, + + //------------------------------------------------------------------------- + + 'asByteArray': function() { + return new Clipperz.ByteArray("0x" + this.asString(16), 16); + }, + + //------------------------------------------------------------------------- + + '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; + }, + + //------------------------------------------------------------------------- + + 'compare': function(aValue) { +/* + var result; + var thisAsString; + var aValueAsString; + + thisAsString = this.asString(10); + aValueAsString = aValue.asString(10); + + result = MochiKit.Base.compare(thisAsString.length, aValueAsString.length); + if (result == 0) { + result = MochiKit.Base.compare(thisAsString, aValueAsString); + } + + return result; +*/ + var result; + + if (equals(this.internalValue(), aValue.internalValue())) { + result = 0; + } else if (greater(this.internalValue(), aValue.internalValue())) { + result = 1; + } else { + result = -1; + } + + 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 { + if (greater(this.internalValue(), value.internalValue())) { + result = multMod(this.internalValue(), value.internalValue(), aModule); + } else { + result = multMod(value.internalValue(), this.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); + }, + + //------------------------------------------------------------------------- + + 'xor': function(aValue) { + var result; + var thisByteArray; + var aValueByteArray; + var xorArray; + + thisByteArray = new Clipperz.ByteArray("0x" + this.asString(16), 16); + aValueByteArray = new Clipperz.ByteArray("0x" + aValue.asString(16), 16); + xorArray = thisByteArray.xorMergeWithBlock(aValueByteArray, 'right'); + result = new Clipperz.Crypto.BigInt(xorArray.toHexString(), 16); + + return result; + }, + + //------------------------------------------------------------------------- + + 'shiftLeft': function(aNumberOfBitsToShift) { + var result; + var internalResult; + var wholeByteToShift; + var bitsLeftToShift; + + wholeByteToShift = Math.floor(aNumberOfBitsToShift / 8); + bitsLeftToShift = aNumberOfBitsToShift % 8; + + if (wholeByteToShift == 0) { + internalResult = this.internalValue(); + } else { + var hexValue; + var i,c; + + hexValue = this.asString(16); + c = wholeByteToShift; + for (i=0; i<c; i++) { + hexValue += "00"; + } + internalResult = str2bigInt(hexValue, 16, 1, 1); + } + + if (bitsLeftToShift > 0) { + leftShift_(internalResult, bitsLeftToShift); + } + result = new Clipperz.Crypto.BigInt(internalResult); + + return result; + }, + + //------------------------------------------------------------------------- + + 'bitSize': function() { + return bitSize(this.internalValue()); + }, + + //------------------------------------------------------------------------- + + 'isBitSet': function(aBitPosition) { + var result; + + if (this.asByteArray().bitAtIndex(aBitPosition) == 0) { + result = false; + } else { + result = true; + }; + + return result; + }, + + //------------------------------------------------------------------------- + __syntaxFix__: "syntax fix" + +}); + +//############################################################################# + +Clipperz.Crypto.BigInt.randomPrime = function(aBitSize) { + return new Clipperz.Crypto.BigInt(randTruePrime(aBitSize)); +} + +//############################################################################# +//############################################################################# + +Clipperz.Crypto.BigInt.ZERO = new Clipperz.Crypto.BigInt(0); + +//############################################################################# + +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") +} |