+ − ////////////////////////////////////////////////////////////////////////////////////////
+ − // Big Integer Library v. 5.1
+ − // Created 2000, last modified 2007
+ − // Leemon Baird
+ − // www.leemon.com
+ − //
+ − // Version history:
+ − //
+ − // v 5.1 8 Oct 2007
+ − // - renamed inverseModInt_ to inverseModInt since it doesn't change its parameters
+ − // - added functions GCD and randBigInt, which call GCD_ and randBigInt_
+ − // - fixed a bug found by Rob Visser (see comment with his name below)
+ − // - improved comments
+ − //
+ − // 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 the arrays must be big enough to hold the answer.
+ − // 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 only 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.
+ − // Those returning a bigInt, string, or Array will dynamically allocate memory for that value.
+ − // Those returning a boolean will return the integer 0 (false) or 1 (true).
+ − // Those returning boolean or int will not allocate memory except possibly on the first time they're called with a given parameter size.
+ − //
+ − // bigInt add(x,y) //return (x+y) for bigInts x and y.
+ − // bigInt addInt(x,n) //return (x+n) where x is a bigInt and n is an integer.
+ − // string bigInt2str(x,base) //return a string form of bigInt x in a given base, with 2 <= base <= 95
+ − // int bitSize(x) //return how many bits long the bigInt x is, not counting leading zeros
+ − // bigInt dup(x) //return a copy of bigInt x
+ − // boolean equals(x,y) //is the bigInt x equal to the bigint y?
+ − // boolean equalsInt(x,y) //is bigint x equal to integer y?
+ − // bigInt expand(x,n) //return a copy of x with at least n elements, adding leading zeros if needed
+ − // Array findPrimes(n) //return array of all primes less than integer n
+ − // bigInt GCD(x,y) //return greatest common divisor of bigInts x and y (each with same number of elements).
+ − // boolean greater(x,y) //is x>y? (x and y are nonnegative bigInts)
+ − // boolean greaterShift(x,y,shift)//is (x <<(shift*bpe)) > y?
+ − // bigInt int2bigInt(t,n,m) //return a bigInt equal to integer t, with at least n bits and m array elements
+ − // bigInt inverseMod(x,n) //return (x**(-1) mod n) for bigInts x and n. If no inverse exists, it returns null
+ − // int inverseModInt(x,n) //return x**(-1) mod n, for integers x and n. Return 0 if there is no inverse
+ − // boolean isZero(x) //is the bigInt x equal to zero?
+ − // boolean millerRabin(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime (as opposed to definitely composite)?
+ − // bigInt mod(x,n) //return a new bigInt equal to (x mod n) for bigInts x and n.
+ − // int modInt(x,n) //return x mod n for bigInt x and integer n.
+ − // bigInt mult(x,y) //return x*y for bigInts x and y. This is faster when y<x.
+ − // bigInt multMod(x,y,n) //return (x*y mod n) for bigInts x,y,n. For greater speed, let y<x.
+ − // boolean negative(x) //is bigInt x negative?
+ − // bigInt powMod(x,y,n) //return (x**y mod n) where x,y,n are bigInts and ** is exponentiation. 0**0=1. Faster for odd n.
+ − // bigInt randBigInt(n,s) //return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1.
+ − // bigInt randTruePrime(k) //return a new, random, k-bit, true prime bigInt using Maurer's algorithm.
+ − // bigInt str2bigInt(s,b,n,m) //return a bigInt for number represented in string s in base b with at least n bits and m array elements
+ − // bigInt sub(x,y) //return (x-y) for bigInts x and y. Negative answers will be 2s complement
+ − // bigInt bigint_trim(x,k) //return a copy of x with exactly k leading zero elements
+ − //
+ − //
+ − // The following functions each have a non-underscored version, which most users should call instead.
+ − // These functions each write to a single parameter, and the caller is responsible for ensuring the array
+ − // passed in is large enough to hold the result.
+ − //
+ − // void addInt_(x,n) //do x=x+n where x is a bigInt and n is an integer
+ − // void add_(x,y) //do x=x+y for bigInts x and y
+ − // void copy_(x,y) //do x=y on bigInts x and y
+ − // void copyInt_(x,n) //do x=n on bigInt x and integer n
+ − // void GCD_(x,y) //set x to the greatest common divisor of bigInts x and y, (y is destroyed). (This never overflows its array).
+ − // boolean inverseMod_(x,n) //do x=x**(-1) mod n, for bigInts x and n. Returns 1 (0) if inverse does (doesn't) exist
+ − // void mod_(x,n) //do x=x mod n for bigInts x and n. (This never overflows its array).
+ − // void mult_(x,y) //do x=x*y for bigInts x and y.
+ − // void multMod_(x,y,n) //do x=x*y mod n for bigInts x,y,n.
+ − // void powMod_(x,y,n) //do x=x**y mod n, where x,y,n are bigInts (n is odd) and ** is exponentiation. 0**0=1.
+ − // void randBigInt_(b,n,s) //do b = an n-bit random BigInt. if s=1, then nth bit (most significant bit) is set to 1. n>=1.
+ − // void randTruePrime_(ans,k) //do ans = a random k-bit true random prime (not just probable prime) with 1 in the msb.
+ − // void sub_(x,y) //do x=x-y for bigInts x and y. Negative answers will be 2s complement.
+ − //
+ − // The following functions do NOT have a non-underscored version.
+ − // They each write a bigInt result to one or more parameters. The caller is responsible for
+ − // ensuring the arrays passed in are large enough to hold the results.
+ − //
+ − // void addShift_(x,y,ys) //do x=x+(y<<(ys*bpe))
+ − // void carry_(x) //do carries and borrows so each element of the bigInt x fits in bpe bits.
+ − // void divide_(x,y,q,r) //divide x by y giving quotient q and remainder r
+ − // int divInt_(x,n) //do x=floor(x/n) for bigInt x and integer n, and return the remainder. (This never overflows its array).
+ − // int eGCD_(x,y,d,a,b) //sets a,b,d to positive bigInts such that d = GCD_(x,y) = a*x-b*y
+ − // void halve_(x) //do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement. (This never overflows its array).
+ − // void leftShift_(x,n) //left shift bigInt x by n bits. n<bpe.
+ − // void linComb_(x,y,a,b) //do x=a*x+b*y for bigInts x and y and integers a and b
+ − // void linCombShift_(x,y,b,ys) //do x=x+b*(y<<(ys*bpe)) for bigInts x and y, and integers b and ys
+ − // void mont_(x,y,n,np) //Montgomery multiplication (see comments where the function is defined)
+ − // void multInt_(x,n) //do x=x*n where x is a bigInt and n is an integer.
+ − // void rightShift_(x,n) //right shift bigInt x by n bits. 0 <= n < bpe. (This never overflows its array).
+ − // void squareMod_(x,n) //do x=x*x mod n for bigInts x,n
+ − // void 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 bigint_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 bigint_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 bigint_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 bigint_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,bigint_trim(y,2),bigint_trim(n,2),0); //this should work without the trim, but doesn't
+ − return bigint_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 bigint_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 bigint_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 ? bigint_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 bigint_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
+ − c=0.1; //c=0.1 in HAC
+ − m=20; //generate this k-bit number by first recursively generating a number that has between k/2 and k-m bits
+ − recLimit=20; //stop recursion when k <=recLimit. Must have recLimit >= 2
+ −
+ − 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
+ − }
+ − }
+ − }
+ − }
+ − }
+ −
+ − //Return an n-bit random BigInt (n>=1). If s=1, then the most significant of those n bits is set to 1.
+ − function randBigInt(n,s) {
+ − var a,b;
+ − a=Math.floor((n-1)/bpe)+2; //# array elements to hold the BigInt with a leading 0 element
+ − b=int2bigInt(0,0,a);
+ − randBigInt_(b,n,s);
+ − return b;
+ − }
+ −
+ − //Set b to an n-bit random BigInt. If s=1, then the most significant of those n bits 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==1)
+ − b[a-1] |= (1<<((n-1)%bpe));
+ − }
+ −
+ − //Return the greatest common divisor of bigInts x and y (each with same number of elements).
+ − function GCD(x,y) {
+ − var xc,yc;
+ − xc=dup(x);
+ − yc=dup(y);
+ − GCD_(xc,yc);
+ − return xc;
+ − }
+ −
+ − //set x to the greatest common divisor of bigInts x and y (each with 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;
+ − }
+ − }
+ −
+ − //this deprecated function is for backward compatibility only.
+ − function inverseModInt_(x,n) {
+ − return inverseModInt(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. (Or q can have more).
+ − //Must have x.length >= y.length >= 2.
+ − 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--); //ky is number of elements in y, not including leading zeros
+ −
+ − //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);
+ −
+ − //Rob Visser discovered a bug: the following line was originally just before the normalization.
+ − for (kx=r.length;r[kx-1]==0 && kx>ky;kx--); //kx is number of elements in normalized x, not including leading zeros
+ −
+ − 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 bigint_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);
+ − }
+ −
+ −
+ − /* rijndael.js Rijndael Reference Implementation
+ − Copyright (c) 2001 Fritz Schneider
+ −
+ − This software is provided as-is, without express or implied warranty.
+ − Permission to use, copy, modify, distribute or sell this software, with or
+ − without fee, for any purpose and by any individual or organization, is hereby
+ − granted, provided that the above copyright notice and this paragraph appear
+ − in all copies. Distribution as a part of an application or binary must
+ − include the above copyright notice in the documentation and/or other materials
+ − provided with the application or distribution.
+ −
+ −
+ − As the above disclaimer notes, you are free to use this code however you
+ − want. However, I would request that you send me an email
+ − (fritz /at/ cs /dot/ ucsd /dot/ edu) to say hi if you find this code useful
+ − or instructional. Seeing that people are using the code acts as
+ − encouragement for me to continue development. If you *really* want to thank
+ − me you can buy the book I wrote with Thomas Powell, _JavaScript:
+ − _The_Complete_Reference_ :)
+ −
+ − This code is an UNOPTIMIZED REFERENCE implementation of Rijndael.
+ − If there is sufficient interest I can write an optimized (word-based,
+ − table-driven) version, although you might want to consider using a
+ − compiled language if speed is critical to your application. As it stands,
+ − one run of the monte carlo test (10,000 encryptions) can take up to
+ − several minutes, depending upon your processor. You shouldn't expect more
+ − than a few kilobytes per second in throughput.
+ −
+ − Also note that there is very little error checking in these functions.
+ − Doing proper error checking is always a good idea, but the ideal
+ − implementation (using the instanceof operator and exceptions) requires
+ − IE5+/NS6+, and I've chosen to implement this code so that it is compatible
+ − with IE4/NS4.
+ −
+ − And finally, because JavaScript doesn't have an explicit byte/char data
+ − type (although JavaScript 2.0 most likely will), when I refer to "byte"
+ − in this code I generally mean "32 bit integer with value in the interval
+ − [0,255]" which I treat as a byte.
+ −
+ − See http://www-cse.ucsd.edu/~fritz/rijndael.html for more documentation
+ − of the (very simple) API provided by this code.
+ −
+ − Fritz Schneider
+ − fritz at cs.ucsd.edu
+ −
+ − */
+ −
+ − // Rijndael parameters -- Valid values are 128, 192, or 256
+ −
+ − var keySizeInBits = ( typeof AES_BITS == 'number' ) ? AES_BITS : 128;
+ − var blockSizeInBits = ( typeof AES_BLOCKSIZE == 'number' ) ? AES_BLOCKSIZE : 128;
+ −
+ − /////// You shouldn't have to modify anything below this line except for
+ − /////// the function getRandomBytes().
+ − //
+ − // Note: in the following code the two dimensional arrays are indexed as
+ − // you would probably expect, as array[row][column]. The state arrays
+ − // are 2d arrays of the form state[4][Nb].
+ −
+ −
+ − // The number of rounds for the cipher, indexed by [Nk][Nb]
+ − var roundsArray = [ ,,,,[,,,,10,, 12,, 14],,
+ − [,,,,12,, 12,, 14],,
+ − [,,,,14,, 14,, 14] ];
+ −
+ − // The number of bytes to shift by in shiftRow, indexed by [Nb][row]
+ − var shiftOffsets = [ ,,,,[,1, 2, 3],,[,1, 2, 3],,[,1, 3, 4] ];
+ −
+ − // The round constants used in subkey expansion
+ − var Rcon = [
+ − 0x01, 0x02, 0x04, 0x08, 0x10, 0x20,
+ − 0x40, 0x80, 0x1b, 0x36, 0x6c, 0xd8,
+ − 0xab, 0x4d, 0x9a, 0x2f, 0x5e, 0xbc,
+ − 0x63, 0xc6, 0x97, 0x35, 0x6a, 0xd4,
+ − 0xb3, 0x7d, 0xfa, 0xef, 0xc5, 0x91 ];
+ −
+ − // Precomputed lookup table for the SBox
+ − var SBox = [
+ − 99, 124, 119, 123, 242, 107, 111, 197, 48, 1, 103, 43, 254, 215, 171,
+ − 118, 202, 130, 201, 125, 250, 89, 71, 240, 173, 212, 162, 175, 156, 164,
+ − 114, 192, 183, 253, 147, 38, 54, 63, 247, 204, 52, 165, 229, 241, 113,
+ − 216, 49, 21, 4, 199, 35, 195, 24, 150, 5, 154, 7, 18, 128, 226,
+ − 235, 39, 178, 117, 9, 131, 44, 26, 27, 110, 90, 160, 82, 59, 214,
+ − 179, 41, 227, 47, 132, 83, 209, 0, 237, 32, 252, 177, 91, 106, 203,
+ − 190, 57, 74, 76, 88, 207, 208, 239, 170, 251, 67, 77, 51, 133, 69,
+ − 249, 2, 127, 80, 60, 159, 168, 81, 163, 64, 143, 146, 157, 56, 245,
+ − 188, 182, 218, 33, 16, 255, 243, 210, 205, 12, 19, 236, 95, 151, 68,
+ − 23, 196, 167, 126, 61, 100, 93, 25, 115, 96, 129, 79, 220, 34, 42,
+ − 144, 136, 70, 238, 184, 20, 222, 94, 11, 219, 224, 50, 58, 10, 73,
+ − 6, 36, 92, 194, 211, 172, 98, 145, 149, 228, 121, 231, 200, 55, 109,
+ − 141, 213, 78, 169, 108, 86, 244, 234, 101, 122, 174, 8, 186, 120, 37,
+ − 46, 28, 166, 180, 198, 232, 221, 116, 31, 75, 189, 139, 138, 112, 62,
+ − 181, 102, 72, 3, 246, 14, 97, 53, 87, 185, 134, 193, 29, 158, 225,
+ − 248, 152, 17, 105, 217, 142, 148, 155, 30, 135, 233, 206, 85, 40, 223,
+ − 140, 161, 137, 13, 191, 230, 66, 104, 65, 153, 45, 15, 176, 84, 187,
+ − 22 ];
+ −
+ − // Precomputed lookup table for the inverse SBox
+ − var SBoxInverse = [
+ − 82, 9, 106, 213, 48, 54, 165, 56, 191, 64, 163, 158, 129, 243, 215,
+ − 251, 124, 227, 57, 130, 155, 47, 255, 135, 52, 142, 67, 68, 196, 222,
+ − 233, 203, 84, 123, 148, 50, 166, 194, 35, 61, 238, 76, 149, 11, 66,
+ − 250, 195, 78, 8, 46, 161, 102, 40, 217, 36, 178, 118, 91, 162, 73,
+ − 109, 139, 209, 37, 114, 248, 246, 100, 134, 104, 152, 22, 212, 164, 92,
+ − 204, 93, 101, 182, 146, 108, 112, 72, 80, 253, 237, 185, 218, 94, 21,
+ − 70, 87, 167, 141, 157, 132, 144, 216, 171, 0, 140, 188, 211, 10, 247,
+ − 228, 88, 5, 184, 179, 69, 6, 208, 44, 30, 143, 202, 63, 15, 2,
+ − 193, 175, 189, 3, 1, 19, 138, 107, 58, 145, 17, 65, 79, 103, 220,
+ − 234, 151, 242, 207, 206, 240, 180, 230, 115, 150, 172, 116, 34, 231, 173,
+ − 53, 133, 226, 249, 55, 232, 28, 117, 223, 110, 71, 241, 26, 113, 29,
+ − 41, 197, 137, 111, 183, 98, 14, 170, 24, 190, 27, 252, 86, 62, 75,
+ − 198, 210, 121, 32, 154, 219, 192, 254, 120, 205, 90, 244, 31, 221, 168,
+ − 51, 136, 7, 199, 49, 177, 18, 16, 89, 39, 128, 236, 95, 96, 81,
+ − 127, 169, 25, 181, 74, 13, 45, 229, 122, 159, 147, 201, 156, 239, 160,
+ − 224, 59, 77, 174, 42, 245, 176, 200, 235, 187, 60, 131, 83, 153, 97,
+ − 23, 43, 4, 126, 186, 119, 214, 38, 225, 105, 20, 99, 85, 33, 12,
+ − 125 ];
+ −
+ − function str_split(string, chunklen)
+ − {
+ − if(!chunklen) chunklen = 1;
+ − ret = new Array();
+ − for ( i = 0; i < string.length; i+=chunklen )
+ − {
+ − ret[ret.length] = string.slice(i, i+chunklen);
+ − }
+ − return ret;
+ − }
+ −
+ − // This method circularly shifts the array left by the number of elements
+ − // given in its parameter. It returns the resulting array and is used for
+ − // the ShiftRow step. Note that shift() and push() could be used for a more
+ − // elegant solution, but they require IE5.5+, so I chose to do it manually.
+ −
+ − function cyclicShiftLeft(theArray, positions) {
+ − var temp = theArray.slice(0, positions);
+ − theArray = theArray.slice(positions).concat(temp);
+ − return theArray;
+ − }
+ −
+ − // Cipher parameters ... do not change these
+ − var Nk = keySizeInBits / 32;
+ − var Nb = blockSizeInBits / 32;
+ − var Nr = roundsArray[Nk][Nb];
+ −
+ − // Multiplies the element "poly" of GF(2^8) by x. See the Rijndael spec.
+ −
+ − function xtime(poly) {
+ − poly <<= 1;
+ − return ((poly & 0x100) ? (poly ^ 0x11B) : (poly));
+ − }
+ −
+ − // Multiplies the two elements of GF(2^8) together and returns the result.
+ − // See the Rijndael spec, but should be straightforward: for each power of
+ − // the indeterminant that has a 1 coefficient in x, add y times that power
+ − // to the result. x and y should be bytes representing elements of GF(2^8)
+ −
+ − function mult_GF256(x, y) {
+ − var bit, result = 0;
+ −
+ − for (bit = 1; bit < 256; bit *= 2, y = xtime(y)) {
+ − if (x & bit)
+ − result ^= y;
+ − }
+ − return result;
+ − }
+ −
+ − // Performs the substitution step of the cipher. State is the 2d array of
+ − // state information (see spec) and direction is string indicating whether
+ − // we are performing the forward substitution ("encrypt") or inverse
+ − // substitution (anything else)
+ −
+ − function byteSub(state, direction) {
+ − var S;
+ − if (direction == "encrypt") // Point S to the SBox we're using
+ − S = SBox;
+ − else
+ − S = SBoxInverse;
+ − for (var i = 0; i < 4; i++) // Substitute for every byte in state
+ − for (var j = 0; j < Nb; j++)
+ − state[i][j] = S[state[i][j]];
+ − }
+ −
+ − // Performs the row shifting step of the cipher.
+ −
+ − function shiftRow(state, direction) {
+ − for (var i=1; i<4; i++) // Row 0 never shifts
+ − if (direction == "encrypt")
+ − state[i] = cyclicShiftLeft(state[i], shiftOffsets[Nb][i]);
+ − else
+ − state[i] = cyclicShiftLeft(state[i], Nb - shiftOffsets[Nb][i]);
+ −
+ − }
+ −
+ − // Performs the column mixing step of the cipher. Most of these steps can
+ − // be combined into table lookups on 32bit values (at least for encryption)
+ − // to greatly increase the speed.
+ −
+ − function mixColumn(state, direction) {
+ − var b = []; // Result of matrix multiplications
+ − for (var j = 0; j < Nb; j++) { // Go through each column...
+ − for (var i = 0; i < 4; i++) { // and for each row in the column...
+ − if (direction == "encrypt")
+ − b[i] = mult_GF256(state[i][j], 2) ^ // perform mixing
+ − mult_GF256(state[(i+1)%4][j], 3) ^
+ − state[(i+2)%4][j] ^
+ − state[(i+3)%4][j];
+ − else
+ − b[i] = mult_GF256(state[i][j], 0xE) ^
+ − mult_GF256(state[(i+1)%4][j], 0xB) ^
+ − mult_GF256(state[(i+2)%4][j], 0xD) ^
+ − mult_GF256(state[(i+3)%4][j], 9);
+ − }
+ − for (var i = 0; i < 4; i++) // Place result back into column
+ − state[i][j] = b[i];
+ − }
+ − }
+ −
+ − // Adds the current round key to the state information. Straightforward.
+ −
+ − function addRoundKey(state, roundKey) {
+ − for (var j = 0; j < Nb; j++) { // Step through columns...
+ − state[0][j] ^= (roundKey[j] & 0xFF); // and XOR
+ − state[1][j] ^= ((roundKey[j]>>8) & 0xFF);
+ − state[2][j] ^= ((roundKey[j]>>16) & 0xFF);
+ − state[3][j] ^= ((roundKey[j]>>24) & 0xFF);
+ − }
+ − }
+ −
+ − // This function creates the expanded key from the input (128/192/256-bit)
+ − // key. The parameter key is an array of bytes holding the value of the key.
+ − // The returned value is an array whose elements are the 32-bit words that
+ − // make up the expanded key.
+ −
+ − function keyExpansion(key) {
+ − var expandedKey = new Array();
+ − var temp;
+ −
+ − // in case the key size or parameters were changed...
+ − Nk = keySizeInBits / 32;
+ − Nb = blockSizeInBits / 32;
+ − Nr = roundsArray[Nk][Nb];
+ −
+ − for (var j=0; j < Nk; j++) // Fill in input key first
+ − expandedKey[j] =
+ − (key[4*j]) | (key[4*j+1]<<8) | (key[4*j+2]<<16) | (key[4*j+3]<<24);
+ −
+ − // Now walk down the rest of the array filling in expanded key bytes as
+ − // per Rijndael's spec
+ − for (j = Nk; j < Nb * (Nr + 1); j++) { // For each word of expanded key
+ − temp = expandedKey[j - 1];
+ − if (j % Nk == 0)
+ − temp = ( (SBox[(temp>>8) & 0xFF]) |
+ − (SBox[(temp>>16) & 0xFF]<<8) |
+ − (SBox[(temp>>24) & 0xFF]<<16) |
+ − (SBox[temp & 0xFF]<<24) ) ^ Rcon[Math.floor(j / Nk) - 1];
+ − else if (Nk > 6 && j % Nk == 4)
+ − temp = (SBox[(temp>>24) & 0xFF]<<24) |
+ − (SBox[(temp>>16) & 0xFF]<<16) |
+ − (SBox[(temp>>8) & 0xFF]<<8) |
+ − (SBox[temp & 0xFF]);
+ − expandedKey[j] = expandedKey[j-Nk] ^ temp;
+ − }
+ − return expandedKey;
+ − }
+ −
+ − // Rijndael's round functions...
+ −
+ − function Round(state, roundKey) {
+ − byteSub(state, "encrypt");
+ − shiftRow(state, "encrypt");
+ − mixColumn(state, "encrypt");
+ − addRoundKey(state, roundKey);
+ − }
+ −
+ − function InverseRound(state, roundKey) {
+ − addRoundKey(state, roundKey);
+ − mixColumn(state, "decrypt");
+ − shiftRow(state, "decrypt");
+ − byteSub(state, "decrypt");
+ − }
+ −
+ − function FinalRound(state, roundKey) {
+ − byteSub(state, "encrypt");
+ − shiftRow(state, "encrypt");
+ − addRoundKey(state, roundKey);
+ − }
+ −
+ − function InverseFinalRound(state, roundKey){
+ − addRoundKey(state, roundKey);
+ − shiftRow(state, "decrypt");
+ − byteSub(state, "decrypt");
+ − }
+ −
+ − // encrypt is the basic encryption function. It takes parameters
+ − // block, an array of bytes representing a plaintext block, and expandedKey,
+ − // an array of words representing the expanded key previously returned by
+ − // keyExpansion(). The ciphertext block is returned as an array of bytes.
+ −
+ − function encrypt(block, expandedKey) {
+ − var i;
+ − if (!block || block.length*8 != blockSizeInBits)
+ − return;
+ − if (!expandedKey)
+ − return;
+ −
+ − block = packBytes(block);
+ − addRoundKey(block, expandedKey);
+ − for (i=1; i<Nr; i++)
+ − Round(block, expandedKey.slice(Nb*i, Nb*(i+1)));
+ − FinalRound(block, expandedKey.slice(Nb*Nr));
+ − return unpackBytes(block);
+ − }
+ −
+ − // decrypt is the basic decryption function. It takes parameters
+ − // block, an array of bytes representing a ciphertext block, and expandedKey,
+ − // an array of words representing the expanded key previously returned by
+ − // keyExpansion(). The decrypted block is returned as an array of bytes.
+ −
+ − function decrypt(block, expandedKey) {
+ − var i;
+ − if (!block || block.length*8 != blockSizeInBits)
+ − return;
+ − if (!expandedKey)
+ − return;
+ −
+ − block = packBytes(block);
+ − InverseFinalRound(block, expandedKey.slice(Nb*Nr));
+ − for (i = Nr - 1; i>0; i--)
+ − InverseRound(block, expandedKey.slice(Nb*i, Nb*(i+1)));
+ − addRoundKey(block, expandedKey);
+ − return unpackBytes(block);
+ − }
+ −
+ − // This function packs an array of bytes into the four row form defined by
+ − // Rijndael. It assumes the length of the array of bytes is divisible by
+ − // four. Bytes are filled in according to the Rijndael spec (starting with
+ − // column 0, row 0 to 3). This function returns a 2d array.
+ −
+ − function packBytes(octets) {
+ − var state = new Array();
+ − if (!octets || octets.length % 4)
+ − return;
+ −
+ − state[0] = new Array(); state[1] = new Array();
+ − state[2] = new Array(); state[3] = new Array();
+ − for (var j=0; j<octets.length; j+= 4) {
+ − state[0][j/4] = octets[j];
+ − state[1][j/4] = octets[j+1];
+ − state[2][j/4] = octets[j+2];
+ − state[3][j/4] = octets[j+3];
+ − }
+ − return state;
+ − }
+ −
+ − // This function unpacks an array of bytes from the four row format preferred
+ − // by Rijndael into a single 1d array of bytes. It assumes the input "packed"
+ − // is a packed array. Bytes are filled in according to the Rijndael spec.
+ − // This function returns a 1d array of bytes.
+ −
+ − function unpackBytes(packed) {
+ − var result = new Array();
+ − for (var j=0; j<packed[0].length; j++) {
+ − result[result.length] = packed[0][j];
+ − result[result.length] = packed[1][j];
+ − result[result.length] = packed[2][j];
+ − result[result.length] = packed[3][j];
+ − }
+ − return result;
+ − }
+ −
+ − // This function takes a prospective plaintext (string or array of bytes)
+ − // and pads it with zero bytes if its length is not a multiple of the block
+ − // size. If plaintext is a string, it is converted to an array of bytes
+ − // in the process. The type checking can be made much nicer using the
+ − // instanceof operator, but this operator is not available until IE5.0 so I
+ − // chose to use the heuristic below.
+ −
+ − function formatPlaintext(plaintext) {
+ − var bpb = blockSizeInBits / 8; // bytes per block
+ − var i;
+ −
+ − // if primitive string or String instance
+ − if (typeof plaintext == "string" || plaintext.split) {
+ − // alert('AUUGH you idiot it\'s NOT A STRING ITS A '+typeof(plaintext)+'!!!');
+ − // return false;
+ − plaintext = plaintext.split("");
+ − // Unicode issues here (ignoring high byte)
+ − for (i=0; i<plaintext.length; i++)
+ − plaintext[i] = plaintext[i].charCodeAt(0) & 0xFF;
+ − }
+ −
+ − for (i = bpb - (plaintext.length % bpb); i > 0 && i < bpb; i--)
+ − plaintext[plaintext.length] = 0;
+ −
+ − return plaintext;
+ − }
+ −
+ − // Returns an array containing "howMany" random bytes. YOU SHOULD CHANGE THIS
+ − // TO RETURN HIGHER QUALITY RANDOM BYTES IF YOU ARE USING THIS FOR A "REAL"
+ − // APPLICATION.
+ −
+ − function getRandomBytes(howMany) {
+ − var i;
+ − var bytes = new Array();
+ − for (i=0; i<howMany; i++)
+ − bytes[i] = Math.round(Math.random()*255);
+ − return bytes;
+ − }
+ −
+ − // rijndaelEncrypt(plaintext, key, mode)
+ − // Encrypts the plaintext using the given key and in the given mode.
+ − // The parameter "plaintext" can either be a string or an array of bytes.
+ − // The parameter "key" must be an array of key bytes. If you have a hex
+ − // string representing the key, invoke hexToByteArray() on it to convert it
+ − // to an array of bytes. The third parameter "mode" is a string indicating
+ − // the encryption mode to use, either "ECB" or "CBC". If the parameter is
+ − // omitted, ECB is assumed.
+ − //
+ − // An array of bytes representing the cihpertext is returned. To convert
+ − // this array to hex, invoke byteArrayToHex() on it. If you are using this
+ − // "for real" it is a good idea to change the function getRandomBytes() to
+ − // something that returns truly random bits.
+ −
+ − function rijndaelEncrypt(plaintext, key, mode) {
+ − var expandedKey, i, aBlock;
+ − var bpb = blockSizeInBits / 8; // bytes per block
+ − var ct; // ciphertext
+ −
+ − if (typeof plaintext != 'object' || typeof key != 'object')
+ − {
+ − alert( 'Invalid params\nplaintext: '+typeof(plaintext)+'\nkey: '+typeof(key) );
+ − return false;
+ − }
+ − if (key.length*8 == keySizeInBits+8)
+ − key.length = keySizeInBits / 8;
+ − if (key.length*8 != keySizeInBits)
+ − {
+ − alert( 'Key length is bad!\nLength: '+key.length+'\nExpected: '+keySizeInBits / 8 );
+ − return false;
+ − }
+ − if (mode == "CBC")
+ − ct = getRandomBytes(bpb); // get IV
+ − else {
+ − mode = "ECB";
+ − ct = new Array();
+ − }
+ −
+ − // convert plaintext to byte array and pad with zeros if necessary.
+ − plaintext = formatPlaintext(plaintext);
+ −
+ − expandedKey = keyExpansion(key);
+ −
+ − for (var block=0; block<plaintext.length / bpb; block++) {
+ − aBlock = plaintext.slice(block*bpb, (block+1)*bpb);
+ − if (mode == "CBC")
+ − for (var i=0; i<bpb; i++)
+ − aBlock[i] ^= ct[block*bpb + i];
+ − ct = ct.concat(encrypt(aBlock, expandedKey));
+ − }
+ −
+ − return ct;
+ − }
+ −
+ − // rijndaelDecrypt(ciphertext, key, mode)
+ − // Decrypts the using the given key and mode. The parameter "ciphertext"
+ − // must be an array of bytes. The parameter "key" must be an array of key
+ − // bytes. If you have a hex string representing the ciphertext or key,
+ − // invoke hexToByteArray() on it to convert it to an array of bytes. The
+ − // parameter "mode" is a string, either "CBC" or "ECB".
+ − //
+ − // An array of bytes representing the plaintext is returned. To convert
+ − // this array to a hex string, invoke byteArrayToHex() on it. To convert it
+ − // to a string of characters, you can use byteArrayToString().
+ −
+ − function rijndaelDecrypt(ciphertext, key, mode) {
+ − var expandedKey;
+ − var bpb = blockSizeInBits / 8; // bytes per block
+ − var pt = new Array(); // plaintext array
+ − var aBlock; // a decrypted block
+ − var block; // current block number
+ −
+ − if (!ciphertext || !key || typeof ciphertext == "string")
+ − return;
+ − if (key.length*8 != keySizeInBits)
+ − return;
+ − if (!mode)
+ − mode = "ECB"; // assume ECB if mode omitted
+ −
+ − expandedKey = keyExpansion(key);
+ −
+ − // work backwards to accomodate CBC mode
+ − for (block=(ciphertext.length / bpb)-1; block>0; block--) {
+ − aBlock =
+ − decrypt(ciphertext.slice(block*bpb,(block+1)*bpb), expandedKey);
+ − if (mode == "CBC")
+ − for (var i=0; i<bpb; i++)
+ − pt[(block-1)*bpb + i] = aBlock[i] ^ ciphertext[(block-1)*bpb + i];
+ − else
+ − pt = aBlock.concat(pt);
+ − }
+ −
+ − // do last block if ECB (skips the IV in CBC)
+ − if (mode == "ECB")
+ − pt = decrypt(ciphertext.slice(0, bpb), expandedKey).concat(pt);
+ −
+ − return pt;
+ − }
+ −
+ − // This method takes a byte array (byteArray) and converts it to a string by
+ − // applying String.fromCharCode() to each value and concatenating the result.
+ − // The resulting string is returned. Note that this function SKIPS zero bytes
+ − // under the assumption that they are padding added in formatPlaintext().
+ − // Obviously, do not invoke this method on raw data that can contain zero
+ − // bytes. It is really only appropriate for printable ASCII/Latin-1
+ − // values. Roll your own function for more robust functionality :)
+ −
+ − function byteArrayToString(byteArray) {
+ − var result = "";
+ − for ( var i=0; i < byteArray.length; i++ )
+ − if (byteArray[i] != 0)
+ − result += '%' + byteArray[i].toString(16);
+ − return decodeURIComponent(result);
+ − }
+ −
+ − // This function takes an array of bytes (byteArray) and converts them
+ − // to a hexadecimal string. Array element 0 is found at the beginning of
+ − // the resulting string, high nibble first. Consecutive elements follow
+ − // similarly, for example [16, 255] --> "10ff". The function returns a
+ − // string.
+ −
+ − function byteArrayToHex(byteArray) {
+ − var result = "";
+ − if (!byteArray)
+ − return;
+ − for (var i=0; i<byteArray.length; i++)
+ − result += ((byteArray[i]<16) ? "0" : "") + byteArray[i].toString(16);
+ −
+ − return result;
+ − }
+ −
+ − // This function converts a string containing hexadecimal digits to an
+ − // array of bytes. The resulting byte array is filled in the order the
+ − // values occur in the string, for example "10FF" --> [16, 255]. This
+ − // function returns an array.
+ −
+ − function hexToByteArray(hexString) {
+ − /*
+ − var byteArray = [];
+ − if (hexString.length % 2) // must have even length
+ − return;
+ − if (hexString.indexOf("0x") == 0 || hexString.indexOf("0X") == 0)
+ − hexString = hexString.substring(2);
+ − for (var i = 0; i<hexString.length; i += 2)
+ − byteArray[Math.floor(i/2)] = parseInt(hexString.slice(i, i+2), 16);
+ − return byteArray;
+ − */
+ − var bytes = new Array();
+ − hexString = str_split(hexString, 2);
+ − //alert(hexString.toString());
+ − //return false;
+ − for( var i in hexString )
+ − {
+ − bytes[bytes.length] = parseInt(hexString[i], 16);
+ − }
+ − //alert(bytes.toString());
+ − return bytes;
+ − }
+ −
+ − function stringToByteArray(text)
+ − {
+ − // Modified for Enano 2009-02-16 to be Unicode-safe
+ − var result = new Array();
+ − text = encodeURIComponent(text);
+ − for ( var i = 0; i < text.length; i++ )
+ − {
+ − var ch = text.charCodeAt(i);
+ − var a = false;
+ − if ( ch == 37 ) // "%"
+ − {
+ − var hexch = text.substr(i, 3);
+ − if ( hexch.match(/^%[a-f0-9][a-f0-9]$/i) )
+ − {
+ − result[result.length] = (unescape(hexch)).charCodeAt(0);
+ − a = true;
+ − i += 2;
+ − }
+ − }
+ − if ( !a )
+ − {
+ − result[result.length] = ch;
+ − }
+ − }
+ − return result;
+ − }
+ −
+ − function aes_self_test()
+ − {
+ − //
+ − // Encryption test
+ − //
+ −
+ − var str = '';
+ − for(i=0;i<keySizeInBits/4;i++)
+ − {
+ − str+='0';
+ − }
+ − str = hexToByteArray(str);
+ − var ct = rijndaelEncrypt(str, str, 'ECB');
+ − ct = byteArrayToHex(ct);
+ − var v;
+ − switch(keySizeInBits)
+ − {
+ − // These test vectors are for 128-bit block size.
+ − case 128:
+ − v = '66e94bd4ef8a2c3b884cfa59ca342b2e';
+ − break;
+ − case 192:
+ − v = 'aae06992acbf52a3e8f4a96ec9300bd7aae06992acbf52a3e8f4a96ec9300bd7';
+ − break;
+ − case 256:
+ − v = 'dc95c078a2408989ad48a21492842087dc95c078a2408989ad48a21492842087';
+ − break;
+ − }
+ − return ( ct == v && md5_vm_test() );
+ − }
+ −
+ − /*
+ − * EnanoMath, an abstraction layer for big-integer (arbitrary precision)
+ − * mathematics.
+ − */
+ −
+ − var EnanoMathLayers = {};
+ −
+ − // EnanoMath layer: Leemon (frontend to BigInt library by Leemon Baird)
+ −
+ − EnanoMathLayers.Leemon = {
+ − Base: 10,
+ − PowMod: function(a, b, c)
+ − {
+ − a = str2bigInt(a, this.Base);
+ − b = str2bigInt(b, this.Base);
+ − c = str2bigInt(c, this.Base);
+ − var result = powMod(a, b, c);
+ − result = bigInt2str(result, this.Base);
+ − return result;
+ − },
+ − RandomInt: function(bits)
+ − {
+ − var result = randBigInt(bits);
+ − return bigInt2str(result, this.Base);
+ − }
+ − }
+ −
+ − var EnanoMath = EnanoMathLayers.Leemon;
+ −
+ − /*
+ − * The Diffie-Hellman key exchange protocol.
+ − */
+ −
+ − // Our prime number as a base for operations.
+ − var dh_prime = '7916586051748534588306961133067968196965257961415756656521818848750723547477673457670019632882524164647651492025728980571833579341743988603191694784406703';
+ −
+ − // g, a primitive root used as an exponent
+ − // (2 and 5 are acceptable, but BigInt is faster with odd numbers)
+ − var dh_g = '5';
+ −
+ − /**
+ − * Generates a Diffie-Hellman private key
+ − * @return string(BigInt)
+ − */
+ −
+ − function dh_gen_private()
+ − {
+ − return EnanoMath.RandomInt(256);
+ − }
+ −
+ − /**
+ − * Calculates the public key from the private key
+ − * @param string(BigInt)
+ − * @return string(BigInt)
+ − */
+ −
+ − function dh_gen_public(b)
+ − {
+ − return EnanoMath.PowMod(dh_g, b, dh_prime);
+ − }
+ −
+ − /**
+ − * Calculates the shared secret.
+ − * @param string(BigInt) Our private key
+ − * @param string(BigInt) Remote party's public key
+ − * @return string(BigInt)
+ − */
+ −
+ − function dh_gen_shared_secret(b, A)
+ − {
+ − return EnanoMath.PowMod(A, b, dh_prime);
+ − }
+ −
+ − /* A JavaScript implementation of the Secure Hash Algorithm, SHA-256
+ − * Version 0.3 Copyright Angel Marin 2003-2004 - http://anmar.eu.org/
+ − * Distributed under the BSD License
+ − * Some bits taken from Paul Johnston's SHA-1 implementation
+ − */
+ − /*
+ − Copyright (c) 2003-2004, Angel Marin
+ − All rights reserved.
+ −
+ − Redistribution and use in source and binary forms, with or without modification,
+ − are permitted provided that the following conditions are met:
+ −
+ − * Redistributions of source code must retain the above copyright notice, this
+ − list of conditions and the following disclaimer.
+ − * Redistributions in binary form must reproduce the above copyright notice,
+ − this list of conditions and the following disclaimer in the documentation
+ − and/or other materials provided with the distribution.
+ − * Neither the name of the <ORGANIZATION> nor the names of its contributors may
+ − be used to endorse or promote products derived from this software without
+ − specific prior written permission.
+ −
+ − THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
+ − ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+ − WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ − IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
+ − INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ − BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ − DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ − LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
+ − OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ − OF THE POSSIBILITY OF SUCH DAMAGE.
+ − */
+ − var chrsz = 8; /* bits per input character. 8 - ASCII; 16 - Unicode */
+ − function safe_add (x, y) {
+ − var lsw = (x & 0xFFFF) + (y & 0xFFFF);
+ − var msw = (x >> 16) + (y >> 16) + (lsw >> 16);
+ − return (msw << 16) | (lsw & 0xFFFF);
+ − }
+ − function S (X, n) {return ( X >>> n ) | (X << (32 - n));}
+ − function R (X, n) {return ( X >>> n );}
+ − function Ch(x, y, z) {return ((x & y) ^ ((~x) & z));}
+ − function Maj(x, y, z) {return ((x & y) ^ (x & z) ^ (y & z));}
+ − function Sigma0256(x) {return (S(x, 2) ^ S(x, 13) ^ S(x, 22));}
+ − function Sigma1256(x) {return (S(x, 6) ^ S(x, 11) ^ S(x, 25));}
+ − function Gamma0256(x) {return (S(x, 7) ^ S(x, 18) ^ R(x, 3));}
+ − function Gamma1256(x) {return (S(x, 17) ^ S(x, 19) ^ R(x, 10));}
+ − function core_sha256 (m, l) {
+ − var K = new Array(0x428A2F98,0x71374491,0xB5C0FBCF,0xE9B5DBA5,0x3956C25B,0x59F111F1,0x923F82A4,0xAB1C5ED5,0xD807AA98,0x12835B01,0x243185BE,0x550C7DC3,0x72BE5D74,0x80DEB1FE,0x9BDC06A7,0xC19BF174,0xE49B69C1,0xEFBE4786,0xFC19DC6,0x240CA1CC,0x2DE92C6F,0x4A7484AA,0x5CB0A9DC,0x76F988DA,0x983E5152,0xA831C66D,0xB00327C8,0xBF597FC7,0xC6E00BF3,0xD5A79147,0x6CA6351,0x14292967,0x27B70A85,0x2E1B2138,0x4D2C6DFC,0x53380D13,0x650A7354,0x766A0ABB,0x81C2C92E,0x92722C85,0xA2BFE8A1,0xA81A664B,0xC24B8B70,0xC76C51A3,0xD192E819,0xD6990624,0xF40E3585,0x106AA070,0x19A4C116,0x1E376C08,0x2748774C,0x34B0BCB5,0x391C0CB3,0x4ED8AA4A,0x5B9CCA4F,0x682E6FF3,0x748F82EE,0x78A5636F,0x84C87814,0x8CC70208,0x90BEFFFA,0xA4506CEB,0xBEF9A3F7,0xC67178F2);
+ − var HASH = new Array(0x6A09E667, 0xBB67AE85, 0x3C6EF372, 0xA54FF53A, 0x510E527F, 0x9B05688C, 0x1F83D9AB, 0x5BE0CD19);
+ − var W = new Array(64);
+ − var a, b, c, d, e, f, g, h, i, j;
+ − var T1, T2;
+ − /* append padding */
+ − m[l >> 5] |= 0x80 << (24 - l % 32);
+ − m[((l + 64 >> 9) << 4) + 15] = l;
+ − for ( var i = 0; i<m.length; i+=16 ) {
+ − a = HASH[0]; b = HASH[1]; c = HASH[2]; d = HASH[3]; e = HASH[4]; f = HASH[5]; g = HASH[6]; h = HASH[7];
+ − for ( var j = 0; j<64; j++) {
+ − if (j < 16) W[j] = m[j + i];
+ − else W[j] = safe_add(safe_add(safe_add(Gamma1256(W[j - 2]), W[j - 7]), Gamma0256(W[j - 15])), W[j - 16]);
+ − T1 = safe_add(safe_add(safe_add(safe_add(h, Sigma1256(e)), Ch(e, f, g)), K[j]), W[j]);
+ − T2 = safe_add(Sigma0256(a), Maj(a, b, c));
+ − h = g; g = f; f = e; e = safe_add(d, T1); d = c; c = b; b = a; a = safe_add(T1, T2);
+ − }
+ − HASH[0] = safe_add(a, HASH[0]); HASH[1] = safe_add(b, HASH[1]); HASH[2] = safe_add(c, HASH[2]); HASH[3] = safe_add(d, HASH[3]); HASH[4] = safe_add(e, HASH[4]); HASH[5] = safe_add(f, HASH[5]); HASH[6] = safe_add(g, HASH[6]); HASH[7] = safe_add(h, HASH[7]);
+ − }
+ − return HASH;
+ − }
+ − function str2binb (str) {
+ − var bin = Array();
+ − var mask = (1 << chrsz) - 1;
+ − for(var i = 0; i < str.length * chrsz; i += chrsz)
+ − bin[i>>5] |= (str.charCodeAt(i / chrsz) & mask) << (24 - i%32);
+ − return bin;
+ − }
+ − function binb2hex (binarray) {
+ − var hexcase = 0; /* hex output format. 0 - lowercase; 1 - uppercase */
+ − var hex_tab = hexcase ? "0123456789ABCDEF" : "0123456789abcdef";
+ − var str = "";
+ − for (var i = 0; i < binarray.length * 4; i++) {
+ − str += hex_tab.charAt((binarray[i>>2] >> ((3 - i%4)*8+4)) & 0xF) + hex_tab.charAt((binarray[i>>2] >> ((3 - i%4)*8 )) & 0xF);
+ − }
+ − return str;
+ − }
+ − function hex_sha256(s){return binb2hex(core_sha256(str2binb(s),s.length * chrsz));}
+ −
+ − // Javascript implementation of the and SHA1 hash algorithms - both written by Paul Johnston, licensed under the BSD license
+ −
+ − // MD5
+ − var hexcase = 0; var b64pad = ""; var chrsz = 8;
+ − function hex_md5(s){ return binl2hex(core_md5(str2binl(s), s.length * chrsz));}
+ − function b64_md5(s){ return binl2b64(core_md5(str2binl(s), s.length * chrsz));}
+ − function str_md5(s){ return binl2str(core_md5(str2binl(s), s.length * chrsz));}
+ − function hex_hmac_md5(key, data) { return binl2hex(core_hmac_md5(key, data)); }
+ − function b64_hmac_md5(key, data) { return binl2b64(core_hmac_md5(key, data)); }
+ − function str_hmac_md5(key, data) { return binl2str(core_hmac_md5(key, data)); }
+ − function md5_vm_test() { return hex_md5("abc") == "900150983cd24fb0d6963f7d28e17f72"; }
+ − function core_md5(x, len) { x[len >> 5] |= 0x80 << ((len) % 32); x[(((len + 64) >>> 9) << 4) + 14] = len; var a = 1732584193; var b = -271733879; var c = -1732584194; var d = 271733878; for(var i = 0; i < x.length; i += 16) { var olda = a; var oldb = b; var oldc = c; var oldd = d; a = md5_ff(a, b, c, d, x[i+ 0], 7 , -680876936);d = md5_ff(d, a, b, c, x[i+ 1], 12, -389564586);c = md5_ff(c, d, a, b, x[i+ 2], 17, 606105819);b = md5_ff(b, c, d, a, x[i+ 3], 22, -1044525330);
+ − a = md5_ff(a, b, c, d, x[i+ 4], 7 , -176418897);d = md5_ff(d, a, b, c, x[i+ 5], 12, 1200080426);c = md5_ff(c, d, a, b, x[i+ 6], 17, -1473231341);b = md5_ff(b, c, d, a, x[i+ 7], 22, -45705983);a = md5_ff(a, b, c, d, x[i+ 8], 7 , 1770035416);d = md5_ff(d, a, b, c, x[i+ 9], 12, -1958414417);c = md5_ff(c, d, a, b, x[i+10], 17, -42063);b = md5_ff(b, c, d, a, x[i+11], 22, -1990404162);a = md5_ff(a, b, c, d, x[i+12], 7 , 1804603682);d = md5_ff(d, a, b, c, x[i+13], 12, -40341101);
+ − c = md5_ff(c, d, a, b, x[i+14], 17, -1502002290);b = md5_ff(b, c, d, a, x[i+15], 22, 1236535329);a = md5_gg(a, b, c, d, x[i+ 1], 5 , -165796510);d = md5_gg(d, a, b, c, x[i+ 6], 9 , -1069501632);c = md5_gg(c, d, a, b, x[i+11], 14, 643717713);b = md5_gg(b, c, d, a, x[i+ 0], 20, -373897302);a = md5_gg(a, b, c, d, x[i+ 5], 5 , -701558691);d = md5_gg(d, a, b, c, x[i+10], 9 , 38016083);c = md5_gg(c, d, a, b, x[i+15], 14, -660478335);b = md5_gg(b, c, d, a, x[i+ 4], 20, -405537848);
+ − a = md5_gg(a, b, c, d, x[i+ 9], 5 , 568446438);d = md5_gg(d, a, b, c, x[i+14], 9 , -1019803690);c = md5_gg(c, d, a, b, x[i+ 3], 14, -187363961);b = md5_gg(b, c, d, a, x[i+ 8], 20, 1163531501);a = md5_gg(a, b, c, d, x[i+13], 5 , -1444681467);d = md5_gg(d, a, b, c, x[i+ 2], 9 , -51403784);c = md5_gg(c, d, a, b, x[i+ 7], 14, 1735328473);b = md5_gg(b, c, d, a, x[i+12], 20, -1926607734);a = md5_hh(a, b, c, d, x[i+ 5], 4 , -378558);d = md5_hh(d, a, b, c, x[i+ 8], 11, -2022574463);
+ − c = md5_hh(c, d, a, b, x[i+11], 16, 1839030562);b = md5_hh(b, c, d, a, x[i+14], 23, -35309556);a = md5_hh(a, b, c, d, x[i+ 1], 4 , -1530992060);d = md5_hh(d, a, b, c, x[i+ 4], 11, 1272893353);c = md5_hh(c, d, a, b, x[i+ 7], 16, -155497632);b = md5_hh(b, c, d, a, x[i+10], 23, -1094730640);a = md5_hh(a, b, c, d, x[i+13], 4 , 681279174);d = md5_hh(d, a, b, c, x[i+ 0], 11, -358537222);c = md5_hh(c, d, a, b, x[i+ 3], 16, -722521979);b = md5_hh(b, c, d, a, x[i+ 6], 23, 76029189);
+ − a = md5_hh(a, b, c, d, x[i+ 9], 4 , -640364487);d = md5_hh(d, a, b, c, x[i+12], 11, -421815835);c = md5_hh(c, d, a, b, x[i+15], 16, 530742520);b = md5_hh(b, c, d, a, x[i+ 2], 23, -995338651);a = md5_ii(a, b, c, d, x[i+ 0], 6 , -198630844);d = md5_ii(d, a, b, c, x[i+ 7], 10, 1126891415);c = md5_ii(c, d, a, b, x[i+14], 15, -1416354905);b = md5_ii(b, c, d, a, x[i+ 5], 21, -57434055);a = md5_ii(a, b, c, d, x[i+12], 6 , 1700485571);d = md5_ii(d, a, b, c, x[i+ 3], 10, -1894986606);
+ − c = md5_ii(c, d, a, b, x[i+10], 15, -1051523);b = md5_ii(b, c, d, a, x[i+ 1], 21, -2054922799);a = md5_ii(a, b, c, d, x[i+ 8], 6 , 1873313359);d = md5_ii(d, a, b, c, x[i+15], 10, -30611744);c = md5_ii(c, d, a, b, x[i+ 6], 15, -1560198380);b = md5_ii(b, c, d, a, x[i+13], 21, 1309151649);a = md5_ii(a, b, c, d, x[i+ 4], 6 , -145523070);d = md5_ii(d, a, b, c, x[i+11], 10, -1120210379);c = md5_ii(c, d, a, b, x[i+ 2], 15, 718787259);b = md5_ii(b, c, d, a, x[i+ 9], 21, -343485551);
+ − a = safe_add(a, olda); b = safe_add(b, oldb); c = safe_add(c, oldc); d = safe_add(d, oldd); } return Array(a, b, c, d); }
+ − function md5_cmn(q, a, b, x, s, t) { return safe_add(bit_rol(safe_add(safe_add(a, q), safe_add(x, t)), s),b); }
+ − function md5_ff(a, b, c, d, x, s, t) { return md5_cmn((b & c) | ((~b) & d), a, b, x, s, t); }
+ − function md5_gg(a, b, c, d, x, s, t) { return md5_cmn((b & d) | (c & (~d)), a, b, x, s, t); }
+ − function md5_hh(a, b, c, d, x, s, t) { return md5_cmn(b ^ c ^ d, a, b, x, s, t); }
+ − function md5_ii(a, b, c, d, x, s, t) { return md5_cmn(c ^ (b | (~d)), a, b, x, s, t); }
+ − function core_hmac_md5(key, data) { var bkey = str2binl(key); if(bkey.length > 16) bkey = core_md5(bkey, key.length * chrsz); var ipad = Array(16), opad = Array(16); for(var i = 0; i < 16; i++) { ipad[i] = bkey[i] ^ 0x36363636; opad[i] = bkey[i] ^ 0x5C5C5C5C; } var hash = core_md5(ipad.concat(str2binl(data)), 512 + data.length * chrsz); return core_md5(opad.concat(hash), 512 + 128); }
+ − function safe_add(x, y) {var lsw = (x & 0xFFFF) + (y & 0xFFFF);var msw = (x >> 16) + (y >> 16) + (lsw >> 16);return (msw << 16) | (lsw & 0xFFFF); }
+ − function bit_rol(num, cnt) { return (num << cnt) | (num >>> (32 - cnt)); }
+ − function str2binl(str) { var bin = Array(); var mask = (1 << chrsz) - 1; for(var i = 0; i < str.length * chrsz; i += chrsz)bin[i>>5] |= (str.charCodeAt(i / chrsz) & mask) << (i%32); return bin;}
+ − function binl2str(bin) { var str = ""; var mask = (1 << chrsz) - 1; for(var i = 0; i < bin.length * 32; i += chrsz) str += String.fromCharCode((bin[i>>5] >>> (i % 32)) & mask); return str; }
+ − function binl2hex(binarray) { var hex_tab = hexcase ? "0123456789ABCDEF" : "0123456789abcdef"; var str = ""; for(var i = 0; i < binarray.length * 4; i++) { str += hex_tab.charAt((binarray[i>>2] >> ((i%4)*8+4)) & 0xF) + hex_tab.charAt((binarray[i>>2] >> ((i%4)*8 )) & 0xF); } return str; }
+ − function binl2b64(binarray) { var tab = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; var str = ""; for(var i = 0; i < binarray.length * 4; i += 3) { var triplet = (((binarray[i >> 2] >> 8 * ( i %4)) & 0xFF) << 16) | (((binarray[i+1 >> 2] >> 8 * ((i+1)%4)) & 0xFF) << 8 ) | ((binarray[i+2 >> 2] >> 8 * ((i+2)%4)) & 0xFF); for(var j = 0; j < 4; j++) { if(i * 8 + j * 6 > binarray.length * 32) str += b64pad; else str += tab.charAt((triplet >> 6*(3-j)) & 0x3F); } } return str; }
+ −
+ − // SHA1
+ − function hex_sha1(s){return binb2hex(core_sha1(str2binb(s),s.length * chrsz));}
+ − function b64_sha1(s){return binb2b64(core_sha1(str2binb(s),s.length * chrsz));}
+ − function str_sha1(s){return binb2str(core_sha1(str2binb(s),s.length * chrsz));}
+ − function hex_hmac_sha1(key, data){ return binb2hex(core_hmac_sha1(key, data));}
+ − function b64_hmac_sha1(key, data){ return binb2b64(core_hmac_sha1(key, data));}
+ − function str_hmac_sha1(key, data){ return binb2str(core_hmac_sha1(key, data));}
+ − function sha1_vm_test() { return hex_sha1("abc") == "a9993e364706816aba3e25717850c26c9cd0d89d"; }
+ − function core_sha1(x, len) { x[len >> 5] |= 0x80 << (24 - len % 32); x[((len + 64 >> 9) << 4) + 15] = len; var w = Array(80); var a = 1732584193; var b = -271733879; var c = -1732584194; var d = 271733878; var e = -1009589776; for(var i = 0; i < x.length; i += 16) { var olda = a; var oldb = b; var oldc = c; var oldd = d; var olde = e; for(var j = 0; j < 80; j++) { if(j < 16) w[j] = x[i + j]; else w[j] = rol(w[j-3] ^ w[j-8] ^ w[j-14] ^ w[j-16], 1); var t = safe_add(safe_add(rol(a, 5), sha1_ft(j, b, c, d)), safe_add(safe_add(e, w[j]), sha1_kt(j))); e = d; d = c; c = rol(b, 30); b = a; a = t; } a = safe_add(a, olda); b = safe_add(b, oldb); c = safe_add(c, oldc); d = safe_add(d, oldd); e = safe_add(e, olde); } return Array(a, b, c, d, e);}
+ − function sha1_ft(t, b, c, d){ if(t < 20) return (b & c) | ((~b) & d); if(t < 40) return b ^ c ^ d; if(t < 60) return (b & c) | (b & d) | (c & d); return b ^ c ^ d;}
+ − function sha1_kt(t){ return (t < 20) ? 1518500249 : (t < 40) ? 1859775393 : (t < 60) ? -1894007588 : -899497514;}
+ − function core_hmac_sha1(key, data){ var bkey = str2binb(key); if(bkey.length > 16) bkey = core_sha1(bkey, key.length * chrsz); var ipad = Array(16), opad = Array(16); for(var i = 0; i < 16; i++) { ipad[i] = bkey[i] ^ 0x36363636; opad[i] = bkey[i] ^ 0x5C5C5C5C; } var hash = core_sha1(ipad.concat(str2binb(data)), 512 + data.length * chrsz); return core_sha1(opad.concat(hash), 512 + 160);}
+ − function safe_add(x, y){ var lsw = (x & 0xFFFF) + (y & 0xFFFF); var msw = (x >> 16) + (y >> 16) + (lsw >> 16); return (msw << 16) | (lsw & 0xFFFF);}
+ − function rol(num, cnt){ return (num << cnt) | (num >>> (32 - cnt));}
+ − function str2binb(str){ var bin = Array(); var mask = (1 << chrsz) - 1; for(var i = 0; i < str.length * chrsz; i += chrsz) bin[i>>5] |= (str.charCodeAt(i / chrsz) & mask) << (32 - chrsz - i%32); return bin;}
+ − function binb2str(bin){ var str = ""; var mask = (1 << chrsz) - 1; for(var i = 0; i < bin.length * 32; i += chrsz) str += String.fromCharCode((bin[i>>5] >>> (32 - chrsz - i%32)) & mask); return str;}
+ − function binb2hex(binarray){ var hex_tab = hexcase ? "0123456789ABCDEF" : "0123456789abcdef"; var str = ""; for(var i = 0; i < binarray.length * 4; i++) { str += hex_tab.charAt((binarray[i>>2] >> ((3 - i%4)*8+4)) & 0xF) + hex_tab.charAt((binarray[i>>2] >> ((3 - i%4)*8 )) & 0xF); } return str;}
+ − function binb2b64(binarray){ var tab = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"; var str = ""; for(var i = 0; i < binarray.length * 4; i += 3) { var triplet = (((binarray[i >> 2] >> 8 * (3 - i %4)) & 0xFF) << 16) | (((binarray[i+1 >> 2] >> 8 * (3 - (i+1)%4)) & 0xFF) << 8 ) | ((binarray[i+2 >> 2] >> 8 * (3 - (i+2)%4)) & 0xFF); for(var j = 0; j < 4; j++) { if(i * 8 + j * 6 > binarray.length * 32) str += b64pad; else str += tab.charAt((triplet >> 6*(3-j)) & 0x3F); } } return str;}
+ −