Telegram Web K with changes to work inside I2P
https://web.telegram.i2p/
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
2169 lines
58 KiB
2169 lines
58 KiB
'use strict' |
|
/* eslint-disable */ |
|
//@flow |
|
|
|
/** * * * * * * * * * * |
|
* Big Integer Library * |
|
* Created 2000 * |
|
* Leemon Baird * |
|
* www.leemon.com * |
|
* * * * * * * * * * * */ |
|
|
|
//////////////////////////////////////////////////////////////////////////////////////// |
|
// 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? (b is bigInt, 1<b<x) |
|
// boolean millerRabinInt(x,b) //does one round of Miller-Rabin base integer b say that bigInt x is possibly prime? (b is int, 1<b<x) |
|
// 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 randProbPrime(k) //return a new, random, k-bit, probable prime bigInt (probability it's composite less than 2^-80). |
|
// 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 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). |
|
// void 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. |
|
//////////////////////////////////////////////////////////////////////////////////////// |
|
|
|
export type Bool = 1 | 0 |
|
|
|
//globals |
|
export var bpe = 0 //bits stored per array element |
|
var mask = 0 //AND this with an array element to chop it down to bpe bits |
|
var 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 |
|
var digitsStr = |
|
'0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz_=!@#$%^&*()[]{}|;:,.<>/?`~ \\\'"+-' |
|
|
|
//initialize the global variables |
|
|
|
//bpe=number of bits in the mantissa on this platform |
|
for (bpe = 0; 1 << (bpe + 1) > 1 << bpe; bpe++); |
|
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 |
|
export var one = int2bigInt(1, 1, 1) //constant used in powMod_() |
|
export var zero = int2bigInt(0, 1, 1) |
|
|
|
//the following global variables are scratchpad memory to |
|
//reduce dynamic memory allocation in the inner loop |
|
var t: number[] | number = new Array(0) |
|
var ss = t //used in mult_() |
|
var s0 = t //used in multMod_(), squareMod_() |
|
// var s1=t; //used in powMod_(), multMod_(), squareMod_() |
|
// var s2=t; //used in powMod_(), multMod_() |
|
var s3 = t //used in powMod_() |
|
var s4 = t, |
|
s5 = t //used in mod_() |
|
var s6 = t //used in bigInt2str() |
|
var s7 = t //used in powMod_() |
|
var T = t //used in GCD_() |
|
var sa = t //used in mont_() |
|
var 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_() |
|
rpprb = t //used in randProbPrimeRounds() (which also uses "primes") |
|
|
|
//////////////////////////////////////////////////////////////////////////////////////// |
|
|
|
var k, buff |
|
|
|
/** |
|
* return array of all primes less than integer n |
|
* |
|
* @param {number} n |
|
* @returns {number[]} |
|
*/ |
|
export function findPrimes(n: number): number[] { |
|
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, with b<x |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} b |
|
* @returns {(0 | 1)} |
|
*/ |
|
export function millerRabinInt(x: number[], b: number): Bool { |
|
if (mr_x1.length !== x.length) { |
|
mr_x1 = dup(x) |
|
mr_r = dup(x) |
|
mr_a = dup(x) |
|
} |
|
|
|
copyInt_(mr_a, b) |
|
return millerRabin(x, mr_a) |
|
} |
|
|
|
/** |
|
* does a single round of Miller-Rabin base b consider x to be a possible prime? |
|
* |
|
* x and b are bigInts with b<x |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} b |
|
* @returns {(0 | 1)} |
|
*/ |
|
export function millerRabin(x: number[], b: number[]): Bool { |
|
var i, j, k, s |
|
|
|
if (mr_x1.length !== x.length) { |
|
mr_x1 = dup(x) |
|
mr_r = dup(x) |
|
mr_a = dup(x) |
|
} |
|
|
|
copy_(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 |
|
//$off |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @returns {number} |
|
*/ |
|
export function bitSize(x: number[]): number { |
|
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 |
|
* |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {number[]} |
|
*/ |
|
export function expand(x: number[], n: number): number[] { |
|
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. |
|
* |
|
* @export |
|
* @param {number} k |
|
* @returns {number[]} |
|
*/ |
|
/* export function randTruePrime(k: number): number[] { |
|
var ans = int2bigInt(0, k, 0) |
|
randTruePrime_(ans, k) |
|
return trim(ans, 1) |
|
} */ |
|
|
|
/** |
|
* return a k-bit random probable prime with probability of error < 2^-80 |
|
* |
|
* @export |
|
* @param {number} k |
|
* @returns {number[]} |
|
*/ |
|
/* export function randProbPrime(k: number): number[] { |
|
if (k >= 600) return randProbPrimeRounds(k, 2) //numbers from HAC table 4.3 |
|
if (k >= 550) return randProbPrimeRounds(k, 4) |
|
if (k >= 500) return randProbPrimeRounds(k, 5) |
|
if (k >= 400) return randProbPrimeRounds(k, 6) |
|
if (k >= 350) return randProbPrimeRounds(k, 7) |
|
if (k >= 300) return randProbPrimeRounds(k, 9) |
|
if (k >= 250) return randProbPrimeRounds(k, 12) //numbers from HAC table 4.4 |
|
if (k >= 200) return randProbPrimeRounds(k, 15) |
|
if (k >= 150) return randProbPrimeRounds(k, 18) |
|
if (k >= 100) return randProbPrimeRounds(k, 27) |
|
return randProbPrimeRounds(k, 40) //number from HAC remark 4.26 (only an estimate) |
|
} */ |
|
|
|
/** |
|
* return a k-bit probable random prime using n rounds of Miller Rabin |
|
* (after trial division with small primes) |
|
* |
|
* @export |
|
* @param {number} k |
|
* @param {number} n |
|
* @returns {number[]} |
|
*/ |
|
/* export function randProbPrimeRounds(k: number, n: number): number[] { |
|
var ans, i, divisible, B |
|
B = 30000 //B is largest prime to use in trial division |
|
ans = int2bigInt(0, k, 0) |
|
|
|
//optimization: try larger and smaller B to find the best limit. |
|
|
|
if (primes.length === 0) primes = findPrimes(30000) //check for divisibility by primes <=30000 |
|
|
|
if (rpprb.length !== ans.length) rpprb = dup(ans) |
|
|
|
for (;;) { |
|
//keep trying random values for ans until one appears to be prime |
|
//optimization: pick a random number times L=2*3*5*...*p, plus a |
|
// random element of the list of all numbers in [0,L) not divisible by any prime up to p. |
|
// This can reduce the amount of random number generation. |
|
|
|
randBigInt_(ans, k, 0) //ans = a random odd number to check |
|
ans[0] |= 1 |
|
divisible = 0 |
|
|
|
//check ans for divisibility by small primes up to B |
|
for (i = 0; i < primes.length && primes[i] <= B; i++) |
|
if (modInt(ans, primes[i]) === 0 && !equalsInt(ans, primes[i])) { |
|
divisible = 1 |
|
break |
|
} |
|
|
|
//optimization: change millerRabin so the base can be bigger than the number being checked, then eliminate the while here. |
|
|
|
//do n rounds of Miller Rabin, with random bases less than ans |
|
for (i = 0; i < n && !divisible; i++) { |
|
randBigInt_(rpprb, k, 0) |
|
while ( |
|
!greater(ans, rpprb) //pick a random rpprb that's < ans |
|
) |
|
randBigInt_(rpprb, k, 0) |
|
if (!millerRabin(ans, rpprb)) divisible = 1 |
|
} |
|
|
|
if (!divisible) return ans |
|
} |
|
} */ |
|
|
|
/** |
|
* return a new bigInt equal to (x mod n) for bigInts x and n. |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} n |
|
* @returns {number[]} |
|
*/ |
|
export function mod(x: number[], n: number[]): number[] { |
|
var ans = dup(x) |
|
mod_(ans, n) |
|
return trim(ans, 1) |
|
} |
|
|
|
/** |
|
* return (x+n) where x is a bigInt and n is an integer. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {number[]} |
|
*/ |
|
/* export function addInt(x: number[], n: number): number[] { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {number[]} |
|
*/ |
|
export function mult(x: number[], y: number[]): number[] { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} n |
|
* @returns {number[]} |
|
*/ |
|
export function powMod(x: number[], y: number[], n: number[]): number[] { |
|
var ans = expand(x, n.length) |
|
powMod_( |
|
//this should work without the trim, but doesn't |
|
ans, |
|
trim(y, 2), |
|
trim(n, 2), |
|
) |
|
return trim(ans, 1) |
|
} |
|
|
|
/** |
|
* Simple pow with no optimizations (in 40x times slower than jsbn's pow) |
|
* @param x bigInt |
|
* @param e |
|
*/ |
|
export function pow(x: number[], e: number) { |
|
let ans = dup(x); |
|
e -= 1; |
|
for(let i = 0; i < e; ++i) { |
|
ans = mult(ans, x); |
|
} |
|
return trim(ans, 1); |
|
} |
|
|
|
/** |
|
* return (x-y) for bigInts x and y |
|
* |
|
* Negative answers will be 2s complement |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {number[]} |
|
*/ |
|
export function sub(x: number[], y: number[]): number[] { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {number[]} |
|
*/ |
|
export function add(x: number[], y: number[]): number[] { |
|
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 |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} n |
|
* @returns {(number[] | null)} |
|
*/ |
|
/* export function inverseMod(x: number[], n: number[]): number[] | null { |
|
var ans = expand(x, n.length) |
|
var 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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} n |
|
* @returns {number[]} |
|
*/ |
|
export function multMod(x: number[], y: number[], n: number[]): number[] { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} ans |
|
* @param {number} k |
|
* @return {void} |
|
*/ |
|
/* export function randTruePrime_(ans: number[], k: number): void { |
|
var c, m, pm, dd, j, r, B, divisible, z, zz, recSize |
|
var w |
|
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 |
|
var 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) //TODO Seems like a bug in eslint, reports as unused |
|
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 = 0.5 |
|
|
|
//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 && !equalsInt(s_n, primes[j])) { |
|
divisible = 1 |
|
break |
|
} |
|
|
|
if (!divisible) |
|
if (!millerRabinInt(s_n, 2)) |
|
//if it passes small primes check, then try a single Miller-Rabin base 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. |
|
* |
|
* @export |
|
* @param {number} n |
|
* @param {number} s |
|
* @returns {number[]} |
|
*/ |
|
/* export function randBigInt(n: number, s: number): number[] { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} b |
|
* @param {number} n |
|
* @param {number} s |
|
* @return {void} |
|
*/ |
|
/* export function randBigInt_(b: number[], n: number, s: number): void { |
|
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). |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {number[]} |
|
*/ |
|
export function GCD(x: number[], y: number[]): number[] { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
*/ |
|
export function GCD_(x: number[], y: number[]): void { |
|
var i: number, xp: number, yp: number, A: number, B, C: number, D: number, q, sing |
|
var qp |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} n |
|
* @returns {(0 | 1)} |
|
*/ |
|
/* export function inverseMod_(x: number[], n: number[]): Bool { |
|
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)) { |
|
while ( |
|
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 |
|
* |
|
* @param {number} x |
|
* @param {number} n |
|
* @returns {number} |
|
*/ |
|
export function inverseModInt(x: number, n: number): number { |
|
var a = 1, |
|
b = 0, |
|
t |
|
for (;;) { |
|
if (x === 1) return a |
|
if (x === 0) return 0 |
|
b -= a * Math.floor(n / x) |
|
//$off |
|
n %= x |
|
|
|
if (n === 1) return b //to avoid negatives, change this b to n-b, and each -= to += |
|
if (n === 0) return 0 |
|
a -= b * Math.floor(x / n) |
|
//$off |
|
x %= n |
|
} |
|
/*:: |
|
declare var never: empty |
|
return never |
|
*/ |
|
} |
|
|
|
//this deprecated function is for backward compatibility only. |
|
/* function inverseModInt_(x: number, n: number) { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} v |
|
* @param {number[]} a |
|
* @param {number[]} b |
|
* @return {void} |
|
*/ |
|
export function eGCD_( |
|
x: number[], |
|
y: number[], |
|
v: number[], |
|
a: number[], |
|
b: number[], |
|
): void { |
|
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)) { |
|
while (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? |
|
* |
|
* @param {number[]} x |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function negative(x: number[]) { |
|
//TODO Flow Bool type inference |
|
return (x[x.length - 1] >> (bpe - 1)) & 1 |
|
} |
|
|
|
/** |
|
* is (x << (shift*bpe)) > y? |
|
* |
|
* x and y are nonnegative bigInts |
|
* shift is a nonnegative integer |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number} shift |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function greaterShift(x: number[], y: number[], shift: number): Bool { |
|
var i, |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function greater(x: number[], y: number[]): Bool { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} q |
|
* @param {number[]} r |
|
* @return {void} |
|
*/ |
|
export function divide_( |
|
x: number[], |
|
y: number[], |
|
q: number[], |
|
r: number[], |
|
): void { |
|
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. |
|
* |
|
* @param {number[]} x |
|
*/ |
|
export function carry_(x: number[]): void { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {number} |
|
*/ |
|
export function modInt(x: number[], n: number): number { |
|
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. |
|
* |
|
* @export |
|
* @param {number} t |
|
* @param {number} bits |
|
* @param {number} minSize |
|
* @returns {number[]} |
|
*/ |
|
export function int2bigInt(t: number, bits: number, minSize: number): number[] { |
|
var i, k |
|
k = Math.ceil(bits / bpe) + 1 |
|
k = minSize > k ? minSize : k |
|
var 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. |
|
* |
|
* @export |
|
* @param {string} s |
|
* @param {number} base |
|
* @param {number} [minSize] |
|
* @returns {number[]} |
|
*/ |
|
export function str2bigInt( |
|
s: string, |
|
base: number, |
|
minSize?: number, |
|
): number[] { |
|
var d, i, 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) //TODO PERF Should we replace that with ~~ (not not)? https://jsperf.com/number-vs-parseint-vs-plus/7 |
|
x = y |
|
d = s.indexOf(',', 0) |
|
if (d < 1) break |
|
//$off |
|
s = s.substring(d + 1) |
|
if (s.length == 0) break |
|
} |
|
//$off |
|
if (x.length < minSize) { |
|
//$off |
|
y = new Array(minSize) |
|
copy_(y, x) |
|
return y |
|
} |
|
return x |
|
} |
|
|
|
x = int2bigInt(0, base * k, 0) |
|
for (i = 0; i < k; i++) { |
|
d = digitsStr.indexOf(s.substring(i, i + 1), 0) |
|
if (base <= 36 && d >= 36) |
|
//convert lowercase to uppercase if base<=36 |
|
d -= 26 |
|
if (d >= base || d < 0) { |
|
//stop at first illegal character |
|
break |
|
} |
|
multInt_(x, base) |
|
addInt_(x, d) |
|
} |
|
|
|
for (k = x.length; k > 0 && !x[k - 1]; k--); //strip off leading zeros |
|
//$off |
|
k = minSize > k + 1 ? minSize : k + 1 |
|
//$off |
|
y = new Array(k) |
|
//$off |
|
kk = k < x.length ? k : x.length |
|
//$off |
|
for (i = 0; i < kk; i++) y[i] = x[i] |
|
//$off |
|
for (; i < k; i++) y[i] = 0 |
|
return y |
|
} |
|
|
|
//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,b,minSize) { |
|
// var d, i, j, base, str, x, y, kk; |
|
// if (typeof b === 'string') { |
|
// base = b.length; |
|
// str = b; |
|
// } else { |
|
// base = b; |
|
// str = digitsStr; |
|
// } |
|
// 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=str.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 |
|
// continue; |
|
// } |
|
// 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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} y |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function equalsInt(x: number[], y: number): Bool { |
|
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 |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function equals(x: number[], y: number[]): Bool { |
|
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? |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @returns {(1 | 0)} |
|
*/ |
|
export function isZero(x: number[]): Bool { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} base |
|
* @returns {string} |
|
*/ |
|
export function bigInt2str(x: number[], base: number): string { |
|
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 |
|
} |
|
|
|
/** |
|
* Convert a bigInt into bytes |
|
* @param x bigInt |
|
* @param littleEndian byte order by default |
|
*/ |
|
export function bigInt2bytes(x: number[], littleEndian = true) { |
|
if(s6.length !== x.length) s6 = dup(x); |
|
else copy_(s6, x); |
|
|
|
const out: number[] = []; |
|
|
|
//console.log('bigInt2bytes'); |
|
while(!isZero(s6)) { |
|
t = divInt_(s6, 256); //t=s6 % base; s6=floor(s6/base); |
|
out.push(t); |
|
//console.log('bigInt2bytes', t); |
|
} |
|
|
|
if(littleEndian) { |
|
out.reverse(); |
|
} |
|
|
|
//console.log('bigInt2bytes', out); |
|
|
|
return out; |
|
} |
|
|
|
/** |
|
* Compare two bigInts and return -1 if x is less, 0 if equals, 1 if greater |
|
* @param x bigInt |
|
* @param y bigInt |
|
*/ |
|
export function cmp(x: number[], y: number[]) { |
|
return greater(x, y) ? 1 : (equals(x, y) ? 0 : -1); |
|
} |
|
|
|
/* Object.assign(self, { |
|
cmp, |
|
str2bigInt, |
|
int2bigInt, |
|
bigInt2str, |
|
one, |
|
divide_, |
|
divInt_, |
|
dup, |
|
negative |
|
}); */ |
|
|
|
/** |
|
* Returns a duplicate of bigInt x |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @returns {number[]} |
|
*/ |
|
export function dup(x: number[]): number[] { |
|
var i |
|
buff = 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). |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @returns {void} |
|
*/ |
|
export function copy_(x: number[], y: number[]): void { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {void} |
|
*/ |
|
export function copyInt_(x: number[], n: number): void { |
|
var i, c |
|
var len = x.length //TODO .length in for loop have perfomance costs. Bench this |
|
for (c = n, i = 0; i < len; 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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {void} |
|
*/ |
|
export function addInt_(x: number[], n: number): void { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
*/ |
|
export function rightShift_(x: number[], n: number): void { |
|
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 |
|
//$off |
|
n %= bpe |
|
} |
|
for (i = 0; i < x.length - 1; i++) { |
|
x[i] = mask & ((x[i + 1] << (bpe - n)) | (x[i] >> n)) |
|
} |
|
x[i] >>= n |
|
} |
|
|
|
/** |
|
* do x=floor(|x|/2)*sgn(x) for bigInt x in 2's complement |
|
* |
|
* @param {number[]} x |
|
* @returns {void} |
|
*/ |
|
export function halve_(x: number[]): void { |
|
var i |
|
for (i = 0; i < x.length - 1; i++) { |
|
x[i] = mask & ((x[i + 1] << (bpe - 1)) | (x[i] >> 1)) |
|
} |
|
x[i] = (x[i] >> 1) | (x[i] & (radix >> 1)) //most significant bit stays the same |
|
} |
|
|
|
/** |
|
* left shift bigInt x by n bits |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {void} |
|
*/ |
|
export function leftShift_(x: number[], n: number): void { |
|
var i |
|
var k = Math.floor(n / bpe) |
|
if (k) { |
|
for ( |
|
i = x.length; |
|
i >= k; |
|
i-- //left shift x by k elements |
|
) |
|
x[i] = x[i - k] |
|
for (; i >= 0; i--) x[i] = 0 |
|
//$off |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {void} |
|
*/ |
|
export function multInt_(x: number[], n: number): void { |
|
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 |
|
* |
|
* @param {number[]} x |
|
* @param {number} n |
|
* @returns {number} remainder |
|
*/ |
|
export function divInt_(x: number[], n: number): number { |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number} a |
|
* @param {number} b |
|
* @returns {void} |
|
*/ |
|
export function linComb_(x: number[], y: number[], a: number, b: number): void { |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number} b |
|
* @param {number} ys |
|
* @returns {void} |
|
*/ |
|
export function linCombShift_( |
|
x: number[], |
|
y: number[], |
|
b: number, |
|
ys: number, |
|
): void { |
|
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 integer ys. |
|
* |
|
* x must be large enough to hold the answer. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number} ys |
|
* @return {void} |
|
*/ |
|
export function addShift_(x: number[], y: number[], ys: number): void { |
|
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 integer ys |
|
* |
|
* x must be large enough to hold the answer |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number} ys |
|
* @return {void} |
|
*/ |
|
export function subShift_(x: number[], y: number[], ys: number): void { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @return {void} |
|
*/ |
|
export function sub_(x: number[], y: number[]): void { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @return {void} |
|
*/ |
|
export function add_(x: number[], y: number[]): void { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @return {void} |
|
*/ |
|
export function mult_(x: number[], y: number[]): void { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} n |
|
* @return {void} |
|
*/ |
|
export function mod_(x: number[], n: number[]): void { |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} n |
|
* @return {void} |
|
*/ |
|
export function multMod_(x: number[], y: number[], n: number[]): void { |
|
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. |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} n |
|
* @return {void} |
|
*/ |
|
export function squareMod_(x: number[], n: number[]): void { |
|
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 |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number} k |
|
* @returns {number[]} |
|
*/ |
|
export function trim(x: number[], k: number): number[] { |
|
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. |
|
* |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} n |
|
* @return {void} |
|
*/ |
|
export function powMod_(x: number[], y: number[], n: number[]): void { |
|
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) |
|
//$off |
|
// @ts-ignore |
|
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 array must have at least as many elemnts as the n array |
|
* It's OK if x and y are the same variable. |
|
* |
|
* must have: |
|
* * x,y < n |
|
* * n is odd |
|
* * np = -(n^(-1)) mod radix |
|
* |
|
* @export |
|
* @param {number[]} x |
|
* @param {number[]} y |
|
* @param {number[]} n |
|
* @param {number} np |
|
* @return {void} |
|
*/ |
|
export function mont_(x: number[], y: number[], n: number[], np: number): void { |
|
var i, j, c, ui, t, ks |
|
var kn = n.length |
|
var ky = y.length |
|
|
|
if (sa.length != kn) sa = new Array(kn) |
|
|
|
copyInt_(sa, 0) |
|
|
|
for (; kn > 0 && n[kn - 1] == 0; kn--); //ignore leading zeros of n |
|
for (; ky > 0 && y[ky - 1] == 0; ky--); //ignore leading zeros of y |
|
ks = sa.length - 1 //sa will never have more than this many nonzero elements. |
|
|
|
//the following loop consumes 95% of the runtime for randTruePrime_() and powMod_() for large numbers |
|
for (i = 0; i < kn; i++) { |
|
t = sa[0] + x[i] * y[0] |
|
ui = ((t & mask) * np) & mask //the inner "& mask" was needed on Safari (but not MSIE) at one time |
|
c = (t + ui * n[0]) >> bpe |
|
t = x[i] |
|
|
|
//do sa=(sa+x[i]*y+ui*n)/b where b=2**bpe. Loop is unrolled 5-fold for speed |
|
j = 1 |
|
for (; j < ky - 4; ) { |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
} |
|
for (; j < ky; ) { |
|
c += sa[j] + ui * n[j] + t * y[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
} |
|
for (; j < kn - 4; ) { |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
} |
|
for (; j < kn; ) { |
|
c += sa[j] + ui * n[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
} |
|
for (; j < ks; ) { |
|
c += sa[j] |
|
sa[j - 1] = c & mask |
|
c >>= bpe |
|
j++ |
|
} |
|
sa[j - 1] = c & mask |
|
} |
|
|
|
if (!greater(n, sa)) sub_(sa, n) |
|
copy_(x, sa) |
|
} |