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fast-srp/lib/jsbn.js
Zarmack Tanen 99e62191dc Fixup for node v0.12.7
2015-09-07 15:32:09 +02:00

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/*
* Basic JavaScript BN library - subset useful for RSA encryption.
*
* Copyright (c) 2003-2005 Tom Wu
* All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS-IS" AND WITHOUT WARRANTY OF ANY KIND,
* EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY
* WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
*
* IN NO EVENT SHALL TOM WU BE LIABLE FOR ANY SPECIAL, INCIDENTAL,
* INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER
* RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER OR NOT ADVISED OF
* THE POSSIBILITY OF DAMAGE, AND ON ANY THEORY OF LIABILITY, ARISING OUT
* OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*
* In addition, the following condition applies:
*
* All redistributions must retain an intact copy of this copyright notice
* and disclaimer.
*/
/*
*
* Copyright (c) 2015 Zarmack Tanen
* Fixed .toString(16) to be compatible with node >0.12.7 because hexWrite()
* only accepts %2=0 strings
*
*
* Added Node.js Buffers support
* 2014 rzcoder
*/
var crypt = require('crypto');
var _ = require('lodash');
// Bits per digit
var dbits;
// JavaScript engine analysis
var canary = 0xdeadbeefcafe;
var j_lm = ((canary & 0xffffff) == 0xefcafe);
// (public) Constructor
function BigInteger(a, b) {
if (a != null) {
if ("number" == typeof a) {
this.fromNumber(a, b);
} else if (Buffer.isBuffer(a)) {
this.fromBuffer(a);
} else if (b == null && "string" != typeof a) {
this.fromByteArray(a);
} else {
this.fromString(a, b);
}
}
}
// return new, unset BigInteger
function nbi() {
return new BigInteger(null);
}
// am: Compute w_j += (x*this_i), propagate carries,
// c is initial carry, returns final carry.
// c < 3*dvalue, x < 2*dvalue, this_i < dvalue
// We need to select the fastest one that works in this environment.
// am1: use a single mult and divide to get the high bits,
// max digit bits should be 26 because
// max internal value = 2*dvalue^2-2*dvalue (< 2^53)
function am1(i, x, w, j, c, n) {
while (--n >= 0) {
var v = x * this[i++] + w[j] + c;
c = Math.floor(v / 0x4000000);
w[j++] = v & 0x3ffffff;
}
return c;
}
// am2 avoids a big mult-and-extract completely.
// Max digit bits should be <= 30 because we do bitwise ops
// on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
function am2(i, x, w, j, c, n) {
var xl = x & 0x7fff, xh = x >> 15;
while (--n >= 0) {
var l = this[i] & 0x7fff;
var h = this[i++] >> 15;
var m = xh * l + h * xl;
l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);
c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
w[j++] = l & 0x3fffffff;
}
return c;
}
// Alternately, set max digit bits to 28 since some
// browsers slow down when dealing with 32-bit numbers.
function am3(i, x, w, j, c, n) {
var xl = x & 0x3fff, xh = x >> 14;
while (--n >= 0) {
var l = this[i] & 0x3fff;
var h = this[i++] >> 14;
var m = xh * l + h * xl;
l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;
c = (l >> 28) + (m >> 14) + xh * h;
w[j++] = l & 0xfffffff;
}
return c;
}
// We need to select the fastest one that works in this environment.
//if (j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
// BigInteger.prototype.am = am2;
// dbits = 30;
//} else if (j_lm && (navigator.appName != "Netscape")) {
// BigInteger.prototype.am = am1;
// dbits = 26;
//} else { // Mozilla/Netscape seems to prefer am3
// BigInteger.prototype.am = am3;
// dbits = 28;
//}
// For node.js, we pick am3 with max dbits to 28.
BigInteger.prototype.am = am3;
dbits = 28;
BigInteger.prototype.DB = dbits;
BigInteger.prototype.DM = ((1 << dbits) - 1);
BigInteger.prototype.DV = (1 << dbits);
var BI_FP = 52;
BigInteger.prototype.FV = Math.pow(2, BI_FP);
BigInteger.prototype.F1 = BI_FP - dbits;
BigInteger.prototype.F2 = 2 * dbits - BI_FP;
// Digit conversions
var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
var BI_RC = new Array();
var rr, vv;
rr = "0".charCodeAt(0);
for (vv = 0; vv <= 9; ++vv) BI_RC[rr++] = vv;
rr = "a".charCodeAt(0);
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
rr = "A".charCodeAt(0);
for (vv = 10; vv < 36; ++vv) BI_RC[rr++] = vv;
function int2char(n) {
return BI_RM.charAt(n);
}
function intAt(s, i) {
var c = BI_RC[s.charCodeAt(i)];
return (c == null) ? -1 : c;
}
// (protected) copy this to r
function bnpCopyTo(r) {
for (var i = this.t - 1; i >= 0; --i) r[i] = this[i];
r.t = this.t;
r.s = this.s;
}
// (protected) set from integer value x, -DV <= x < DV
function bnpFromInt(x) {
this.t = 1;
this.s = (x < 0) ? -1 : 0;
if (x > 0) this[0] = x;
else if (x < -1) this[0] = x + DV;
else this.t = 0;
}
// return bigint initialized to value
function nbv(i) {
var r = nbi();
r.fromInt(i);
return r;
}
// (protected) set from string and radix
function bnpFromString(data, radix, unsigned) {
var k;
switch (radix) {
case 2:
k = 1;
break;
case 4:
k = 2;
break;
case 8:
k = 3;
break;
case 16:
k = 4;
break;
case 32:
k = 5;
break;
case 256:
k = 8;
break;
default:
this.fromRadix(data, radix);
return;
}
this.t = 0;
this.s = 0;
var i = data.length;
var mi = false;
var sh = 0;
while (--i >= 0) {
var x = (k == 8) ? data[i] & 0xff : intAt(data, i);
if (x < 0) {
if (data.charAt(i) == "-") mi = true;
continue;
}
mi = false;
if (sh === 0)
this[this.t++] = x;
else if (sh + k > this.DB) {
this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh;
this[this.t++] = (x >> (this.DB - sh));
}
else
this[this.t - 1] |= x << sh;
sh += k;
if (sh >= this.DB) sh -= this.DB;
}
if ((!unsigned) && k == 8 && (data[0] & 0x80) != 0) {
this.s = -1;
if (sh > 0) this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh;
}
this.clamp();
if (mi) BigInteger.ZERO.subTo(this, this);
}
function bnpFromByteArray(a, unsigned) {
this.fromString(a, 256, unsigned)
}
function bnpFromBuffer(a) {
this.fromString(a, 256, true)
}
// (protected) clamp off excess high words
function bnpClamp() {
var c = this.s & this.DM;
while (this.t > 0 && this[this.t - 1] == c) --this.t;
}
// (public) return string representation in given radix
function bnToString(b) {
if (this.s < 0) return "-" + this.negate().toString(b);
var k;
if (b == 16) k = 4;
else if (b == 8) k = 3;
else if (b == 2) k = 1;
else if (b == 32) k = 5;
else if (b == 4) k = 2;
else return this.toRadix(b);
var km = (1 << k) - 1, d, m = false, r = "", i = this.t;
var p = this.DB - (i * this.DB) % k;
if (i-- > 0) {
if (p < this.DB && (d = this[i] >> p) > 0) {
m = true;
r = int2char(d);
}
while (i >= 0) {
if (p < k) {
d = (this[i] & ((1 << p) - 1)) << (k - p);
d |= this[--i] >> (p += this.DB - k);
}
else {
d = (this[i] >> (p -= k)) & km;
if (p <= 0) {
p += this.DB;
--i;
}
}
if (d > 0) m = true;
if (m) r += int2char(d);
}
}
//! Fix to be compatible with node >0.12.7 Buffer.js
if(b == 16 && r.length % 2 != 0)
r = "0" + r;
return m ? r : "0";
}
// (public) -this
function bnNegate() {
var r = nbi();
BigInteger.ZERO.subTo(this, r);
return r;
}
// (public) |this|
function bnAbs() {
return (this.s < 0) ? this.negate() : this;
}
// (public) return + if this > a, - if this < a, 0 if equal
function bnCompareTo(a) {
var r = this.s - a.s;
if (r != 0) return r;
var i = this.t;
r = i - a.t;
if (r != 0) return (this.s < 0) ? -r : r;
while (--i >= 0) if ((r = this[i] - a[i]) != 0) return r;
return 0;
}
function bnEqual(a) {
console.log(this.compareTo(a));
return (this.compareTo(a) == 0) ? true: false;
}
function bnGreater(a) {
return (this.compareTo(a) > 0) ? true : false;
}
function bnGreaterOrEqual(a) {
return (this.compareTo(a) > 0) ? true : false;
}
function bnLesser(a) {
return (this.compareTo(a) < 0) ? true : false;
}
function bnLesserOrEqual(a) {
return (this.compareTo(a) <= 0) ? true : false;
}
// returns bit length of the integer x
function nbits(x) {
var r = 1, t;
if ((t = x >>> 16) != 0) {
x = t;
r += 16;
}
if ((t = x >> 8) != 0) {
x = t;
r += 8;
}
if ((t = x >> 4) != 0) {
x = t;
r += 4;
}
if ((t = x >> 2) != 0) {
x = t;
r += 2;
}
if ((t = x >> 1) != 0) {
x = t;
r += 1;
}
return r;
}
// (public) return the number of bits in "this"
function bnBitLength() {
if (this.t <= 0) return 0;
return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));
}
// (protected) r = this << n*DB
function bnpDLShiftTo(n, r) {
var i;
for (i = this.t - 1; i >= 0; --i) r[i + n] = this[i];
for (i = n - 1; i >= 0; --i) r[i] = 0;
r.t = this.t + n;
r.s = this.s;
}
// (protected) r = this >> n*DB
function bnpDRShiftTo(n, r) {
for (var i = n; i < this.t; ++i) r[i - n] = this[i];
r.t = Math.max(this.t - n, 0);
r.s = this.s;
}
// (protected) r = this << n
function bnpLShiftTo(n, r) {
var bs = n % this.DB;
var cbs = this.DB - bs;
var bm = (1 << cbs) - 1;
var ds = Math.floor(n / this.DB), c = (this.s << bs) & this.DM, i;
for (i = this.t - 1; i >= 0; --i) {
r[i + ds + 1] = (this[i] >> cbs) | c;
c = (this[i] & bm) << bs;
}
for (i = ds - 1; i >= 0; --i) r[i] = 0;
r[ds] = c;
r.t = this.t + ds + 1;
r.s = this.s;
r.clamp();
}
// (protected) r = this >> n
function bnpRShiftTo(n, r) {
r.s = this.s;
var ds = Math.floor(n / this.DB);
if (ds >= this.t) {
r.t = 0;
return;
}
var bs = n % this.DB;
var cbs = this.DB - bs;
var bm = (1 << bs) - 1;
r[0] = this[ds] >> bs;
for (var i = ds + 1; i < this.t; ++i) {
r[i - ds - 1] |= (this[i] & bm) << cbs;
r[i - ds] = this[i] >> bs;
}
if (bs > 0) r[this.t - ds - 1] |= (this.s & bm) << cbs;
r.t = this.t - ds;
r.clamp();
}
// (protected) r = this - a
function bnpSubTo(a, r) {
var i = 0, c = 0, m = Math.min(a.t, this.t);
while (i < m) {
c += this[i] - a[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
if (a.t < this.t) {
c -= a.s;
while (i < this.t) {
c += this[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while (i < a.t) {
c -= a[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
c -= a.s;
}
r.s = (c < 0) ? -1 : 0;
if (c < -1) r[i++] = this.DV + c;
else if (c > 0) r[i++] = c;
r.t = i;
r.clamp();
}
// (protected) r = this * a, r != this,a (HAC 14.12)
// "this" should be the larger one if appropriate.
function bnpMultiplyTo(a, r) {
var x = this.abs(), y = a.abs();
var i = x.t;
r.t = i + y.t;
while (--i >= 0) r[i] = 0;
for (i = 0; i < y.t; ++i) r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);
r.s = 0;
r.clamp();
if (this.s != a.s) BigInteger.ZERO.subTo(r, r);
}
// (protected) r = this^2, r != this (HAC 14.16)
function bnpSquareTo(r) {
var x = this.abs();
var i = r.t = 2 * x.t;
while (--i >= 0) r[i] = 0;
for (i = 0; i < x.t - 1; ++i) {
var c = x.am(i, x[i], r, 2 * i, 0, 1);
if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
r[i + x.t] -= x.DV;
r[i + x.t + 1] = 1;
}
}
if (r.t > 0) r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);
r.s = 0;
r.clamp();
}
// (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
// r != q, this != m. q or r may be null.
function bnpDivRemTo(m, q, r) {
var pm = m.abs();
if (pm.t <= 0) return;
var pt = this.abs();
if (pt.t < pm.t) {
if (q != null) q.fromInt(0);
if (r != null) this.copyTo(r);
return;
}
if (r == null) r = nbi();
var y = nbi(), ts = this.s, ms = m.s;
var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus
if (nsh > 0) {
pm.lShiftTo(nsh, y);
pt.lShiftTo(nsh, r);
}
else {
pm.copyTo(y);
pt.copyTo(r);
}
var ys = y.t;
var y0 = y[ys - 1];
if (y0 === 0) return;
var yt = y0 * (1 << this.F1) + ((ys > 1) ? y[ys - 2] >> this.F2 : 0);
var d1 = this.FV / yt, d2 = (1 << this.F1) / yt, e = 1 << this.F2;
var i = r.t, j = i - ys, t = (q == null) ? nbi() : q;
y.dlShiftTo(j, t);
if (r.compareTo(t) >= 0) {
r[r.t++] = 1;
r.subTo(t, r);
}
BigInteger.ONE.dlShiftTo(ys, t);
t.subTo(y, y); // "negative" y so we can replace sub with am later
while (y.t < ys) y[y.t++] = 0;
while (--j >= 0) {
// Estimate quotient digit
var qd = (r[--i] == y0) ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);
if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) { // Try it out
y.dlShiftTo(j, t);
r.subTo(t, r);
while (r[i] < --qd) r.subTo(t, r);
}
}
if (q != null) {
r.drShiftTo(ys, q);
if (ts != ms) BigInteger.ZERO.subTo(q, q);
}
r.t = ys;
r.clamp();
if (nsh > 0) r.rShiftTo(nsh, r); // Denormalize remainder
if (ts < 0) BigInteger.ZERO.subTo(r, r);
}
// (public) this mod a
function bnMod(a) {
var r = nbi();
this.abs().divRemTo(a, null, r);
if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) a.subTo(r, r);
return r;
}
// Modular reduction using "classic" algorithm
function Classic(m) {
this.m = m;
}
function cConvert(x) {
if (x.s < 0 || x.compareTo(this.m) >= 0) return x.mod(this.m);
else return x;
}
function cRevert(x) {
return x;
}
function cReduce(x) {
x.divRemTo(this.m, null, x);
}
function cMulTo(x, y, r) {
x.multiplyTo(y, r);
this.reduce(r);
}
function cSqrTo(x, r) {
x.squareTo(r);
this.reduce(r);
}
Classic.prototype.convert = cConvert;
Classic.prototype.revert = cRevert;
Classic.prototype.reduce = cReduce;
Classic.prototype.mulTo = cMulTo;
Classic.prototype.sqrTo = cSqrTo;
// (protected) return "-1/this % 2^DB"; useful for Mont. reduction
// justification:
// xy == 1 (mod m)
// xy = 1+km
// xy(2-xy) = (1+km)(1-km)
// x[y(2-xy)] = 1-k^2m^2
// x[y(2-xy)] == 1 (mod m^2)
// if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
// should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
// JS multiply "overflows" differently from C/C++, so care is needed here.
function bnpInvDigit() {
if (this.t < 1) return 0;
var x = this[0];
if ((x & 1) === 0) return 0;
var y = x & 3; // y == 1/x mod 2^2
y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
// last step - calculate inverse mod DV directly;
// assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits
// we really want the negative inverse, and -DV < y < DV
return (y > 0) ? this.DV - y : -y;
}
// Montgomery reduction
function Montgomery(m) {
this.m = m;
this.mp = m.invDigit();
this.mpl = this.mp & 0x7fff;
this.mph = this.mp >> 15;
this.um = (1 << (m.DB - 15)) - 1;
this.mt2 = 2 * m.t;
}
// xR mod m
function montConvert(x) {
var r = nbi();
x.abs().dlShiftTo(this.m.t, r);
r.divRemTo(this.m, null, r);
if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) this.m.subTo(r, r);
return r;
}
// x/R mod m
function montRevert(x) {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
// x = x/R mod m (HAC 14.32)
function montReduce(x) {
while (x.t <= this.mt2) // pad x so am has enough room later
x[x.t++] = 0;
for (var i = 0; i < this.m.t; ++i) {
// faster way of calculating u0 = x[i]*mp mod DV
var j = x[i] & 0x7fff;
var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM;
// use am to combine the multiply-shift-add into one call
j = i + this.m.t;
x[j] += this.m.am(0, u0, x, i, 0, this.m.t);
// propagate carry
while (x[j] >= x.DV) {
x[j] -= x.DV;
x[++j]++;
}
}
x.clamp();
x.drShiftTo(this.m.t, x);
if (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
}
// r = "x^2/R mod m"; x != r
function montSqrTo(x, r) {
x.squareTo(r);
this.reduce(r);
}
// r = "xy/R mod m"; x,y != r
function montMulTo(x, y, r) {
x.multiplyTo(y, r);
this.reduce(r);
}
Montgomery.prototype.convert = montConvert;
Montgomery.prototype.revert = montRevert;
Montgomery.prototype.reduce = montReduce;
Montgomery.prototype.mulTo = montMulTo;
Montgomery.prototype.sqrTo = montSqrTo;
// (protected) true iff this is even
function bnpIsEven() {
return ((this.t > 0) ? (this[0] & 1) : this.s) === 0;
}
// (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
function bnpExp(e, z) {
if (e > 0xffffffff || e < 1) return BigInteger.ONE;
var r = nbi(), r2 = nbi(), g = z.convert(this), i = nbits(e) - 1;
g.copyTo(r);
while (--i >= 0) {
z.sqrTo(r, r2);
if ((e & (1 << i)) > 0) z.mulTo(r2, g, r);
else {
var t = r;
r = r2;
r2 = t;
}
}
return z.revert(r);
}
// (public) this^e % m, 0 <= e < 2^32
function bnModPowInt(e, m) {
var z;
if (e < 256 || m.isEven()) z = new Classic(m); else z = new Montgomery(m);
return this.exp(e, z);
}
// Copyright (c) 2005-2009 Tom Wu
// All Rights Reserved.
// See "LICENSE" for details.
// Extended JavaScript BN functions, required for RSA private ops.
// Version 1.1: new BigInteger("0", 10) returns "proper" zero
// Version 1.2: square() API, isProbablePrime fix
//(public)
function bnClone() {
var r = nbi();
this.copyTo(r);
return r;
}
//(public) return value as integer
function bnIntValue() {
if (this.s < 0) {
if (this.t == 1) return this[0] - this.DV;
else if (this.t === 0) return -1;
}
else if (this.t == 1) return this[0];
else if (this.t === 0) return 0;
// assumes 16 < DB < 32
return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];
}
//(public) return value as byte
function bnByteValue() {
return (this.t == 0) ? this.s : (this[0] << 24) >> 24;
}
//(public) return value as short (assumes DB>=16)
function bnShortValue() {
return (this.t == 0) ? this.s : (this[0] << 16) >> 16;
}
//(protected) return x s.t. r^x < DV
function bnpChunkSize(r) {
return Math.floor(Math.LN2 * this.DB / Math.log(r));
}
//(public) 0 if this === 0, 1 if this > 0
function bnSigNum() {
if (this.s < 0) return -1;
else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) return 0;
else return 1;
}
//(protected) convert to radix string
function bnpToRadix(b) {
if (b == null) b = 10;
if (this.signum() === 0 || b < 2 || b > 36) return "0";
var cs = this.chunkSize(b);
var a = Math.pow(b, cs);
var d = nbv(a), y = nbi(), z = nbi(), r = "";
this.divRemTo(d, y, z);
while (y.signum() > 0) {
r = (a + z.intValue()).toString(b).substr(1) + r;
y.divRemTo(d, y, z);
}
return z.intValue().toString(b) + r;
}
//(protected) convert from radix string
function bnpFromRadix(s, b) {
this.fromInt(0);
if (b == null) b = 10;
var cs = this.chunkSize(b);
var d = Math.pow(b, cs), mi = false, j = 0, w = 0;
for (var i = 0; i < s.length; ++i) {
var x = intAt(s, i);
if (x < 0) {
if (s.charAt(i) == "-" && this.signum() === 0) mi = true;
continue;
}
w = b * w + x;
if (++j >= cs) {
this.dMultiply(d);
this.dAddOffset(w, 0);
j = 0;
w = 0;
}
}
if (j > 0) {
this.dMultiply(Math.pow(b, j));
this.dAddOffset(w, 0);
}
if (mi) BigInteger.ZERO.subTo(this, this);
}
//(protected) alternate constructor
function bnpFromNumber(a, b) {
if ("number" == typeof b) {
// new BigInteger(int,int,RNG)
if (a < 2) this.fromInt(1);
else {
this.fromNumber(a);
if (!this.testBit(a - 1)) // force MSB set
this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
if (this.isEven()) this.dAddOffset(1, 0); // force odd
while (!this.isProbablePrime(b)) {
this.dAddOffset(2, 0);
if (this.bitLength() > a) this.subTo(BigInteger.ONE.shiftLeft(a - 1), this);
}
}
} else {
// new BigInteger(int,RNG)
var x = crypt.randomBytes((a >> 3) + 1)
var t = a & 7;
if (t > 0)
x[0] &= ((1 << t) - 1);
else
x[0] = 0;
this.fromByteArray(x);
}
}
//(public) convert to bigendian byte array
function bnToByteArray() {
var i = this.t, r = new Array();
r[0] = this.s;
var p = this.DB - (i * this.DB) % 8, d, k = 0;
if (i-- > 0) {
if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p)
r[k++] = d | (this.s << (this.DB - p));
while (i >= 0) {
if (p < 8) {
d = (this[i] & ((1 << p) - 1)) << (8 - p);
d |= this[--i] >> (p += this.DB - 8);
}
else {
d = (this[i] >> (p -= 8)) & 0xff;
if (p <= 0) {
p += this.DB;
--i;
}
}
if ((d & 0x80) != 0) d |= -256;
if (k === 0 && (this.s & 0x80) != (d & 0x80)) ++k;
if (k > 0 || d != this.s) r[k++] = d;
}
}
return r;
}
/**
* return Buffer object
* @param trim {boolean} slice buffer if first element == 0
* @returns {Buffer}
*/
function bnToBuffer(trimOrSize) {
var res = new Buffer(this.toByteArray());
if (trimOrSize === true && res[0] === 0) {
res = res.slice(1);
} else if (_.isNumber(trimOrSize)) {
if (res.length > trimOrSize) {
for (var i = 0; i < res.length - trimOrSize; i++) {
if (res[i] !== 0) {
return null;
}
}
return res.slice(res.length - trimOrSize);
} else if (res.length < trimOrSize) {
var padded = new Buffer(trimOrSize);
padded.fill(0, 0, trimOrSize - res.length);
res.copy(padded, trimOrSize - res.length);
return padded;
}
}
return res;
}
function bnEquals(a) {
return (this.compareTo(a) == 0);
}
function bnMin(a) {
return (this.compareTo(a) < 0) ? this : a;
}
function bnMax(a) {
return (this.compareTo(a) > 0) ? this : a;
}
//(protected) r = this op a (bitwise)
function bnpBitwiseTo(a, op, r) {
var i, f, m = Math.min(a.t, this.t);
for (i = 0; i < m; ++i) r[i] = op(this[i], a[i]);
if (a.t < this.t) {
f = a.s & this.DM;
for (i = m; i < this.t; ++i) r[i] = op(this[i], f);
r.t = this.t;
}
else {
f = this.s & this.DM;
for (i = m; i < a.t; ++i) r[i] = op(f, a[i]);
r.t = a.t;
}
r.s = op(this.s, a.s);
r.clamp();
}
//(public) this & a
function op_and(x, y) {
return x & y;
}
function bnAnd(a) {
var r = nbi();
this.bitwiseTo(a, op_and, r);
return r;
}
//(public) this | a
function op_or(x, y) {
return x | y;
}
function bnOr(a) {
var r = nbi();
this.bitwiseTo(a, op_or, r);
return r;
}
//(public) this ^ a
function op_xor(x, y) {
return x ^ y;
}
function bnXor(a) {
var r = nbi();
this.bitwiseTo(a, op_xor, r);
return r;
}
//(public) this & ~a
function op_andnot(x, y) {
return x & ~y;
}
function bnAndNot(a) {
var r = nbi();
this.bitwiseTo(a, op_andnot, r);
return r;
}
//(public) ~this
function bnNot() {
var r = nbi();
for (var i = 0; i < this.t; ++i) r[i] = this.DM & ~this[i];
r.t = this.t;
r.s = ~this.s;
return r;
}
//(public) this << n
function bnShiftLeft(n) {
var r = nbi();
if (n < 0) this.rShiftTo(-n, r); else this.lShiftTo(n, r);
return r;
}
//(public) this >> n
function bnShiftRight(n) {
var r = nbi();
if (n < 0) this.lShiftTo(-n, r); else this.rShiftTo(n, r);
return r;
}
//return index of lowest 1-bit in x, x < 2^31
function lbit(x) {
if (x === 0) return -1;
var r = 0;
if ((x & 0xffff) === 0) {
x >>= 16;
r += 16;
}
if ((x & 0xff) === 0) {
x >>= 8;
r += 8;
}
if ((x & 0xf) === 0) {
x >>= 4;
r += 4;
}
if ((x & 3) === 0) {
x >>= 2;
r += 2;
}
if ((x & 1) === 0) ++r;
return r;
}
//(public) returns index of lowest 1-bit (or -1 if none)
function bnGetLowestSetBit() {
for (var i = 0; i < this.t; ++i)
if (this[i] != 0) return i * this.DB + lbit(this[i]);
if (this.s < 0) return this.t * this.DB;
return -1;
}
//return number of 1 bits in x
function cbit(x) {
var r = 0;
while (x != 0) {
x &= x - 1;
++r;
}
return r;
}
//(public) return number of set bits
function bnBitCount() {
var r = 0, x = this.s & this.DM;
for (var i = 0; i < this.t; ++i) r += cbit(this[i] ^ x);
return r;
}
//(public) true iff nth bit is set
function bnTestBit(n) {
var j = Math.floor(n / this.DB);
if (j >= this.t) return (this.s != 0);
return ((this[j] & (1 << (n % this.DB))) != 0);
}
//(protected) this op (1<<n)
function bnpChangeBit(n, op) {
var r = BigInteger.ONE.shiftLeft(n);
this.bitwiseTo(r, op, r);
return r;
}
//(public) this | (1<<n)
function bnSetBit(n) {
return this.changeBit(n, op_or);
}
//(public) this & ~(1<<n)
function bnClearBit(n) {
return this.changeBit(n, op_andnot);
}
//(public) this ^ (1<<n)
function bnFlipBit(n) {
return this.changeBit(n, op_xor);
}
//(protected) r = this + a
function bnpAddTo(a, r) {
var i = 0, c = 0, m = Math.min(a.t, this.t);
while (i < m) {
c += this[i] + a[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
if (a.t < this.t) {
c += a.s;
while (i < this.t) {
c += this[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
c += this.s;
}
else {
c += this.s;
while (i < a.t) {
c += a[i];
r[i++] = c & this.DM;
c >>= this.DB;
}
c += a.s;
}
r.s = (c < 0) ? -1 : 0;
if (c > 0) r[i++] = c;
else if (c < -1) r[i++] = this.DV + c;
r.t = i;
r.clamp();
}
//(public) this + a
function bnAdd(a) {
var r = nbi();
this.addTo(a, r);
return r;
}
//(public) this - a
function bnSubtract(a) {
var r = nbi();
this.subTo(a, r);
return r;
}
//(public) this * a
function bnMultiply(a) {
var r = nbi();
this.multiplyTo(a, r);
return r;
}
// (public) this^2
function bnSquare() {
var r = nbi();
this.squareTo(r);
return r;
}
//(public) this / a
function bnDivide(a) {
var r = nbi();
this.divRemTo(a, r, null);
return r;
}
//(public) this % a
function bnRemainder(a) {
var r = nbi();
this.divRemTo(a, null, r);
return r;
}
//(public) [this/a,this%a]
function bnDivideAndRemainder(a) {
var q = nbi(), r = nbi();
this.divRemTo(a, q, r);
return new Array(q, r);
}
//(protected) this *= n, this >= 0, 1 < n < DV
function bnpDMultiply(n) {
this[this.t] = this.am(0, n - 1, this, 0, 0, this.t);
++this.t;
this.clamp();
}
//(protected) this += n << w words, this >= 0
function bnpDAddOffset(n, w) {
if (n === 0) return;
while (this.t <= w) this[this.t++] = 0;
this[w] += n;
while (this[w] >= this.DV) {
this[w] -= this.DV;
if (++w >= this.t) this[this.t++] = 0;
++this[w];
}
}
//A "null" reducer
function NullExp() {
}
function nNop(x) {
return x;
}
function nMulTo(x, y, r) {
x.multiplyTo(y, r);
}
function nSqrTo(x, r) {
x.squareTo(r);
}
NullExp.prototype.convert = nNop;
NullExp.prototype.revert = nNop;
NullExp.prototype.mulTo = nMulTo;
NullExp.prototype.sqrTo = nSqrTo;
//(public) this^e
function bnPow(e) {
return this.exp(e, new NullExp());
}
//(protected) r = lower n words of "this * a", a.t <= n
//"this" should be the larger one if appropriate.
function bnpMultiplyLowerTo(a, n, r) {
var i = Math.min(this.t + a.t, n);
r.s = 0; // assumes a,this >= 0
r.t = i;
while (i > 0) r[--i] = 0;
var j;
for (j = r.t - this.t; i < j; ++i) r[i + this.t] = this.am(0, a[i], r, i, 0, this.t);
for (j = Math.min(a.t, n); i < j; ++i) this.am(0, a[i], r, i, 0, n - i);
r.clamp();
}
//(protected) r = "this * a" without lower n words, n > 0
//"this" should be the larger one if appropriate.
function bnpMultiplyUpperTo(a, n, r) {
--n;
var i = r.t = this.t + a.t - n;
r.s = 0; // assumes a,this >= 0
while (--i >= 0) r[i] = 0;
for (i = Math.max(n - this.t, 0); i < a.t; ++i)
r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n);
r.clamp();
r.drShiftTo(1, r);
}
//Barrett modular reduction
function Barrett(m) {
// setup Barrett
this.r2 = nbi();
this.q3 = nbi();
BigInteger.ONE.dlShiftTo(2 * m.t, this.r2);
this.mu = this.r2.divide(m);
this.m = m;
}
function barrettConvert(x) {
if (x.s < 0 || x.t > 2 * this.m.t) return x.mod(this.m);
else if (x.compareTo(this.m) < 0) return x;
else {
var r = nbi();
x.copyTo(r);
this.reduce(r);
return r;
}
}
function barrettRevert(x) {
return x;
}
//x = x mod m (HAC 14.42)
function barrettReduce(x) {
x.drShiftTo(this.m.t - 1, this.r2);
if (x.t > this.m.t + 1) {
x.t = this.m.t + 1;
x.clamp();
}
this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3);
this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2);
while (x.compareTo(this.r2) < 0) x.dAddOffset(1, this.m.t + 1);
x.subTo(this.r2, x);
while (x.compareTo(this.m) >= 0) x.subTo(this.m, x);
}
//r = x^2 mod m; x != r
function barrettSqrTo(x, r) {
x.squareTo(r);
this.reduce(r);
}
//r = x*y mod m; x,y != r
function barrettMulTo(x, y, r) {
x.multiplyTo(y, r);
this.reduce(r);
}
Barrett.prototype.convert = barrettConvert;
Barrett.prototype.revert = barrettRevert;
Barrett.prototype.reduce = barrettReduce;
Barrett.prototype.mulTo = barrettMulTo;
Barrett.prototype.sqrTo = barrettSqrTo;
//(public) this^e % m (HAC 14.85)
function bnModPow(e, m) {
var i = e.bitLength(), k, r = nbv(1), z;
if (i <= 0) return r;
else if (i < 18) k = 1;
else if (i < 48) k = 3;
else if (i < 144) k = 4;
else if (i < 768) k = 5;
else k = 6;
if (i < 8)
z = new Classic(m);
else if (m.isEven())
z = new Barrett(m);
else
z = new Montgomery(m);
// precomputation
var g = new Array(), n = 3, k1 = k - 1, km = (1 << k) - 1;
g[1] = z.convert(this);
if (k > 1) {
var g2 = nbi();
z.sqrTo(g[1], g2);
while (n <= km) {
g[n] = nbi();
z.mulTo(g2, g[n - 2], g[n]);
n += 2;
}
}
var j = e.t - 1, w, is1 = true, r2 = nbi(), t;
i = nbits(e[j]) - 1;
while (j >= 0) {
if (i >= k1) w = (e[j] >> (i - k1)) & km;
else {
w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
if (j > 0) w |= e[j - 1] >> (this.DB + i - k1);
}
n = k;
while ((w & 1) === 0) {
w >>= 1;
--n;
}
if ((i -= n) < 0) {
i += this.DB;
--j;
}
if (is1) { // ret == 1, don't bother squaring or multiplying it
g[w].copyTo(r);
is1 = false;
}
else {
while (n > 1) {
z.sqrTo(r, r2);
z.sqrTo(r2, r);
n -= 2;
}
if (n > 0) z.sqrTo(r, r2); else {
t = r;
r = r2;
r2 = t;
}
z.mulTo(r2, g[w], r);
}
while (j >= 0 && (e[j] & (1 << i)) === 0) {
z.sqrTo(r, r2);
t = r;
r = r2;
r2 = t;
if (--i < 0) {
i = this.DB - 1;
--j;
}
}
}
return z.revert(r);
}
//(public) gcd(this,a) (HAC 14.54)
function bnGCD(a) {
var x = (this.s < 0) ? this.negate() : this.clone();
var y = (a.s < 0) ? a.negate() : a.clone();
if (x.compareTo(y) < 0) {
var t = x;
x = y;
y = t;
}
var i = x.getLowestSetBit(), g = y.getLowestSetBit();
if (g < 0) return x;
if (i < g) g = i;
if (g > 0) {
x.rShiftTo(g, x);
y.rShiftTo(g, y);
}
while (x.signum() > 0) {
if ((i = x.getLowestSetBit()) > 0) x.rShiftTo(i, x);
if ((i = y.getLowestSetBit()) > 0) y.rShiftTo(i, y);
if (x.compareTo(y) >= 0) {
x.subTo(y, x);
x.rShiftTo(1, x);
}
else {
y.subTo(x, y);
y.rShiftTo(1, y);
}
}
if (g > 0) y.lShiftTo(g, y);
return y;
}
//(protected) this % n, n < 2^26
function bnpModInt(n) {
if (n <= 0) return 0;
var d = this.DV % n, r = (this.s < 0) ? n - 1 : 0;
if (this.t > 0)
if (d === 0) r = this[0] % n;
else for (var i = this.t - 1; i >= 0; --i) r = (d * r + this[i]) % n;
return r;
}
//(public) 1/this % m (HAC 14.61)
function bnModInverse(m) {
var ac = m.isEven();
if ((this.isEven() && ac) || m.signum() === 0) return BigInteger.ZERO;
var u = m.clone(), v = this.clone();
var a = nbv(1), b = nbv(0), c = nbv(0), d = nbv(1);
while (u.signum() != 0) {
while (u.isEven()) {
u.rShiftTo(1, u);
if (ac) {
if (!a.isEven() || !b.isEven()) {
a.addTo(this, a);
b.subTo(m, b);
}
a.rShiftTo(1, a);
}
else if (!b.isEven()) b.subTo(m, b);
b.rShiftTo(1, b);
}
while (v.isEven()) {
v.rShiftTo(1, v);
if (ac) {
if (!c.isEven() || !d.isEven()) {
c.addTo(this, c);
d.subTo(m, d);
}
c.rShiftTo(1, c);
}
else if (!d.isEven()) d.subTo(m, d);
d.rShiftTo(1, d);
}
if (u.compareTo(v) >= 0) {
u.subTo(v, u);
if (ac) a.subTo(c, a);
b.subTo(d, b);
}
else {
v.subTo(u, v);
if (ac) c.subTo(a, c);
d.subTo(b, d);
}
}
if (v.compareTo(BigInteger.ONE) != 0) return BigInteger.ZERO;
if (d.compareTo(m) >= 0) return d.subtract(m);
if (d.signum() < 0) d.addTo(m, d); else return d;
if (d.signum() < 0) return d.add(m); else return d;
}
var lowprimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];
var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];
//(public) test primality with certainty >= 1-.5^t
function bnIsProbablePrime(t) {
var i, x = this.abs();
if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
for (i = 0; i < lowprimes.length; ++i)
if (x[0] == lowprimes[i]) return true;
return false;
}
if (x.isEven()) return false;
i = 1;
while (i < lowprimes.length) {
var m = lowprimes[i], j = i + 1;
while (j < lowprimes.length && m < lplim) m *= lowprimes[j++];
m = x.modInt(m);
while (i < j) if (m % lowprimes[i++] === 0) return false;
}
return x.millerRabin(t);
}
//(protected) true if probably prime (HAC 4.24, Miller-Rabin)
function bnpMillerRabin(t) {
var n1 = this.subtract(BigInteger.ONE);
var k = n1.getLowestSetBit();
if (k <= 0) return false;
var r = n1.shiftRight(k);
t = (t + 1) >> 1;
if (t > lowprimes.length) t = lowprimes.length;
var a = nbi();
for (var i = 0; i < t; ++i) {
//Pick bases at random, instead of starting at 2
a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]);
var y = a.modPow(r, this);
if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
var j = 1;
while (j++ < k && y.compareTo(n1) != 0) {
y = y.modPowInt(2, this);
if (y.compareTo(BigInteger.ONE) === 0) return false;
}
if (y.compareTo(n1) != 0) return false;
}
}
return true;
}
// protected
BigInteger.prototype.copyTo = bnpCopyTo;
BigInteger.prototype.fromInt = bnpFromInt;
BigInteger.prototype.fromString = bnpFromString;
BigInteger.prototype.fromByteArray = bnpFromByteArray;
BigInteger.prototype.fromBuffer = bnpFromBuffer;
BigInteger.prototype.clamp = bnpClamp;
BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
BigInteger.prototype.drShiftTo = bnpDRShiftTo;
BigInteger.prototype.lShiftTo = bnpLShiftTo;
BigInteger.prototype.rShiftTo = bnpRShiftTo;
BigInteger.prototype.subTo = bnpSubTo;
BigInteger.prototype.multiplyTo = bnpMultiplyTo;
BigInteger.prototype.squareTo = bnpSquareTo;
BigInteger.prototype.divRemTo = bnpDivRemTo;
BigInteger.prototype.invDigit = bnpInvDigit;
BigInteger.prototype.isEven = bnpIsEven;
BigInteger.prototype.exp = bnpExp;
BigInteger.prototype.chunkSize = bnpChunkSize;
BigInteger.prototype.toRadix = bnpToRadix;
BigInteger.prototype.fromRadix = bnpFromRadix;
BigInteger.prototype.fromNumber = bnpFromNumber;
BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
BigInteger.prototype.changeBit = bnpChangeBit;
BigInteger.prototype.addTo = bnpAddTo;
BigInteger.prototype.dMultiply = bnpDMultiply;
BigInteger.prototype.dAddOffset = bnpDAddOffset;
BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
BigInteger.prototype.modInt = bnpModInt;
BigInteger.prototype.millerRabin = bnpMillerRabin;
// public
BigInteger.prototype.toString = bnToString;
BigInteger.prototype.negate = bnNegate;
BigInteger.prototype.abs = bnAbs;
BigInteger.prototype.compareTo = bnCompareTo;
BigInteger.prototype.bitLength = bnBitLength;
BigInteger.prototype.mod = bnMod;
BigInteger.prototype.modPowInt = bnModPowInt;
BigInteger.prototype.clone = bnClone;
BigInteger.prototype.intValue = bnIntValue;
BigInteger.prototype.byteValue = bnByteValue;
BigInteger.prototype.shortValue = bnShortValue;
BigInteger.prototype.signum = bnSigNum;
BigInteger.prototype.toByteArray = bnToByteArray;
BigInteger.prototype.toBuffer = bnToBuffer;
BigInteger.prototype.equals = bnEquals;
BigInteger.prototype.eq = bnEqual;
BigInteger.prototype.gt = bnGreater;
BigInteger.prototype.gte = bnGreaterOrEqual;
BigInteger.prototype.lt = bnLesser;
BigInteger.prototype.lte = bnLesserOrEqual;
BigInteger.prototype.min = bnMin;
BigInteger.prototype.max = bnMax;
BigInteger.prototype.and = bnAnd;
BigInteger.prototype.or = bnOr;
BigInteger.prototype.xor = bnXor;
BigInteger.prototype.andNot = bnAndNot;
BigInteger.prototype.not = bnNot;
BigInteger.prototype.shiftLeft = bnShiftLeft;
BigInteger.prototype.shiftRight = bnShiftRight;
BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
BigInteger.prototype.bitCount = bnBitCount;
BigInteger.prototype.testBit = bnTestBit;
BigInteger.prototype.setBit = bnSetBit;
BigInteger.prototype.clearBit = bnClearBit;
BigInteger.prototype.flipBit = bnFlipBit;
BigInteger.prototype.add = bnAdd;
BigInteger.prototype.subtract = bnSubtract;
BigInteger.prototype.multiply = bnMultiply;
BigInteger.prototype.divide = bnDivide;
BigInteger.prototype.remainder = bnRemainder;
BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
BigInteger.prototype.modPow = bnModPow;
BigInteger.prototype.modInverse = bnModInverse;
BigInteger.prototype.pow = bnPow;
BigInteger.prototype.gcd = bnGCD;
BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
BigInteger.int2char = int2char;
// "constants"
BigInteger.ZERO = nbv(0);
BigInteger.ONE = nbv(1);
// JSBN-specific extension
BigInteger.prototype.square = bnSquare;
//BigInteger interfaces not implemented in jsbn:
//BigInteger(int signum, byte[] magnitude)
//double doubleValue()
//float floatValue()
//int hashCode()
//long longValue()
//static BigInteger valueOf(long val)
module.exports = BigInteger;
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