(function () { // Copyright (c) 2005 Tom Wu // All Rights Reserved. // See "LICENSE" for details. // Basic JavaScript BN library - subset useful for RSA encryption. // Bits per digit var dbits; // JavaScript engine analysis var canary = 0xdeadbeefcafe; var j_lm = (canary & 0xffffff) == 0xefcafe; // (public) Constructor function BigInteger(a, b, c) { if (a != null) if ('number' == typeof a) this.fromNumber(a, b, c); else if (b == null && 'string' != typeof a) this.fromString(a, 256); 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; } var inBrowser = typeof navigator !== 'undefined'; if (inBrowser && j_lm && navigator.appName == 'Microsoft Internet Explorer') { BigInteger.prototype.am = am2; dbits = 30; } else if (inBrowser && j_lm && navigator.appName != 'Netscape') { BigInteger.prototype.am = am1; dbits = 26; } else { // Mozilla/Netscape seems to prefer am3 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 + this.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(s, b) { // Auto-detect string notations if (!b && s.length >= 2 && s[0] === '0') { var isDetected = true; switch (s[1]) { case 'x': // Hexadecimal notation b = 16; break; case 'b': // Binary notation b = 2; break; case 'o': // Octal notation b = 8; break; default: isDetected = false; } // Remove the notation string if any has been detected if (isDetected) { s = s.substr(2); } } var k; if (b == 16) k = 4; else if (b == 8) k = 3; else if (b == 256) k = 8; // byte array else if (b == 2) k = 1; else if (b == 32) k = 5; else if (b == 4) k = 2; else { this.fromRadix(s, b); return; } this.t = 0; this.s = 0; var i = s.length, mi = false, sh = 0; while (--i >= 0) { var x = k == 8 ? s[i] & 0xff : intAt(s, i); if (x < 0) { if (s.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 (k == 8 && (s[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); } // (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); } } 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; } // 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); } // protected BigInteger.prototype.copyTo = bnpCopyTo; BigInteger.prototype.fromInt = bnpFromInt; BigInteger.prototype.fromString = bnpFromString; 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; // 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; // "constants" BigInteger.ZERO = nbv(0); BigInteger.ONE = nbv(1); BigInteger.valueOf = nbv; // 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, c) { if ('number' == typeof b) { // new BigInteger(int,int,RNG) if (a < 2) this.fromInt(1); else { this.fromNumber(a, c); 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 = new Array(), t = a & 7; x.length = (a >> 3) + 1; b.nextBytes(x); if (t > 0) x[0] &= (1 << t) - 1; else x[0] = 0; this.fromString(x, 256); } } // (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; } 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<>= 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.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.clone = bnClone; BigInteger.prototype.intValue = bnIntValue; BigInteger.prototype.byteValue = bnByteValue; BigInteger.prototype.shortValue = bnShortValue; BigInteger.prototype.signum = bnSigNum; BigInteger.prototype.toByteArray = bnToByteArray; BigInteger.prototype.equals = bnEquals; 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; // JSBN-specific extension BigInteger.prototype.square = bnSquare; // Expose the Barrett function BigInteger.prototype.Barrett = Barrett; // BigInteger interfaces not implemented in jsbn: // BigInteger(int signum, byte[] magnitude) // double doubleValue() // float floatValue() // int hashCode() // long longValue() // static BigInteger valueOf(long val) // Imported from bitcoinjs-lib /** * Turns a byte array into a big integer. * * This function will interpret a byte array as a big integer in big * endian notation and ignore leading zeros. */ BigInteger.fromByteArrayUnsigned = function (ba) { if (!ba.length) { return new BigInteger.valueOf(0); } else if (ba[0] & 0x80) { // Prepend a zero so the BigInteger class doesn't mistake this // for a negative integer. return new BigInteger([0].concat(ba)); } else { return new BigInteger(ba); } }; /** * Parse a signed big integer byte representation. * * For details on the format please see BigInteger.toByteArraySigned. */ BigInteger.fromByteArraySigned = function (ba) { // Check for negative value if (ba[0] & 0x80) { // Remove sign bit ba[0] &= 0x7f; return BigInteger.fromByteArrayUnsigned(ba).negate(); } else { return BigInteger.fromByteArrayUnsigned(ba); } }; /** * Returns a byte array representation of the big integer. * * This returns the absolute of the contained value in big endian * form. A value of zero results in an empty array. */ BigInteger.prototype.toByteArrayUnsigned = function () { var ba = this.abs().toByteArray(); // Empty array, nothing to do if (!ba.length) { return ba; } // remove leading 0 if (ba[0] === 0) { ba = ba.slice(1); } // all values must be positive for (var i = 0; i < ba.length; ++i) { ba[i] = (ba[i] < 0) ? ba[i] + 256 : ba[i]; } return ba; }; /* * Converts big integer to signed byte representation. * * The format for this value uses the most significant bit as a sign * bit. If the most significant bit is already occupied by the * absolute value, an extra byte is prepended and the sign bit is set * there. * * Examples: * * 0 => 0x00 * 1 => 0x01 * -1 => 0x81 * 127 => 0x7f * -127 => 0xff * 128 => 0x0080 * -128 => 0x8080 * 255 => 0x00ff * -255 => 0x80ff * 16300 => 0x3fac * -16300 => 0xbfac * 62300 => 0x00f35c * -62300 => 0x80f35c */ BigInteger.prototype.toByteArraySigned = function () { var val = this.toByteArrayUnsigned(); var neg = this.s < 0; // if the first bit is set, we always unshift // either unshift 0x80 or 0x00 if (val[0] & 0x80) { val.unshift((neg) ? 0x80 : 0x00); } // if the first bit isn't set, set it if negative else if (neg) { val[0] |= 0x80; } return val; }; // Random number generator - requires a PRNG backend, e.g. prng4.js // For best results, put code like // // in your main HTML document. var rng_state; var rng_pool; var rng_pptr; // Mix in a 32-bit integer into the pool function rng_seed_int(x) { rng_pool[rng_pptr++] ^= x & 255; rng_pool[rng_pptr++] ^= (x >> 8) & 255; rng_pool[rng_pptr++] ^= (x >> 16) & 255; rng_pool[rng_pptr++] ^= (x >> 24) & 255; if (rng_pptr >= rng_psize) rng_pptr -= rng_psize; } // Mix in the current time (w/milliseconds) into the pool function rng_seed_time() { rng_seed_int(new Date().getTime()); } // Initialize the pool with junk if needed. if (rng_pool == null) { rng_pool = new Array(); rng_pptr = 0; var t; if (typeof window !== 'undefined' && window.crypto) { if (window.crypto.getRandomValues) { // Use webcrypto if available var ua = new Uint8Array(32); window.crypto.getRandomValues(ua); for (t = 0; t < 32; ++t) rng_pool[rng_pptr++] = ua[t]; } else if ( navigator.appName == 'Netscape' && navigator.appVersion < '5' ) { // Extract entropy (256 bits) from NS4 RNG if available var z = window.crypto.random(32); for (t = 0; t < z.length; ++t) rng_pool[rng_pptr++] = z.charCodeAt(t) & 255; } } while (rng_pptr < rng_psize) { // extract some randomness from Math.random() t = Math.floor(65536 * Math.random()); rng_pool[rng_pptr++] = t >>> 8; rng_pool[rng_pptr++] = t & 255; } rng_pptr = 0; rng_seed_time(); } function rng_get_byte() { if (rng_state == null) { rng_seed_time(); rng_state = prng_newstate(); rng_state.init(rng_pool); for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr) rng_pool[rng_pptr] = 0; rng_pptr = 0; } // TODO: allow reseeding after first request return rng_state.next(); } function rng_get_bytes(ba) { var i; for (i = 0; i < ba.length; ++i) ba[i] = rng_get_byte(); } function SecureRandom() { } SecureRandom.prototype.nextBytes = rng_get_bytes; // prng4.js - uses Arcfour as a PRNG function Arcfour() { this.i = 0; this.j = 0; this.S = new Array(); } // Initialize arcfour context from key, an array of ints, each from [0..255] function ARC4init(key) { var i, j, t; for (i = 0; i < 256; ++i) this.S[i] = i; j = 0; for (i = 0; i < 256; ++i) { j = (j + this.S[i] + key[i % key.length]) & 255; t = this.S[i]; this.S[i] = this.S[j]; this.S[j] = t; } this.i = 0; this.j = 0; } function ARC4next() { var t; this.i = (this.i + 1) & 255; this.j = (this.j + this.S[this.i]) & 255; t = this.S[this.i]; this.S[this.i] = this.S[this.j]; this.S[this.j] = t; return this.S[(t + this.S[this.i]) & 255]; } Arcfour.prototype.init = ARC4init; Arcfour.prototype.next = ARC4next; // Plug in your RNG constructor here function prng_newstate() { return new Arcfour(); } // Pool size must be a multiple of 4 and greater than 32. // An array of bytes the size of the pool will be passed to init() var rng_psize = 256; if (typeof exports !== 'undefined') { exports = module.exports = { default: BigInteger, BigInteger: BigInteger, SecureRandom: SecureRandom, }; } else { this.jsbn = { BigInteger: BigInteger, SecureRandom: SecureRandom, }; } }.call(this));