- BN.prototype.copy = function copy (dest) {
- dest.words = new Array(this.length);
- for (var i = 0; i < this.length; i++) {
- dest.words[i] = this.words[i];
- }
- dest.length = this.length;
- dest.negative = this.negative;
- dest.red = this.red;
- };
-
- BN.prototype.clone = function clone () {
- var r = new BN(null);
- this.copy(r);
- return r;
- };
-
- BN.prototype._expand = function _expand (size) {
- while (this.length < size) {
- this.words[this.length++] = 0;
- }
- return this;
- };
-
- // Remove leading `0` from `this`
- BN.prototype.strip = function strip () {
- while (this.length > 1 && this.words[this.length - 1] === 0) {
- this.length--;
- }
- return this._normSign();
- };
-
- BN.prototype._normSign = function _normSign () {
- // -0 = 0
- if (this.length === 1 && this.words[0] === 0) {
- this.negative = 0;
- }
- return this;
- };
-
- BN.prototype.inspect = function inspect () {
- return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>';
- };
-
- /*
-
- var zeros = [];
- var groupSizes = [];
- var groupBases = [];
-
- var s = '';
- var i = -1;
- while (++i < BN.wordSize) {
- zeros[i] = s;
- s += '0';
- }
- groupSizes[0] = 0;
- groupSizes[1] = 0;
- groupBases[0] = 0;
- groupBases[1] = 0;
- var base = 2 - 1;
- while (++base < 36 + 1) {
- var groupSize = 0;
- var groupBase = 1;
- while (groupBase < (1 << BN.wordSize) / base) {
- groupBase *= base;
- groupSize += 1;
- }
- groupSizes[base] = groupSize;
- groupBases[base] = groupBase;
- }
-
- */
-
- var zeros = [
- '',
- '0',
- '00',
- '000',
- '0000',
- '00000',
- '000000',
- '0000000',
- '00000000',
- '000000000',
- '0000000000',
- '00000000000',
- '000000000000',
- '0000000000000',
- '00000000000000',
- '000000000000000',
- '0000000000000000',
- '00000000000000000',
- '000000000000000000',
- '0000000000000000000',
- '00000000000000000000',
- '000000000000000000000',
- '0000000000000000000000',
- '00000000000000000000000',
- '000000000000000000000000',
- '0000000000000000000000000'
- ];
-
- var groupSizes = [
- 0, 0,
- 25, 16, 12, 11, 10, 9, 8,
- 8, 7, 7, 7, 7, 6, 6,
- 6, 6, 6, 6, 6, 5, 5,
- 5, 5, 5, 5, 5, 5, 5,
- 5, 5, 5, 5, 5, 5, 5
- ];
-
- var groupBases = [
- 0, 0,
- 33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216,
- 43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625,
- 16777216, 24137569, 34012224, 47045881, 64000000, 4084101, 5153632,
- 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149,
- 24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176
- ];
-
- BN.prototype.toString = function toString (base, padding) {
- base = base || 10;
- padding = padding | 0 || 1;
-
- var out;
- if (base === 16 || base === 'hex') {
- out = '';
- var off = 0;
- var carry = 0;
- for (var i = 0; i < this.length; i++) {
- var w = this.words[i];
- var word = (((w << off) | carry) & 0xffffff).toString(16);
- carry = (w >>> (24 - off)) & 0xffffff;
- if (carry !== 0 || i !== this.length - 1) {
- out = zeros[6 - word.length] + word + out;
- } else {
- out = word + out;
- }
- off += 2;
- if (off >= 26) {
- off -= 26;
- i--;
- }
- }
- if (carry !== 0) {
- out = carry.toString(16) + out;
- }
- while (out.length % padding !== 0) {
- out = '0' + out;
- }
- if (this.negative !== 0) {
- out = '-' + out;
- }
- return out;
- }
-
- if (base === (base | 0) && base >= 2 && base <= 36) {
- // var groupSize = Math.floor(BN.wordSize * Math.LN2 / Math.log(base));
- var groupSize = groupSizes[base];
- // var groupBase = Math.pow(base, groupSize);
- var groupBase = groupBases[base];
- out = '';
- var c = this.clone();
- c.negative = 0;
- while (!c.isZero()) {
- var r = c.modn(groupBase).toString(base);
- c = c.idivn(groupBase);
-
- if (!c.isZero()) {
- out = zeros[groupSize - r.length] + r + out;
- } else {
- out = r + out;
- }
- }
- if (this.isZero()) {
- out = '0' + out;
- }
- while (out.length % padding !== 0) {
- out = '0' + out;
- }
- if (this.negative !== 0) {
- out = '-' + out;
- }
- return out;
- }
-
- assert(false, 'Base should be between 2 and 36');
- };
-
- BN.prototype.toNumber = function toNumber () {
- var ret = this.words[0];
- if (this.length === 2) {
- ret += this.words[1] * 0x4000000;
- } else if (this.length === 3 && this.words[2] === 0x01) {
- // NOTE: at this stage it is known that the top bit is set
- ret += 0x10000000000000 + (this.words[1] * 0x4000000);
- } else if (this.length > 2) {
- assert(false, 'Number can only safely store up to 53 bits');
- }
- return (this.negative !== 0) ? -ret : ret;
- };
-
- BN.prototype.toJSON = function toJSON () {
- return this.toString(16);
- };
-
- BN.prototype.toBuffer = function toBuffer (endian, length) {
- assert(typeof Buffer !== 'undefined');
- return this.toArrayLike(Buffer, endian, length);
- };
-
- BN.prototype.toArray = function toArray (endian, length) {
- return this.toArrayLike(Array, endian, length);
- };
-
- BN.prototype.toArrayLike = function toArrayLike (ArrayType, endian, length) {
- var byteLength = this.byteLength();
- var reqLength = length || Math.max(1, byteLength);
- assert(byteLength <= reqLength, 'byte array longer than desired length');
- assert(reqLength > 0, 'Requested array length <= 0');
-
- this.strip();
- var littleEndian = endian === 'le';
- var res = new ArrayType(reqLength);
-
- var b, i;
- var q = this.clone();
- if (!littleEndian) {
- // Assume big-endian
- for (i = 0; i < reqLength - byteLength; i++) {
- res[i] = 0;
- }
-
- for (i = 0; !q.isZero(); i++) {
- b = q.andln(0xff);
- q.iushrn(8);
-
- res[reqLength - i - 1] = b;
- }
- } else {
- for (i = 0; !q.isZero(); i++) {
- b = q.andln(0xff);
- q.iushrn(8);
-
- res[i] = b;
- }
-
- for (; i < reqLength; i++) {
- res[i] = 0;
- }
- }
-
- return res;
- };
-
- if (Math.clz32) {
- BN.prototype._countBits = function _countBits (w) {
- return 32 - Math.clz32(w);
- };
- } else {
- BN.prototype._countBits = function _countBits (w) {
- var t = w;
- var r = 0;
- if (t >= 0x1000) {
- r += 13;
- t >>>= 13;
- }
- if (t >= 0x40) {
- r += 7;
- t >>>= 7;
- }
- if (t >= 0x8) {
- r += 4;
- t >>>= 4;
- }
- if (t >= 0x02) {
- r += 2;
- t >>>= 2;
- }
- return r + t;
- };
- }
-
- BN.prototype._zeroBits = function _zeroBits (w) {
- // Short-cut
- if (w === 0) return 26;
-
- var t = w;
- var r = 0;
- if ((t & 0x1fff) === 0) {
- r += 13;
- t >>>= 13;
- }
- if ((t & 0x7f) === 0) {
- r += 7;
- t >>>= 7;
- }
- if ((t & 0xf) === 0) {
- r += 4;
- t >>>= 4;
- }
- if ((t & 0x3) === 0) {
- r += 2;
- t >>>= 2;
- }
- if ((t & 0x1) === 0) {
- r++;
- }
- return r;
- };
-
- // Return number of used bits in a BN
- BN.prototype.bitLength = function bitLength () {
- var w = this.words[this.length - 1];
- var hi = this._countBits(w);
- return (this.length - 1) * 26 + hi;
- };
-
- function toBitArray (num) {
- var w = new Array(num.bitLength());
-
- for (var bit = 0; bit < w.length; bit++) {
- var off = (bit / 26) | 0;
- var wbit = bit % 26;
-
- w[bit] = (num.words[off] & (1 << wbit)) >>> wbit;
- }
-
- return w;
- }
-
- // Number of trailing zero bits
- BN.prototype.zeroBits = function zeroBits () {
- if (this.isZero()) return 0;
-
- var r = 0;
- for (var i = 0; i < this.length; i++) {
- var b = this._zeroBits(this.words[i]);
- r += b;
- if (b !== 26) break;
- }
- return r;
- };
-
- BN.prototype.byteLength = function byteLength () {
- return Math.ceil(this.bitLength() / 8);
- };
-
- BN.prototype.toTwos = function toTwos (width) {
- if (this.negative !== 0) {
- return this.abs().inotn(width).iaddn(1);
- }
- return this.clone();
- };
-
- BN.prototype.fromTwos = function fromTwos (width) {
- if (this.testn(width - 1)) {
- return this.notn(width).iaddn(1).ineg();
- }
- return this.clone();
- };
-
- BN.prototype.isNeg = function isNeg () {
- return this.negative !== 0;
- };
-
- // Return negative clone of `this`
- BN.prototype.neg = function neg () {
- return this.clone().ineg();
- };
-
- BN.prototype.ineg = function ineg () {
- if (!this.isZero()) {
- this.negative ^= 1;
- }
-
- return this;
- };
-
- // Or `num` with `this` in-place
- BN.prototype.iuor = function iuor (num) {
- while (this.length < num.length) {
- this.words[this.length++] = 0;
- }
-
- for (var i = 0; i < num.length; i++) {
- this.words[i] = this.words[i] | num.words[i];
- }
-
- return this.strip();
- };
-
- BN.prototype.ior = function ior (num) {
- assert((this.negative | num.negative) === 0);
- return this.iuor(num);
- };
-
- // Or `num` with `this`
- BN.prototype.or = function or (num) {
- if (this.length > num.length) return this.clone().ior(num);
- return num.clone().ior(this);
- };
-
- BN.prototype.uor = function uor (num) {
- if (this.length > num.length) return this.clone().iuor(num);
- return num.clone().iuor(this);
- };
-
- // And `num` with `this` in-place
- BN.prototype.iuand = function iuand (num) {
- // b = min-length(num, this)
- var b;
- if (this.length > num.length) {
- b = num;
- } else {
- b = this;
- }
-
- for (var i = 0; i < b.length; i++) {
- this.words[i] = this.words[i] & num.words[i];
- }
-
- this.length = b.length;
-
- return this.strip();
- };
-
- BN.prototype.iand = function iand (num) {
- assert((this.negative | num.negative) === 0);
- return this.iuand(num);
- };
-
- // And `num` with `this`
- BN.prototype.and = function and (num) {
- if (this.length > num.length) return this.clone().iand(num);
- return num.clone().iand(this);
- };
-
- BN.prototype.uand = function uand (num) {
- if (this.length > num.length) return this.clone().iuand(num);
- return num.clone().iuand(this);
- };
-
- // Xor `num` with `this` in-place
- BN.prototype.iuxor = function iuxor (num) {
- // a.length > b.length
- var a;
- var b;
- if (this.length > num.length) {
- a = this;
- b = num;
- } else {
- a = num;
- b = this;
- }
-
- for (var i = 0; i < b.length; i++) {
- this.words[i] = a.words[i] ^ b.words[i];
- }
-
- if (this !== a) {
- for (; i < a.length; i++) {
- this.words[i] = a.words[i];
- }
- }
-
- this.length = a.length;
-
- return this.strip();
- };
-
- BN.prototype.ixor = function ixor (num) {
- assert((this.negative | num.negative) === 0);
- return this.iuxor(num);
- };
-
- // Xor `num` with `this`
- BN.prototype.xor = function xor (num) {
- if (this.length > num.length) return this.clone().ixor(num);
- return num.clone().ixor(this);
- };
-
- BN.prototype.uxor = function uxor (num) {
- if (this.length > num.length) return this.clone().iuxor(num);
- return num.clone().iuxor(this);
- };
-
- // Not ``this`` with ``width`` bitwidth
- BN.prototype.inotn = function inotn (width) {
- assert(typeof width === 'number' && width >= 0);
-
- var bytesNeeded = Math.ceil(width / 26) | 0;
- var bitsLeft = width % 26;
-
- // Extend the buffer with leading zeroes
- this._expand(bytesNeeded);
-
- if (bitsLeft > 0) {
- bytesNeeded--;
- }
-
- // Handle complete words
- for (var i = 0; i < bytesNeeded; i++) {
- this.words[i] = ~this.words[i] & 0x3ffffff;
- }
-
- // Handle the residue
- if (bitsLeft > 0) {
- this.words[i] = ~this.words[i] & (0x3ffffff >> (26 - bitsLeft));
- }
-
- // And remove leading zeroes
- return this.strip();
- };
-
- BN.prototype.notn = function notn (width) {
- return this.clone().inotn(width);
- };
-
- // Set `bit` of `this`
- BN.prototype.setn = function setn (bit, val) {
- assert(typeof bit === 'number' && bit >= 0);
-
- var off = (bit / 26) | 0;
- var wbit = bit % 26;
-
- this._expand(off + 1);
-
- if (val) {
- this.words[off] = this.words[off] | (1 << wbit);
- } else {
- this.words[off] = this.words[off] & ~(1 << wbit);
- }
-
- return this.strip();
- };
-
- // Add `num` to `this` in-place
- BN.prototype.iadd = function iadd (num) {
- var r;
-
- // negative + positive
- if (this.negative !== 0 && num.negative === 0) {
- this.negative = 0;
- r = this.isub(num);
- this.negative ^= 1;
- return this._normSign();
-
- // positive + negative
- } else if (this.negative === 0 && num.negative !== 0) {
- num.negative = 0;
- r = this.isub(num);
- num.negative = 1;
- return r._normSign();
- }
-
- // a.length > b.length
- var a, b;
- if (this.length > num.length) {
- a = this;
- b = num;
- } else {
- a = num;
- b = this;
- }
-
- var carry = 0;
- for (var i = 0; i < b.length; i++) {
- r = (a.words[i] | 0) + (b.words[i] | 0) + carry;
- this.words[i] = r & 0x3ffffff;
- carry = r >>> 26;
- }
- for (; carry !== 0 && i < a.length; i++) {
- r = (a.words[i] | 0) + carry;
- this.words[i] = r & 0x3ffffff;
- carry = r >>> 26;
- }
-
- this.length = a.length;
- if (carry !== 0) {
- this.words[this.length] = carry;
- this.length++;
- // Copy the rest of the words
- } else if (a !== this) {
- for (; i < a.length; i++) {
- this.words[i] = a.words[i];
- }
- }
-
- return this;
- };
-
- // Add `num` to `this`
- BN.prototype.add = function add (num) {
- var res;
- if (num.negative !== 0 && this.negative === 0) {
- num.negative = 0;
- res = this.sub(num);
- num.negative ^= 1;
- return res;
- } else if (num.negative === 0 && this.negative !== 0) {
- this.negative = 0;
- res = num.sub(this);
- this.negative = 1;
- return res;
- }
-
- if (this.length > num.length) return this.clone().iadd(num);
-
- return num.clone().iadd(this);
- };
-
- // Subtract `num` from `this` in-place
- BN.prototype.isub = function isub (num) {
- // this - (-num) = this + num
- if (num.negative !== 0) {
- num.negative = 0;
- var r = this.iadd(num);
- num.negative = 1;
- return r._normSign();
-
- // -this - num = -(this + num)
- } else if (this.negative !== 0) {
- this.negative = 0;
- this.iadd(num);
- this.negative = 1;
- return this._normSign();
- }
-
- // At this point both numbers are positive
- var cmp = this.cmp(num);
-
- // Optimization - zeroify
- if (cmp === 0) {
- this.negative = 0;
- this.length = 1;
- this.words[0] = 0;
- return this;
- }
-
- // a > b
- var a, b;
- if (cmp > 0) {
- a = this;
- b = num;
- } else {
- a = num;
- b = this;
- }
-
- var carry = 0;
- for (var i = 0; i < b.length; i++) {
- r = (a.words[i] | 0) - (b.words[i] | 0) + carry;
- carry = r >> 26;
- this.words[i] = r & 0x3ffffff;
- }
- for (; carry !== 0 && i < a.length; i++) {
- r = (a.words[i] | 0) + carry;
- carry = r >> 26;
- this.words[i] = r & 0x3ffffff;
- }
-
- // Copy rest of the words
- if (carry === 0 && i < a.length && a !== this) {
- for (; i < a.length; i++) {
- this.words[i] = a.words[i];
- }
- }
-
- this.length = Math.max(this.length, i);
-
- if (a !== this) {
- this.negative = 1;
- }
-
- return this.strip();
- };
-
- // Subtract `num` from `this`
- BN.prototype.sub = function sub (num) {
- return this.clone().isub(num);
- };
-
- function smallMulTo (self, num, out) {
- out.negative = num.negative ^ self.negative;
- var len = (self.length + num.length) | 0;
- out.length = len;
- len = (len - 1) | 0;
-
- // Peel one iteration (compiler can't do it, because of code complexity)
- var a = self.words[0] | 0;
- var b = num.words[0] | 0;
- var r = a * b;
-
- var lo = r & 0x3ffffff;
- var carry = (r / 0x4000000) | 0;
- out.words[0] = lo;
-
- for (var k = 1; k < len; k++) {
- // Sum all words with the same `i + j = k` and accumulate `ncarry`,
- // note that ncarry could be >= 0x3ffffff
- var ncarry = carry >>> 26;
- var rword = carry & 0x3ffffff;
- var maxJ = Math.min(k, num.length - 1);
- for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
- var i = (k - j) | 0;
- a = self.words[i] | 0;
- b = num.words[j] | 0;
- r = a * b + rword;
- ncarry += (r / 0x4000000) | 0;
- rword = r & 0x3ffffff;
- }
- out.words[k] = rword | 0;
- carry = ncarry | 0;
- }
- if (carry !== 0) {
- out.words[k] = carry | 0;
- } else {
- out.length--;
- }
-
- return out.strip();
- }
-
- // TODO(indutny): it may be reasonable to omit it for users who don't need
- // to work with 256-bit numbers, otherwise it gives 20% improvement for 256-bit
- // multiplication (like elliptic secp256k1).
- var comb10MulTo = function comb10MulTo (self, num, out) {
- var a = self.words;
- var b = num.words;
- var o = out.words;
- var c = 0;
- var lo;
- var mid;
- var hi;
- var a0 = a[0] | 0;
- var al0 = a0 & 0x1fff;
- var ah0 = a0 >>> 13;
- var a1 = a[1] | 0;
- var al1 = a1 & 0x1fff;
- var ah1 = a1 >>> 13;
- var a2 = a[2] | 0;
- var al2 = a2 & 0x1fff;
- var ah2 = a2 >>> 13;
- var a3 = a[3] | 0;
- var al3 = a3 & 0x1fff;
- var ah3 = a3 >>> 13;
- var a4 = a[4] | 0;
- var al4 = a4 & 0x1fff;
- var ah4 = a4 >>> 13;
- var a5 = a[5] | 0;
- var al5 = a5 & 0x1fff;
- var ah5 = a5 >>> 13;
- var a6 = a[6] | 0;
- var al6 = a6 & 0x1fff;
- var ah6 = a6 >>> 13;
- var a7 = a[7] | 0;
- var al7 = a7 & 0x1fff;
- var ah7 = a7 >>> 13;
- var a8 = a[8] | 0;
- var al8 = a8 & 0x1fff;
- var ah8 = a8 >>> 13;
- var a9 = a[9] | 0;
- var al9 = a9 & 0x1fff;
- var ah9 = a9 >>> 13;
- var b0 = b[0] | 0;
- var bl0 = b0 & 0x1fff;
- var bh0 = b0 >>> 13;
- var b1 = b[1] | 0;
- var bl1 = b1 & 0x1fff;
- var bh1 = b1 >>> 13;
- var b2 = b[2] | 0;
- var bl2 = b2 & 0x1fff;
- var bh2 = b2 >>> 13;
- var b3 = b[3] | 0;
- var bl3 = b3 & 0x1fff;
- var bh3 = b3 >>> 13;
- var b4 = b[4] | 0;
- var bl4 = b4 & 0x1fff;
- var bh4 = b4 >>> 13;
- var b5 = b[5] | 0;
- var bl5 = b5 & 0x1fff;
- var bh5 = b5 >>> 13;
- var b6 = b[6] | 0;
- var bl6 = b6 & 0x1fff;
- var bh6 = b6 >>> 13;
- var b7 = b[7] | 0;
- var bl7 = b7 & 0x1fff;
- var bh7 = b7 >>> 13;
- var b8 = b[8] | 0;
- var bl8 = b8 & 0x1fff;
- var bh8 = b8 >>> 13;
- var b9 = b[9] | 0;
- var bl9 = b9 & 0x1fff;
- var bh9 = b9 >>> 13;
-
- out.negative = self.negative ^ num.negative;
- out.length = 19;
- /* k = 0 */
- lo = Math.imul(al0, bl0);
- mid = Math.imul(al0, bh0);
- mid = (mid + Math.imul(ah0, bl0)) | 0;
- hi = Math.imul(ah0, bh0);
- var w0 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w0 >>> 26)) | 0;
- w0 &= 0x3ffffff;
- /* k = 1 */
- lo = Math.imul(al1, bl0);
- mid = Math.imul(al1, bh0);
- mid = (mid + Math.imul(ah1, bl0)) | 0;
- hi = Math.imul(ah1, bh0);
- lo = (lo + Math.imul(al0, bl1)) | 0;
- mid = (mid + Math.imul(al0, bh1)) | 0;
- mid = (mid + Math.imul(ah0, bl1)) | 0;
- hi = (hi + Math.imul(ah0, bh1)) | 0;
- var w1 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w1 >>> 26)) | 0;
- w1 &= 0x3ffffff;
- /* k = 2 */
- lo = Math.imul(al2, bl0);
- mid = Math.imul(al2, bh0);
- mid = (mid + Math.imul(ah2, bl0)) | 0;
- hi = Math.imul(ah2, bh0);
- lo = (lo + Math.imul(al1, bl1)) | 0;
- mid = (mid + Math.imul(al1, bh1)) | 0;
- mid = (mid + Math.imul(ah1, bl1)) | 0;
- hi = (hi + Math.imul(ah1, bh1)) | 0;
- lo = (lo + Math.imul(al0, bl2)) | 0;
- mid = (mid + Math.imul(al0, bh2)) | 0;
- mid = (mid + Math.imul(ah0, bl2)) | 0;
- hi = (hi + Math.imul(ah0, bh2)) | 0;
- var w2 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w2 >>> 26)) | 0;
- w2 &= 0x3ffffff;
- /* k = 3 */
- lo = Math.imul(al3, bl0);
- mid = Math.imul(al3, bh0);
- mid = (mid + Math.imul(ah3, bl0)) | 0;
- hi = Math.imul(ah3, bh0);
- lo = (lo + Math.imul(al2, bl1)) | 0;
- mid = (mid + Math.imul(al2, bh1)) | 0;
- mid = (mid + Math.imul(ah2, bl1)) | 0;
- hi = (hi + Math.imul(ah2, bh1)) | 0;
- lo = (lo + Math.imul(al1, bl2)) | 0;
- mid = (mid + Math.imul(al1, bh2)) | 0;
- mid = (mid + Math.imul(ah1, bl2)) | 0;
- hi = (hi + Math.imul(ah1, bh2)) | 0;
- lo = (lo + Math.imul(al0, bl3)) | 0;
- mid = (mid + Math.imul(al0, bh3)) | 0;
- mid = (mid + Math.imul(ah0, bl3)) | 0;
- hi = (hi + Math.imul(ah0, bh3)) | 0;
- var w3 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w3 >>> 26)) | 0;
- w3 &= 0x3ffffff;
- /* k = 4 */
- lo = Math.imul(al4, bl0);
- mid = Math.imul(al4, bh0);
- mid = (mid + Math.imul(ah4, bl0)) | 0;
- hi = Math.imul(ah4, bh0);
- lo = (lo + Math.imul(al3, bl1)) | 0;
- mid = (mid + Math.imul(al3, bh1)) | 0;
- mid = (mid + Math.imul(ah3, bl1)) | 0;
- hi = (hi + Math.imul(ah3, bh1)) | 0;
- lo = (lo + Math.imul(al2, bl2)) | 0;
- mid = (mid + Math.imul(al2, bh2)) | 0;
- mid = (mid + Math.imul(ah2, bl2)) | 0;
- hi = (hi + Math.imul(ah2, bh2)) | 0;
- lo = (lo + Math.imul(al1, bl3)) | 0;
- mid = (mid + Math.imul(al1, bh3)) | 0;
- mid = (mid + Math.imul(ah1, bl3)) | 0;
- hi = (hi + Math.imul(ah1, bh3)) | 0;
- lo = (lo + Math.imul(al0, bl4)) | 0;
- mid = (mid + Math.imul(al0, bh4)) | 0;
- mid = (mid + Math.imul(ah0, bl4)) | 0;
- hi = (hi + Math.imul(ah0, bh4)) | 0;
- var w4 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w4 >>> 26)) | 0;
- w4 &= 0x3ffffff;
- /* k = 5 */
- lo = Math.imul(al5, bl0);
- mid = Math.imul(al5, bh0);
- mid = (mid + Math.imul(ah5, bl0)) | 0;
- hi = Math.imul(ah5, bh0);
- lo = (lo + Math.imul(al4, bl1)) | 0;
- mid = (mid + Math.imul(al4, bh1)) | 0;
- mid = (mid + Math.imul(ah4, bl1)) | 0;
- hi = (hi + Math.imul(ah4, bh1)) | 0;
- lo = (lo + Math.imul(al3, bl2)) | 0;
- mid = (mid + Math.imul(al3, bh2)) | 0;
- mid = (mid + Math.imul(ah3, bl2)) | 0;
- hi = (hi + Math.imul(ah3, bh2)) | 0;
- lo = (lo + Math.imul(al2, bl3)) | 0;
- mid = (mid + Math.imul(al2, bh3)) | 0;
- mid = (mid + Math.imul(ah2, bl3)) | 0;
- hi = (hi + Math.imul(ah2, bh3)) | 0;
- lo = (lo + Math.imul(al1, bl4)) | 0;
- mid = (mid + Math.imul(al1, bh4)) | 0;
- mid = (mid + Math.imul(ah1, bl4)) | 0;
- hi = (hi + Math.imul(ah1, bh4)) | 0;
- lo = (lo + Math.imul(al0, bl5)) | 0;
- mid = (mid + Math.imul(al0, bh5)) | 0;
- mid = (mid + Math.imul(ah0, bl5)) | 0;
- hi = (hi + Math.imul(ah0, bh5)) | 0;
- var w5 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w5 >>> 26)) | 0;
- w5 &= 0x3ffffff;
- /* k = 6 */
- lo = Math.imul(al6, bl0);
- mid = Math.imul(al6, bh0);
- mid = (mid + Math.imul(ah6, bl0)) | 0;
- hi = Math.imul(ah6, bh0);
- lo = (lo + Math.imul(al5, bl1)) | 0;
- mid = (mid + Math.imul(al5, bh1)) | 0;
- mid = (mid + Math.imul(ah5, bl1)) | 0;
- hi = (hi + Math.imul(ah5, bh1)) | 0;
- lo = (lo + Math.imul(al4, bl2)) | 0;
- mid = (mid + Math.imul(al4, bh2)) | 0;
- mid = (mid + Math.imul(ah4, bl2)) | 0;
- hi = (hi + Math.imul(ah4, bh2)) | 0;
- lo = (lo + Math.imul(al3, bl3)) | 0;
- mid = (mid + Math.imul(al3, bh3)) | 0;
- mid = (mid + Math.imul(ah3, bl3)) | 0;
- hi = (hi + Math.imul(ah3, bh3)) | 0;
- lo = (lo + Math.imul(al2, bl4)) | 0;
- mid = (mid + Math.imul(al2, bh4)) | 0;
- mid = (mid + Math.imul(ah2, bl4)) | 0;
- hi = (hi + Math.imul(ah2, bh4)) | 0;
- lo = (lo + Math.imul(al1, bl5)) | 0;
- mid = (mid + Math.imul(al1, bh5)) | 0;
- mid = (mid + Math.imul(ah1, bl5)) | 0;
- hi = (hi + Math.imul(ah1, bh5)) | 0;
- lo = (lo + Math.imul(al0, bl6)) | 0;
- mid = (mid + Math.imul(al0, bh6)) | 0;
- mid = (mid + Math.imul(ah0, bl6)) | 0;
- hi = (hi + Math.imul(ah0, bh6)) | 0;
- var w6 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w6 >>> 26)) | 0;
- w6 &= 0x3ffffff;
- /* k = 7 */
- lo = Math.imul(al7, bl0);
- mid = Math.imul(al7, bh0);
- mid = (mid + Math.imul(ah7, bl0)) | 0;
- hi = Math.imul(ah7, bh0);
- lo = (lo + Math.imul(al6, bl1)) | 0;
- mid = (mid + Math.imul(al6, bh1)) | 0;
- mid = (mid + Math.imul(ah6, bl1)) | 0;
- hi = (hi + Math.imul(ah6, bh1)) | 0;
- lo = (lo + Math.imul(al5, bl2)) | 0;
- mid = (mid + Math.imul(al5, bh2)) | 0;
- mid = (mid + Math.imul(ah5, bl2)) | 0;
- hi = (hi + Math.imul(ah5, bh2)) | 0;
- lo = (lo + Math.imul(al4, bl3)) | 0;
- mid = (mid + Math.imul(al4, bh3)) | 0;
- mid = (mid + Math.imul(ah4, bl3)) | 0;
- hi = (hi + Math.imul(ah4, bh3)) | 0;
- lo = (lo + Math.imul(al3, bl4)) | 0;
- mid = (mid + Math.imul(al3, bh4)) | 0;
- mid = (mid + Math.imul(ah3, bl4)) | 0;
- hi = (hi + Math.imul(ah3, bh4)) | 0;
- lo = (lo + Math.imul(al2, bl5)) | 0;
- mid = (mid + Math.imul(al2, bh5)) | 0;
- mid = (mid + Math.imul(ah2, bl5)) | 0;
- hi = (hi + Math.imul(ah2, bh5)) | 0;
- lo = (lo + Math.imul(al1, bl6)) | 0;
- mid = (mid + Math.imul(al1, bh6)) | 0;
- mid = (mid + Math.imul(ah1, bl6)) | 0;
- hi = (hi + Math.imul(ah1, bh6)) | 0;
- lo = (lo + Math.imul(al0, bl7)) | 0;
- mid = (mid + Math.imul(al0, bh7)) | 0;
- mid = (mid + Math.imul(ah0, bl7)) | 0;
- hi = (hi + Math.imul(ah0, bh7)) | 0;
- var w7 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w7 >>> 26)) | 0;
- w7 &= 0x3ffffff;
- /* k = 8 */
- lo = Math.imul(al8, bl0);
- mid = Math.imul(al8, bh0);
- mid = (mid + Math.imul(ah8, bl0)) | 0;
- hi = Math.imul(ah8, bh0);
- lo = (lo + Math.imul(al7, bl1)) | 0;
- mid = (mid + Math.imul(al7, bh1)) | 0;
- mid = (mid + Math.imul(ah7, bl1)) | 0;
- hi = (hi + Math.imul(ah7, bh1)) | 0;
- lo = (lo + Math.imul(al6, bl2)) | 0;
- mid = (mid + Math.imul(al6, bh2)) | 0;
- mid = (mid + Math.imul(ah6, bl2)) | 0;
- hi = (hi + Math.imul(ah6, bh2)) | 0;
- lo = (lo + Math.imul(al5, bl3)) | 0;
- mid = (mid + Math.imul(al5, bh3)) | 0;
- mid = (mid + Math.imul(ah5, bl3)) | 0;
- hi = (hi + Math.imul(ah5, bh3)) | 0;
- lo = (lo + Math.imul(al4, bl4)) | 0;
- mid = (mid + Math.imul(al4, bh4)) | 0;
- mid = (mid + Math.imul(ah4, bl4)) | 0;
- hi = (hi + Math.imul(ah4, bh4)) | 0;
- lo = (lo + Math.imul(al3, bl5)) | 0;
- mid = (mid + Math.imul(al3, bh5)) | 0;
- mid = (mid + Math.imul(ah3, bl5)) | 0;
- hi = (hi + Math.imul(ah3, bh5)) | 0;
- lo = (lo + Math.imul(al2, bl6)) | 0;
- mid = (mid + Math.imul(al2, bh6)) | 0;
- mid = (mid + Math.imul(ah2, bl6)) | 0;
- hi = (hi + Math.imul(ah2, bh6)) | 0;
- lo = (lo + Math.imul(al1, bl7)) | 0;
- mid = (mid + Math.imul(al1, bh7)) | 0;
- mid = (mid + Math.imul(ah1, bl7)) | 0;
- hi = (hi + Math.imul(ah1, bh7)) | 0;
- lo = (lo + Math.imul(al0, bl8)) | 0;
- mid = (mid + Math.imul(al0, bh8)) | 0;
- mid = (mid + Math.imul(ah0, bl8)) | 0;
- hi = (hi + Math.imul(ah0, bh8)) | 0;
- var w8 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w8 >>> 26)) | 0;
- w8 &= 0x3ffffff;
- /* k = 9 */
- lo = Math.imul(al9, bl0);
- mid = Math.imul(al9, bh0);
- mid = (mid + Math.imul(ah9, bl0)) | 0;
- hi = Math.imul(ah9, bh0);
- lo = (lo + Math.imul(al8, bl1)) | 0;
- mid = (mid + Math.imul(al8, bh1)) | 0;
- mid = (mid + Math.imul(ah8, bl1)) | 0;
- hi = (hi + Math.imul(ah8, bh1)) | 0;
- lo = (lo + Math.imul(al7, bl2)) | 0;
- mid = (mid + Math.imul(al7, bh2)) | 0;
- mid = (mid + Math.imul(ah7, bl2)) | 0;
- hi = (hi + Math.imul(ah7, bh2)) | 0;
- lo = (lo + Math.imul(al6, bl3)) | 0;
- mid = (mid + Math.imul(al6, bh3)) | 0;
- mid = (mid + Math.imul(ah6, bl3)) | 0;
- hi = (hi + Math.imul(ah6, bh3)) | 0;
- lo = (lo + Math.imul(al5, bl4)) | 0;
- mid = (mid + Math.imul(al5, bh4)) | 0;
- mid = (mid + Math.imul(ah5, bl4)) | 0;
- hi = (hi + Math.imul(ah5, bh4)) | 0;
- lo = (lo + Math.imul(al4, bl5)) | 0;
- mid = (mid + Math.imul(al4, bh5)) | 0;
- mid = (mid + Math.imul(ah4, bl5)) | 0;
- hi = (hi + Math.imul(ah4, bh5)) | 0;
- lo = (lo + Math.imul(al3, bl6)) | 0;
- mid = (mid + Math.imul(al3, bh6)) | 0;
- mid = (mid + Math.imul(ah3, bl6)) | 0;
- hi = (hi + Math.imul(ah3, bh6)) | 0;
- lo = (lo + Math.imul(al2, bl7)) | 0;
- mid = (mid + Math.imul(al2, bh7)) | 0;
- mid = (mid + Math.imul(ah2, bl7)) | 0;
- hi = (hi + Math.imul(ah2, bh7)) | 0;
- lo = (lo + Math.imul(al1, bl8)) | 0;
- mid = (mid + Math.imul(al1, bh8)) | 0;
- mid = (mid + Math.imul(ah1, bl8)) | 0;
- hi = (hi + Math.imul(ah1, bh8)) | 0;
- lo = (lo + Math.imul(al0, bl9)) | 0;
- mid = (mid + Math.imul(al0, bh9)) | 0;
- mid = (mid + Math.imul(ah0, bl9)) | 0;
- hi = (hi + Math.imul(ah0, bh9)) | 0;
- var w9 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w9 >>> 26)) | 0;
- w9 &= 0x3ffffff;
- /* k = 10 */
- lo = Math.imul(al9, bl1);
- mid = Math.imul(al9, bh1);
- mid = (mid + Math.imul(ah9, bl1)) | 0;
- hi = Math.imul(ah9, bh1);
- lo = (lo + Math.imul(al8, bl2)) | 0;
- mid = (mid + Math.imul(al8, bh2)) | 0;
- mid = (mid + Math.imul(ah8, bl2)) | 0;
- hi = (hi + Math.imul(ah8, bh2)) | 0;
- lo = (lo + Math.imul(al7, bl3)) | 0;
- mid = (mid + Math.imul(al7, bh3)) | 0;
- mid = (mid + Math.imul(ah7, bl3)) | 0;
- hi = (hi + Math.imul(ah7, bh3)) | 0;
- lo = (lo + Math.imul(al6, bl4)) | 0;
- mid = (mid + Math.imul(al6, bh4)) | 0;
- mid = (mid + Math.imul(ah6, bl4)) | 0;
- hi = (hi + Math.imul(ah6, bh4)) | 0;
- lo = (lo + Math.imul(al5, bl5)) | 0;
- mid = (mid + Math.imul(al5, bh5)) | 0;
- mid = (mid + Math.imul(ah5, bl5)) | 0;
- hi = (hi + Math.imul(ah5, bh5)) | 0;
- lo = (lo + Math.imul(al4, bl6)) | 0;
- mid = (mid + Math.imul(al4, bh6)) | 0;
- mid = (mid + Math.imul(ah4, bl6)) | 0;
- hi = (hi + Math.imul(ah4, bh6)) | 0;
- lo = (lo + Math.imul(al3, bl7)) | 0;
- mid = (mid + Math.imul(al3, bh7)) | 0;
- mid = (mid + Math.imul(ah3, bl7)) | 0;
- hi = (hi + Math.imul(ah3, bh7)) | 0;
- lo = (lo + Math.imul(al2, bl8)) | 0;
- mid = (mid + Math.imul(al2, bh8)) | 0;
- mid = (mid + Math.imul(ah2, bl8)) | 0;
- hi = (hi + Math.imul(ah2, bh8)) | 0;
- lo = (lo + Math.imul(al1, bl9)) | 0;
- mid = (mid + Math.imul(al1, bh9)) | 0;
- mid = (mid + Math.imul(ah1, bl9)) | 0;
- hi = (hi + Math.imul(ah1, bh9)) | 0;
- var w10 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w10 >>> 26)) | 0;
- w10 &= 0x3ffffff;
- /* k = 11 */
- lo = Math.imul(al9, bl2);
- mid = Math.imul(al9, bh2);
- mid = (mid + Math.imul(ah9, bl2)) | 0;
- hi = Math.imul(ah9, bh2);
- lo = (lo + Math.imul(al8, bl3)) | 0;
- mid = (mid + Math.imul(al8, bh3)) | 0;
- mid = (mid + Math.imul(ah8, bl3)) | 0;
- hi = (hi + Math.imul(ah8, bh3)) | 0;
- lo = (lo + Math.imul(al7, bl4)) | 0;
- mid = (mid + Math.imul(al7, bh4)) | 0;
- mid = (mid + Math.imul(ah7, bl4)) | 0;
- hi = (hi + Math.imul(ah7, bh4)) | 0;
- lo = (lo + Math.imul(al6, bl5)) | 0;
- mid = (mid + Math.imul(al6, bh5)) | 0;
- mid = (mid + Math.imul(ah6, bl5)) | 0;
- hi = (hi + Math.imul(ah6, bh5)) | 0;
- lo = (lo + Math.imul(al5, bl6)) | 0;
- mid = (mid + Math.imul(al5, bh6)) | 0;
- mid = (mid + Math.imul(ah5, bl6)) | 0;
- hi = (hi + Math.imul(ah5, bh6)) | 0;
- lo = (lo + Math.imul(al4, bl7)) | 0;
- mid = (mid + Math.imul(al4, bh7)) | 0;
- mid = (mid + Math.imul(ah4, bl7)) | 0;
- hi = (hi + Math.imul(ah4, bh7)) | 0;
- lo = (lo + Math.imul(al3, bl8)) | 0;
- mid = (mid + Math.imul(al3, bh8)) | 0;
- mid = (mid + Math.imul(ah3, bl8)) | 0;
- hi = (hi + Math.imul(ah3, bh8)) | 0;
- lo = (lo + Math.imul(al2, bl9)) | 0;
- mid = (mid + Math.imul(al2, bh9)) | 0;
- mid = (mid + Math.imul(ah2, bl9)) | 0;
- hi = (hi + Math.imul(ah2, bh9)) | 0;
- var w11 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w11 >>> 26)) | 0;
- w11 &= 0x3ffffff;
- /* k = 12 */
- lo = Math.imul(al9, bl3);
- mid = Math.imul(al9, bh3);
- mid = (mid + Math.imul(ah9, bl3)) | 0;
- hi = Math.imul(ah9, bh3);
- lo = (lo + Math.imul(al8, bl4)) | 0;
- mid = (mid + Math.imul(al8, bh4)) | 0;
- mid = (mid + Math.imul(ah8, bl4)) | 0;
- hi = (hi + Math.imul(ah8, bh4)) | 0;
- lo = (lo + Math.imul(al7, bl5)) | 0;
- mid = (mid + Math.imul(al7, bh5)) | 0;
- mid = (mid + Math.imul(ah7, bl5)) | 0;
- hi = (hi + Math.imul(ah7, bh5)) | 0;
- lo = (lo + Math.imul(al6, bl6)) | 0;
- mid = (mid + Math.imul(al6, bh6)) | 0;
- mid = (mid + Math.imul(ah6, bl6)) | 0;
- hi = (hi + Math.imul(ah6, bh6)) | 0;
- lo = (lo + Math.imul(al5, bl7)) | 0;
- mid = (mid + Math.imul(al5, bh7)) | 0;
- mid = (mid + Math.imul(ah5, bl7)) | 0;
- hi = (hi + Math.imul(ah5, bh7)) | 0;
- lo = (lo + Math.imul(al4, bl8)) | 0;
- mid = (mid + Math.imul(al4, bh8)) | 0;
- mid = (mid + Math.imul(ah4, bl8)) | 0;
- hi = (hi + Math.imul(ah4, bh8)) | 0;
- lo = (lo + Math.imul(al3, bl9)) | 0;
- mid = (mid + Math.imul(al3, bh9)) | 0;
- mid = (mid + Math.imul(ah3, bl9)) | 0;
- hi = (hi + Math.imul(ah3, bh9)) | 0;
- var w12 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w12 >>> 26)) | 0;
- w12 &= 0x3ffffff;
- /* k = 13 */
- lo = Math.imul(al9, bl4);
- mid = Math.imul(al9, bh4);
- mid = (mid + Math.imul(ah9, bl4)) | 0;
- hi = Math.imul(ah9, bh4);
- lo = (lo + Math.imul(al8, bl5)) | 0;
- mid = (mid + Math.imul(al8, bh5)) | 0;
- mid = (mid + Math.imul(ah8, bl5)) | 0;
- hi = (hi + Math.imul(ah8, bh5)) | 0;
- lo = (lo + Math.imul(al7, bl6)) | 0;
- mid = (mid + Math.imul(al7, bh6)) | 0;
- mid = (mid + Math.imul(ah7, bl6)) | 0;
- hi = (hi + Math.imul(ah7, bh6)) | 0;
- lo = (lo + Math.imul(al6, bl7)) | 0;
- mid = (mid + Math.imul(al6, bh7)) | 0;
- mid = (mid + Math.imul(ah6, bl7)) | 0;
- hi = (hi + Math.imul(ah6, bh7)) | 0;
- lo = (lo + Math.imul(al5, bl8)) | 0;
- mid = (mid + Math.imul(al5, bh8)) | 0;
- mid = (mid + Math.imul(ah5, bl8)) | 0;
- hi = (hi + Math.imul(ah5, bh8)) | 0;
- lo = (lo + Math.imul(al4, bl9)) | 0;
- mid = (mid + Math.imul(al4, bh9)) | 0;
- mid = (mid + Math.imul(ah4, bl9)) | 0;
- hi = (hi + Math.imul(ah4, bh9)) | 0;
- var w13 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w13 >>> 26)) | 0;
- w13 &= 0x3ffffff;
- /* k = 14 */
- lo = Math.imul(al9, bl5);
- mid = Math.imul(al9, bh5);
- mid = (mid + Math.imul(ah9, bl5)) | 0;
- hi = Math.imul(ah9, bh5);
- lo = (lo + Math.imul(al8, bl6)) | 0;
- mid = (mid + Math.imul(al8, bh6)) | 0;
- mid = (mid + Math.imul(ah8, bl6)) | 0;
- hi = (hi + Math.imul(ah8, bh6)) | 0;
- lo = (lo + Math.imul(al7, bl7)) | 0;
- mid = (mid + Math.imul(al7, bh7)) | 0;
- mid = (mid + Math.imul(ah7, bl7)) | 0;
- hi = (hi + Math.imul(ah7, bh7)) | 0;
- lo = (lo + Math.imul(al6, bl8)) | 0;
- mid = (mid + Math.imul(al6, bh8)) | 0;
- mid = (mid + Math.imul(ah6, bl8)) | 0;
- hi = (hi + Math.imul(ah6, bh8)) | 0;
- lo = (lo + Math.imul(al5, bl9)) | 0;
- mid = (mid + Math.imul(al5, bh9)) | 0;
- mid = (mid + Math.imul(ah5, bl9)) | 0;
- hi = (hi + Math.imul(ah5, bh9)) | 0;
- var w14 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w14 >>> 26)) | 0;
- w14 &= 0x3ffffff;
- /* k = 15 */
- lo = Math.imul(al9, bl6);
- mid = Math.imul(al9, bh6);
- mid = (mid + Math.imul(ah9, bl6)) | 0;
- hi = Math.imul(ah9, bh6);
- lo = (lo + Math.imul(al8, bl7)) | 0;
- mid = (mid + Math.imul(al8, bh7)) | 0;
- mid = (mid + Math.imul(ah8, bl7)) | 0;
- hi = (hi + Math.imul(ah8, bh7)) | 0;
- lo = (lo + Math.imul(al7, bl8)) | 0;
- mid = (mid + Math.imul(al7, bh8)) | 0;
- mid = (mid + Math.imul(ah7, bl8)) | 0;
- hi = (hi + Math.imul(ah7, bh8)) | 0;
- lo = (lo + Math.imul(al6, bl9)) | 0;
- mid = (mid + Math.imul(al6, bh9)) | 0;
- mid = (mid + Math.imul(ah6, bl9)) | 0;
- hi = (hi + Math.imul(ah6, bh9)) | 0;
- var w15 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w15 >>> 26)) | 0;
- w15 &= 0x3ffffff;
- /* k = 16 */
- lo = Math.imul(al9, bl7);
- mid = Math.imul(al9, bh7);
- mid = (mid + Math.imul(ah9, bl7)) | 0;
- hi = Math.imul(ah9, bh7);
- lo = (lo + Math.imul(al8, bl8)) | 0;
- mid = (mid + Math.imul(al8, bh8)) | 0;
- mid = (mid + Math.imul(ah8, bl8)) | 0;
- hi = (hi + Math.imul(ah8, bh8)) | 0;
- lo = (lo + Math.imul(al7, bl9)) | 0;
- mid = (mid + Math.imul(al7, bh9)) | 0;
- mid = (mid + Math.imul(ah7, bl9)) | 0;
- hi = (hi + Math.imul(ah7, bh9)) | 0;
- var w16 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w16 >>> 26)) | 0;
- w16 &= 0x3ffffff;
- /* k = 17 */
- lo = Math.imul(al9, bl8);
- mid = Math.imul(al9, bh8);
- mid = (mid + Math.imul(ah9, bl8)) | 0;
- hi = Math.imul(ah9, bh8);
- lo = (lo + Math.imul(al8, bl9)) | 0;
- mid = (mid + Math.imul(al8, bh9)) | 0;
- mid = (mid + Math.imul(ah8, bl9)) | 0;
- hi = (hi + Math.imul(ah8, bh9)) | 0;
- var w17 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w17 >>> 26)) | 0;
- w17 &= 0x3ffffff;
- /* k = 18 */
- lo = Math.imul(al9, bl9);
- mid = Math.imul(al9, bh9);
- mid = (mid + Math.imul(ah9, bl9)) | 0;
- hi = Math.imul(ah9, bh9);
- var w18 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
- c = (((hi + (mid >>> 13)) | 0) + (w18 >>> 26)) | 0;
- w18 &= 0x3ffffff;
- o[0] = w0;
- o[1] = w1;
- o[2] = w2;
- o[3] = w3;
- o[4] = w4;
- o[5] = w5;
- o[6] = w6;
- o[7] = w7;
- o[8] = w8;
- o[9] = w9;
- o[10] = w10;
- o[11] = w11;
- o[12] = w12;
- o[13] = w13;
- o[14] = w14;
- o[15] = w15;
- o[16] = w16;
- o[17] = w17;
- o[18] = w18;
- if (c !== 0) {
- o[19] = c;
- out.length++;
- }
- return out;
- };
-
- // Polyfill comb
- if (!Math.imul) {
- comb10MulTo = smallMulTo;
- }
-
- function bigMulTo (self, num, out) {
- out.negative = num.negative ^ self.negative;
- out.length = self.length + num.length;
-
- var carry = 0;
- var hncarry = 0;
- for (var k = 0; k < out.length - 1; k++) {
- // Sum all words with the same `i + j = k` and accumulate `ncarry`,
- // note that ncarry could be >= 0x3ffffff
- var ncarry = hncarry;
- hncarry = 0;
- var rword = carry & 0x3ffffff;
- var maxJ = Math.min(k, num.length - 1);
- for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
- var i = k - j;
- var a = self.words[i] | 0;
- var b = num.words[j] | 0;
- var r = a * b;
-
- var lo = r & 0x3ffffff;
- ncarry = (ncarry + ((r / 0x4000000) | 0)) | 0;
- lo = (lo + rword) | 0;
- rword = lo & 0x3ffffff;
- ncarry = (ncarry + (lo >>> 26)) | 0;
-
- hncarry += ncarry >>> 26;
- ncarry &= 0x3ffffff;
- }
- out.words[k] = rword;
- carry = ncarry;
- ncarry = hncarry;
- }
- if (carry !== 0) {
- out.words[k] = carry;
- } else {
- out.length--;
- }
-
- return out.strip();
- }
-
- function jumboMulTo (self, num, out) {
- var fftm = new FFTM();
- return fftm.mulp(self, num, out);
- }
-
- BN.prototype.mulTo = function mulTo (num, out) {
- var res;
- var len = this.length + num.length;
- if (this.length === 10 && num.length === 10) {
- res = comb10MulTo(this, num, out);
- } else if (len < 63) {
- res = smallMulTo(this, num, out);
- } else if (len < 1024) {
- res = bigMulTo(this, num, out);
- } else {
- res = jumboMulTo(this, num, out);
- }
-
- return res;
- };
-
- // Cooley-Tukey algorithm for FFT
- // slightly revisited to rely on looping instead of recursion
-
- function FFTM (x, y) {
- this.x = x;
- this.y = y;
- }
-
- FFTM.prototype.makeRBT = function makeRBT (N) {
- var t = new Array(N);
- var l = BN.prototype._countBits(N) - 1;
- for (var i = 0; i < N; i++) {
- t[i] = this.revBin(i, l, N);
- }
-
- return t;
- };
-
- // Returns binary-reversed representation of `x`
- FFTM.prototype.revBin = function revBin (x, l, N) {
- if (x === 0 || x === N - 1) return x;
-
- var rb = 0;
- for (var i = 0; i < l; i++) {
- rb |= (x & 1) << (l - i - 1);
- x >>= 1;
- }
-
- return rb;
- };
-
- // Performs "tweedling" phase, therefore 'emulating'
- // behaviour of the recursive algorithm
- FFTM.prototype.permute = function permute (rbt, rws, iws, rtws, itws, N) {
- for (var i = 0; i < N; i++) {
- rtws[i] = rws[rbt[i]];
- itws[i] = iws[rbt[i]];
- }
- };
-
- FFTM.prototype.transform = function transform (rws, iws, rtws, itws, N, rbt) {
- this.permute(rbt, rws, iws, rtws, itws, N);
-
- for (var s = 1; s < N; s <<= 1) {
- var l = s << 1;
-
- var rtwdf = Math.cos(2 * Math.PI / l);
- var itwdf = Math.sin(2 * Math.PI / l);
-
- for (var p = 0; p < N; p += l) {
- var rtwdf_ = rtwdf;
- var itwdf_ = itwdf;
-
- for (var j = 0; j < s; j++) {
- var re = rtws[p + j];
- var ie = itws[p + j];
-
- var ro = rtws[p + j + s];
- var io = itws[p + j + s];
-
- var rx = rtwdf_ * ro - itwdf_ * io;
-
- io = rtwdf_ * io + itwdf_ * ro;
- ro = rx;
-
- rtws[p + j] = re + ro;
- itws[p + j] = ie + io;
-
- rtws[p + j + s] = re - ro;
- itws[p + j + s] = ie - io;
-
- /* jshint maxdepth : false */
- if (j !== l) {
- rx = rtwdf * rtwdf_ - itwdf * itwdf_;
-
- itwdf_ = rtwdf * itwdf_ + itwdf * rtwdf_;
- rtwdf_ = rx;
- }
- }
- }
- }
- };
-
- FFTM.prototype.guessLen13b = function guessLen13b (n, m) {
- var N = Math.max(m, n) | 1;
- var odd = N & 1;
- var i = 0;
- for (N = N / 2 | 0; N; N = N >>> 1) {
- i++;
- }
-
- return 1 << i + 1 + odd;
- };
-
- FFTM.prototype.conjugate = function conjugate (rws, iws, N) {
- if (N <= 1) return;
-
- for (var i = 0; i < N / 2; i++) {
- var t = rws[i];
-
- rws[i] = rws[N - i - 1];
- rws[N - i - 1] = t;
-
- t = iws[i];
-
- iws[i] = -iws[N - i - 1];
- iws[N - i - 1] = -t;
- }
- };
-
- FFTM.prototype.normalize13b = function normalize13b (ws, N) {
- var carry = 0;
- for (var i = 0; i < N / 2; i++) {
- var w = Math.round(ws[2 * i + 1] / N) * 0x2000 +
- Math.round(ws[2 * i] / N) +
- carry;
-
- ws[i] = w & 0x3ffffff;
-
- if (w < 0x4000000) {
- carry = 0;
- } else {
- carry = w / 0x4000000 | 0;
- }
- }
-
- return ws;
- };
-
- FFTM.prototype.convert13b = function convert13b (ws, len, rws, N) {
- var carry = 0;
- for (var i = 0; i < len; i++) {
- carry = carry + (ws[i] | 0);
-
- rws[2 * i] = carry & 0x1fff; carry = carry >>> 13;
- rws[2 * i + 1] = carry & 0x1fff; carry = carry >>> 13;
- }
-
- // Pad with zeroes
- for (i = 2 * len; i < N; ++i) {
- rws[i] = 0;
- }
-
- assert(carry === 0);
- assert((carry & ~0x1fff) === 0);
- };
-
- FFTM.prototype.stub = function stub (N) {
- var ph = new Array(N);
- for (var i = 0; i < N; i++) {
- ph[i] = 0;
- }
-
- return ph;
- };
-
- FFTM.prototype.mulp = function mulp (x, y, out) {
- var N = 2 * this.guessLen13b(x.length, y.length);
-
- var rbt = this.makeRBT(N);
-
- var _ = this.stub(N);
-
- var rws = new Array(N);
- var rwst = new Array(N);
- var iwst = new Array(N);
-
- var nrws = new Array(N);
- var nrwst = new Array(N);
- var niwst = new Array(N);
-
- var rmws = out.words;
- rmws.length = N;
-
- this.convert13b(x.words, x.length, rws, N);
- this.convert13b(y.words, y.length, nrws, N);
-
- this.transform(rws, _, rwst, iwst, N, rbt);
- this.transform(nrws, _, nrwst, niwst, N, rbt);
-
- for (var i = 0; i < N; i++) {
- var rx = rwst[i] * nrwst[i] - iwst[i] * niwst[i];
- iwst[i] = rwst[i] * niwst[i] + iwst[i] * nrwst[i];
- rwst[i] = rx;
- }
-
- this.conjugate(rwst, iwst, N);
- this.transform(rwst, iwst, rmws, _, N, rbt);
- this.conjugate(rmws, _, N);
- this.normalize13b(rmws, N);
-
- out.negative = x.negative ^ y.negative;
- out.length = x.length + y.length;
- return out.strip();
- };
-
- // Multiply `this` by `num`
- BN.prototype.mul = function mul (num) {
- var out = new BN(null);
- out.words = new Array(this.length + num.length);
- return this.mulTo(num, out);
- };
-
- // Multiply employing FFT
- BN.prototype.mulf = function mulf (num) {
- var out = new BN(null);
- out.words = new Array(this.length + num.length);
- return jumboMulTo(this, num, out);
- };
-
- // In-place Multiplication
- BN.prototype.imul = function imul (num) {
- return this.clone().mulTo(num, this);
- };
-
- BN.prototype.imuln = function imuln (num) {
- assert(typeof num === 'number');
- assert(num < 0x4000000);
-
- // Carry
- var carry = 0;
- for (var i = 0; i < this.length; i++) {
- var w = (this.words[i] | 0) * num;
- var lo = (w & 0x3ffffff) + (carry & 0x3ffffff);
- carry >>= 26;
- carry += (w / 0x4000000) | 0;
- // NOTE: lo is 27bit maximum
- carry += lo >>> 26;
- this.words[i] = lo & 0x3ffffff;
- }
-
- if (carry !== 0) {
- this.words[i] = carry;
- this.length++;
- }
-
- return this;
- };
-
- BN.prototype.muln = function muln (num) {
- return this.clone().imuln(num);
- };
-
- // `this` * `this`
- BN.prototype.sqr = function sqr () {
- return this.mul(this);
- };
-
- // `this` * `this` in-place
- BN.prototype.isqr = function isqr () {
- return this.imul(this.clone());
- };
-
- // Math.pow(`this`, `num`)
- BN.prototype.pow = function pow (num) {
- var w = toBitArray(num);
- if (w.length === 0) return new BN(1);
-
- // Skip leading zeroes
- var res = this;
- for (var i = 0; i < w.length; i++, res = res.sqr()) {
- if (w[i] !== 0) break;
- }
-
- if (++i < w.length) {
- for (var q = res.sqr(); i < w.length; i++, q = q.sqr()) {
- if (w[i] === 0) continue;
-
- res = res.mul(q);
- }
- }
-
- return res;
- };
-
- // Shift-left in-place
- BN.prototype.iushln = function iushln (bits) {
- assert(typeof bits === 'number' && bits >= 0);
- var r = bits % 26;
- var s = (bits - r) / 26;
- var carryMask = (0x3ffffff >>> (26 - r)) << (26 - r);
- var i;
-
- if (r !== 0) {
- var carry = 0;
-
- for (i = 0; i < this.length; i++) {
- var newCarry = this.words[i] & carryMask;
- var c = ((this.words[i] | 0) - newCarry) << r;
- this.words[i] = c | carry;
- carry = newCarry >>> (26 - r);
- }
-
- if (carry) {
- this.words[i] = carry;
- this.length++;
- }
- }
-
- if (s !== 0) {
- for (i = this.length - 1; i >= 0; i--) {
- this.words[i + s] = this.words[i];
- }
-
- for (i = 0; i < s; i++) {
- this.words[i] = 0;
- }
-
- this.length += s;
- }
-
- return this.strip();
- };
-
- BN.prototype.ishln = function ishln (bits) {
- // TODO(indutny): implement me
- assert(this.negative === 0);
- return this.iushln(bits);
- };
-
- // Shift-right in-place
- // NOTE: `hint` is a lowest bit before trailing zeroes
- // NOTE: if `extended` is present - it will be filled with destroyed bits
- BN.prototype.iushrn = function iushrn (bits, hint, extended) {
- assert(typeof bits === 'number' && bits >= 0);
- var h;
- if (hint) {
- h = (hint - (hint % 26)) / 26;
- } else {
- h = 0;
- }
-
- var r = bits % 26;
- var s = Math.min((bits - r) / 26, this.length);
- var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
- var maskedWords = extended;
-
- h -= s;
- h = Math.max(0, h);
-
- // Extended mode, copy masked part
- if (maskedWords) {
- for (var i = 0; i < s; i++) {
- maskedWords.words[i] = this.words[i];
- }
- maskedWords.length = s;
- }
-
- if (s === 0) {
- // No-op, we should not move anything at all
- } else if (this.length > s) {
- this.length -= s;
- for (i = 0; i < this.length; i++) {
- this.words[i] = this.words[i + s];
- }
- } else {
- this.words[0] = 0;
- this.length = 1;
- }
-
- var carry = 0;
- for (i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
- var word = this.words[i] | 0;
- this.words[i] = (carry << (26 - r)) | (word >>> r);
- carry = word & mask;
- }
-
- // Push carried bits as a mask
- if (maskedWords && carry !== 0) {
- maskedWords.words[maskedWords.length++] = carry;
- }
-
- if (this.length === 0) {
- this.words[0] = 0;
- this.length = 1;
- }
-
- return this.strip();
- };
-
- BN.prototype.ishrn = function ishrn (bits, hint, extended) {
- // TODO(indutny): implement me
- assert(this.negative === 0);
- return this.iushrn(bits, hint, extended);
- };
-
- // Shift-left
- BN.prototype.shln = function shln (bits) {
- return this.clone().ishln(bits);
- };
-
- BN.prototype.ushln = function ushln (bits) {
- return this.clone().iushln(bits);
- };
-
- // Shift-right
- BN.prototype.shrn = function shrn (bits) {
- return this.clone().ishrn(bits);
- };
-
- BN.prototype.ushrn = function ushrn (bits) {
- return this.clone().iushrn(bits);
- };
-
- // Test if n bit is set
- BN.prototype.testn = function testn (bit) {
- assert(typeof bit === 'number' && bit >= 0);
- var r = bit % 26;
- var s = (bit - r) / 26;
- var q = 1 << r;
-
- // Fast case: bit is much higher than all existing words
- if (this.length <= s) return false;
-
- // Check bit and return
- var w = this.words[s];
-
- return !!(w & q);
- };
-
- // Return only lowers bits of number (in-place)
- BN.prototype.imaskn = function imaskn (bits) {
- assert(typeof bits === 'number' && bits >= 0);
- var r = bits % 26;
- var s = (bits - r) / 26;
-
- assert(this.negative === 0, 'imaskn works only with positive numbers');
-
- if (this.length <= s) {
- return this;
- }
-
- if (r !== 0) {
- s++;
- }
- this.length = Math.min(s, this.length);
-
- if (r !== 0) {
- var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
- this.words[this.length - 1] &= mask;
- }
-
- return this.strip();
- };
-
- // Return only lowers bits of number
- BN.prototype.maskn = function maskn (bits) {
- return this.clone().imaskn(bits);
- };
-
- // Add plain number `num` to `this`
- BN.prototype.iaddn = function iaddn (num) {
- assert(typeof num === 'number');
- assert(num < 0x4000000);
- if (num < 0) return this.isubn(-num);
-
- // Possible sign change
- if (this.negative !== 0) {
- if (this.length === 1 && (this.words[0] | 0) < num) {
- this.words[0] = num - (this.words[0] | 0);
- this.negative = 0;
- return this;
- }
-
- this.negative = 0;
- this.isubn(num);
- this.negative = 1;
- return this;
- }
-
- // Add without checks
- return this._iaddn(num);
- };
-
- BN.prototype._iaddn = function _iaddn (num) {
- this.words[0] += num;
-
- // Carry
- for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) {
- this.words[i] -= 0x4000000;
- if (i === this.length - 1) {
- this.words[i + 1] = 1;
- } else {
- this.words[i + 1]++;
- }
- }
- this.length = Math.max(this.length, i + 1);
-
- return this;
- };
-
- // Subtract plain number `num` from `this`
- BN.prototype.isubn = function isubn (num) {
- assert(typeof num === 'number');
- assert(num < 0x4000000);
- if (num < 0) return this.iaddn(-num);
-
- if (this.negative !== 0) {
- this.negative = 0;
- this.iaddn(num);
- this.negative = 1;
- return this;
- }
-
- this.words[0] -= num;
-
- if (this.length === 1 && this.words[0] < 0) {
- this.words[0] = -this.words[0];
- this.negative = 1;
- } else {
- // Carry
- for (var i = 0; i < this.length && this.words[i] < 0; i++) {
- this.words[i] += 0x4000000;
- this.words[i + 1] -= 1;
- }
- }
-
- return this.strip();
- };
-
- BN.prototype.addn = function addn (num) {
- return this.clone().iaddn(num);
- };
-
- BN.prototype.subn = function subn (num) {
- return this.clone().isubn(num);
- };
-
- BN.prototype.iabs = function iabs () {
- this.negative = 0;
-
- return this;
- };
-
- BN.prototype.abs = function abs () {
- return this.clone().iabs();
- };
-
- BN.prototype._ishlnsubmul = function _ishlnsubmul (num, mul, shift) {
- var len = num.length + shift;
- var i;
-
- this._expand(len);
-
- var w;
- var carry = 0;
- for (i = 0; i < num.length; i++) {
- w = (this.words[i + shift] | 0) + carry;
- var right = (num.words[i] | 0) * mul;
- w -= right & 0x3ffffff;
- carry = (w >> 26) - ((right / 0x4000000) | 0);
- this.words[i + shift] = w & 0x3ffffff;
- }
- for (; i < this.length - shift; i++) {
- w = (this.words[i + shift] | 0) + carry;
- carry = w >> 26;
- this.words[i + shift] = w & 0x3ffffff;
- }
-
- if (carry === 0) return this.strip();
-
- // Subtraction overflow
- assert(carry === -1);
- carry = 0;
- for (i = 0; i < this.length; i++) {
- w = -(this.words[i] | 0) + carry;
- carry = w >> 26;
- this.words[i] = w & 0x3ffffff;
- }
- this.negative = 1;
-
- return this.strip();
- };
-
- BN.prototype._wordDiv = function _wordDiv (num, mode) {
- var shift = this.length - num.length;
-
- var a = this.clone();
- var b = num;
-
- // Normalize
- var bhi = b.words[b.length - 1] | 0;
- var bhiBits = this._countBits(bhi);
- shift = 26 - bhiBits;
- if (shift !== 0) {
- b = b.ushln(shift);
- a.iushln(shift);
- bhi = b.words[b.length - 1] | 0;
- }
-
- // Initialize quotient
- var m = a.length - b.length;
- var q;
-
- if (mode !== 'mod') {
- q = new BN(null);
- q.length = m + 1;
- q.words = new Array(q.length);
- for (var i = 0; i < q.length; i++) {
- q.words[i] = 0;
- }
- }
-
- var diff = a.clone()._ishlnsubmul(b, 1, m);
- if (diff.negative === 0) {
- a = diff;
- if (q) {
- q.words[m] = 1;
- }
- }
-
- for (var j = m - 1; j >= 0; j--) {
- var qj = (a.words[b.length + j] | 0) * 0x4000000 +
- (a.words[b.length + j - 1] | 0);
-
- // NOTE: (qj / bhi) is (0x3ffffff * 0x4000000 + 0x3ffffff) / 0x2000000 max
- // (0x7ffffff)
- qj = Math.min((qj / bhi) | 0, 0x3ffffff);
-
- a._ishlnsubmul(b, qj, j);
- while (a.negative !== 0) {
- qj--;
- a.negative = 0;
- a._ishlnsubmul(b, 1, j);
- if (!a.isZero()) {
- a.negative ^= 1;
- }
- }
- if (q) {
- q.words[j] = qj;
- }
- }
- if (q) {
- q.strip();
- }
- a.strip();
-
- // Denormalize
- if (mode !== 'div' && shift !== 0) {
- a.iushrn(shift);
- }
-
- return {
- div: q || null,
- mod: a
- };
- };
-
- // NOTE: 1) `mode` can be set to `mod` to request mod only,
- // to `div` to request div only, or be absent to
- // request both div & mod
- // 2) `positive` is true if unsigned mod is requested
- BN.prototype.divmod = function divmod (num, mode, positive) {
- assert(!num.isZero());
-
- if (this.isZero()) {
- return {
- div: new BN(0),
- mod: new BN(0)
- };
- }
-
- var div, mod, res;
- if (this.negative !== 0 && num.negative === 0) {
- res = this.neg().divmod(num, mode);
-
- if (mode !== 'mod') {
- div = res.div.neg();
- }
-
- if (mode !== 'div') {
- mod = res.mod.neg();
- if (positive && mod.negative !== 0) {
- mod.iadd(num);
- }
- }
-
- return {
- div: div,
- mod: mod
- };
- }
-
- if (this.negative === 0 && num.negative !== 0) {
- res = this.divmod(num.neg(), mode);
-
- if (mode !== 'mod') {
- div = res.div.neg();
- }
-
- return {
- div: div,
- mod: res.mod
- };
- }
-
- if ((this.negative & num.negative) !== 0) {
- res = this.neg().divmod(num.neg(), mode);
-
- if (mode !== 'div') {
- mod = res.mod.neg();
- if (positive && mod.negative !== 0) {
- mod.isub(num);
- }
- }
-
- return {
- div: res.div,
- mod: mod
- };
- }
-
- // Both numbers are positive at this point
-
- // Strip both numbers to approximate shift value
- if (num.length > this.length || this.cmp(num) < 0) {
- return {
- div: new BN(0),
- mod: this
- };
- }
-
- // Very short reduction
- if (num.length === 1) {
- if (mode === 'div') {
- return {
- div: this.divn(num.words[0]),
- mod: null
- };
- }
-
- if (mode === 'mod') {
- return {
- div: null,
- mod: new BN(this.modn(num.words[0]))
- };
- }
-
- return {
- div: this.divn(num.words[0]),
- mod: new BN(this.modn(num.words[0]))
- };
- }
-
- return this._wordDiv(num, mode);
- };
-
- // Find `this` / `num`
- BN.prototype.div = function div (num) {
- return this.divmod(num, 'div', false).div;
- };
-
- // Find `this` % `num`
- BN.prototype.mod = function mod (num) {
- return this.divmod(num, 'mod', false).mod;
- };
-
- BN.prototype.umod = function umod (num) {
- return this.divmod(num, 'mod', true).mod;
- };
-
- // Find Round(`this` / `num`)
- BN.prototype.divRound = function divRound (num) {
- var dm = this.divmod(num);
-
- // Fast case - exact division
- if (dm.mod.isZero()) return dm.div;
-
- var mod = dm.div.negative !== 0 ? dm.mod.isub(num) : dm.mod;
-
- var half = num.ushrn(1);
- var r2 = num.andln(1);
- var cmp = mod.cmp(half);
-
- // Round down
- if (cmp < 0 || r2 === 1 && cmp === 0) return dm.div;
-
- // Round up
- return dm.div.negative !== 0 ? dm.div.isubn(1) : dm.div.iaddn(1);
- };
-
- BN.prototype.modn = function modn (num) {
- assert(num <= 0x3ffffff);
- var p = (1 << 26) % num;
-
- var acc = 0;
- for (var i = this.length - 1; i >= 0; i--) {
- acc = (p * acc + (this.words[i] | 0)) % num;
- }
-
- return acc;
- };
-
- // In-place division by number
- BN.prototype.idivn = function idivn (num) {
- assert(num <= 0x3ffffff);
-
- var carry = 0;
- for (var i = this.length - 1; i >= 0; i--) {
- var w = (this.words[i] | 0) + carry * 0x4000000;
- this.words[i] = (w / num) | 0;
- carry = w % num;
- }
-
- return this.strip();
- };
-
- BN.prototype.divn = function divn (num) {
- return this.clone().idivn(num);
- };
-
- BN.prototype.egcd = function egcd (p) {
- assert(p.negative === 0);
- assert(!p.isZero());
-
- var x = this;
- var y = p.clone();
-
- if (x.negative !== 0) {
- x = x.umod(p);
- } else {
- x = x.clone();
- }
-
- // A * x + B * y = x
- var A = new BN(1);
- var B = new BN(0);
-
- // C * x + D * y = y
- var C = new BN(0);
- var D = new BN(1);
-
- var g = 0;
-
- while (x.isEven() && y.isEven()) {
- x.iushrn(1);
- y.iushrn(1);
- ++g;
- }
-
- var yp = y.clone();
- var xp = x.clone();
-
- while (!x.isZero()) {
- for (var i = 0, im = 1; (x.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
- if (i > 0) {
- x.iushrn(i);
- while (i-- > 0) {
- if (A.isOdd() || B.isOdd()) {
- A.iadd(yp);
- B.isub(xp);
- }
-
- A.iushrn(1);
- B.iushrn(1);
- }
- }
-
- for (var j = 0, jm = 1; (y.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
- if (j > 0) {
- y.iushrn(j);
- while (j-- > 0) {
- if (C.isOdd() || D.isOdd()) {
- C.iadd(yp);
- D.isub(xp);
- }
-
- C.iushrn(1);
- D.iushrn(1);
- }
- }
-
- if (x.cmp(y) >= 0) {
- x.isub(y);
- A.isub(C);
- B.isub(D);
- } else {
- y.isub(x);
- C.isub(A);
- D.isub(B);
- }
- }
-
- return {
- a: C,
- b: D,
- gcd: y.iushln(g)
- };
- };
-
- // This is reduced incarnation of the binary EEA
- // above, designated to invert members of the
- // _prime_ fields F(p) at a maximal speed
- BN.prototype._invmp = function _invmp (p) {
- assert(p.negative === 0);
- assert(!p.isZero());
-
- var a = this;
- var b = p.clone();
-
- if (a.negative !== 0) {
- a = a.umod(p);
- } else {
- a = a.clone();
- }
-
- var x1 = new BN(1);
- var x2 = new BN(0);
-
- var delta = b.clone();
-
- while (a.cmpn(1) > 0 && b.cmpn(1) > 0) {
- for (var i = 0, im = 1; (a.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
- if (i > 0) {
- a.iushrn(i);
- while (i-- > 0) {
- if (x1.isOdd()) {
- x1.iadd(delta);
- }
-
- x1.iushrn(1);
- }
- }
-
- for (var j = 0, jm = 1; (b.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
- if (j > 0) {
- b.iushrn(j);
- while (j-- > 0) {
- if (x2.isOdd()) {
- x2.iadd(delta);
- }
-
- x2.iushrn(1);
- }
- }
-
- if (a.cmp(b) >= 0) {
- a.isub(b);
- x1.isub(x2);
- } else {
- b.isub(a);
- x2.isub(x1);
- }
- }
-
- var res;
- if (a.cmpn(1) === 0) {
- res = x1;
- } else {
- res = x2;
- }
-
- if (res.cmpn(0) < 0) {
- res.iadd(p);
- }
-
- return res;
- };
-
- BN.prototype.gcd = function gcd (num) {
- if (this.isZero()) return num.abs();
- if (num.isZero()) return this.abs();
-
- var a = this.clone();
- var b = num.clone();
- a.negative = 0;
- b.negative = 0;
-
- // Remove common factor of two
- for (var shift = 0; a.isEven() && b.isEven(); shift++) {
- a.iushrn(1);
- b.iushrn(1);
- }
-
- do {
- while (a.isEven()) {
- a.iushrn(1);
- }
- while (b.isEven()) {
- b.iushrn(1);
- }
-
- var r = a.cmp(b);
- if (r < 0) {
- // Swap `a` and `b` to make `a` always bigger than `b`
- var t = a;
- a = b;
- b = t;
- } else if (r === 0 || b.cmpn(1) === 0) {
- break;
- }
-
- a.isub(b);
- } while (true);
-
- return b.iushln(shift);
- };
-
- // Invert number in the field F(num)
- BN.prototype.invm = function invm (num) {
- return this.egcd(num).a.umod(num);
- };
-
- BN.prototype.isEven = function isEven () {
- return (this.words[0] & 1) === 0;
- };
-
- BN.prototype.isOdd = function isOdd () {
- return (this.words[0] & 1) === 1;
- };
-
- // And first word and num
- BN.prototype.andln = function andln (num) {
- return this.words[0] & num;
- };
-
- // Increment at the bit position in-line
- BN.prototype.bincn = function bincn (bit) {
- assert(typeof bit === 'number');
- var r = bit % 26;
- var s = (bit - r) / 26;
- var q = 1 << r;
-
- // Fast case: bit is much higher than all existing words
- if (this.length <= s) {
- this._expand(s + 1);
- this.words[s] |= q;
- return this;
- }
-
- // Add bit and propagate, if needed
- var carry = q;
- for (var i = s; carry !== 0 && i < this.length; i++) {
- var w = this.words[i] | 0;
- w += carry;
- carry = w >>> 26;
- w &= 0x3ffffff;
- this.words[i] = w;
- }
- if (carry !== 0) {
- this.words[i] = carry;
- this.length++;
- }
- return this;
- };
-
- BN.prototype.isZero = function isZero () {
- return this.length === 1 && this.words[0] === 0;
- };
-
- BN.prototype.cmpn = function cmpn (num) {
- var negative = num < 0;
-
- if (this.negative !== 0 && !negative) return -1;
- if (this.negative === 0 && negative) return 1;
-
- this.strip();
-
- var res;
- if (this.length > 1) {
- res = 1;
- } else {
- if (negative) {
- num = -num;
- }
-
- assert(num <= 0x3ffffff, 'Number is too big');
-
- var w = this.words[0] | 0;
- res = w === num ? 0 : w < num ? -1 : 1;
- }
- if (this.negative !== 0) return -res | 0;
- return res;
- };
-
- // Compare two numbers and return:
- // 1 - if `this` > `num`
- // 0 - if `this` == `num`
- // -1 - if `this` < `num`
- BN.prototype.cmp = function cmp (num) {
- if (this.negative !== 0 && num.negative === 0) return -1;
- if (this.negative === 0 && num.negative !== 0) return 1;
-
- var res = this.ucmp(num);
- if (this.negative !== 0) return -res | 0;
- return res;
- };
-
- // Unsigned comparison
- BN.prototype.ucmp = function ucmp (num) {
- // At this point both numbers have the same sign
- if (this.length > num.length) return 1;
- if (this.length < num.length) return -1;
-
- var res = 0;
- for (var i = this.length - 1; i >= 0; i--) {
- var a = this.words[i] | 0;
- var b = num.words[i] | 0;
-
- if (a === b) continue;
- if (a < b) {
- res = -1;
- } else if (a > b) {
- res = 1;
- }
- break;
- }
- return res;
- };
-
- BN.prototype.gtn = function gtn (num) {
- return this.cmpn(num) === 1;
- };
-
- BN.prototype.gt = function gt (num) {
- return this.cmp(num) === 1;
- };
-
- BN.prototype.gten = function gten (num) {
- return this.cmpn(num) >= 0;
- };
-
- BN.prototype.gte = function gte (num) {
- return this.cmp(num) >= 0;
- };
-
- BN.prototype.ltn = function ltn (num) {
- return this.cmpn(num) === -1;
- };
-
- BN.prototype.lt = function lt (num) {
- return this.cmp(num) === -1;
- };
-
- BN.prototype.lten = function lten (num) {
- return this.cmpn(num) <= 0;
- };
-
- BN.prototype.lte = function lte (num) {
- return this.cmp(num) <= 0;
- };
-
- BN.prototype.eqn = function eqn (num) {
- return this.cmpn(num) === 0;
- };
-
- BN.prototype.eq = function eq (num) {
- return this.cmp(num) === 0;
- };
-
- //
- // A reduce context, could be using montgomery or something better, depending
- // on the `m` itself.
- //
- BN.red = function red (num) {
- return new Red(num);
- };
-
- BN.prototype.toRed = function toRed (ctx) {
- assert(!this.red, 'Already a number in reduction context');
- assert(this.negative === 0, 'red works only with positives');
- return ctx.convertTo(this)._forceRed(ctx);
- };
-
- BN.prototype.fromRed = function fromRed () {
- assert(this.red, 'fromRed works only with numbers in reduction context');
- return this.red.convertFrom(this);
- };
-
- BN.prototype._forceRed = function _forceRed (ctx) {
- this.red = ctx;
- return this;
- };
-
- BN.prototype.forceRed = function forceRed (ctx) {
- assert(!this.red, 'Already a number in reduction context');
- return this._forceRed(ctx);
- };
-
- BN.prototype.redAdd = function redAdd (num) {
- assert(this.red, 'redAdd works only with red numbers');
- return this.red.add(this, num);
- };
-
- BN.prototype.redIAdd = function redIAdd (num) {
- assert(this.red, 'redIAdd works only with red numbers');
- return this.red.iadd(this, num);
- };
-
- BN.prototype.redSub = function redSub (num) {
- assert(this.red, 'redSub works only with red numbers');
- return this.red.sub(this, num);
- };
-
- BN.prototype.redISub = function redISub (num) {
- assert(this.red, 'redISub works only with red numbers');
- return this.red.isub(this, num);
- };
-
- BN.prototype.redShl = function redShl (num) {
- assert(this.red, 'redShl works only with red numbers');
- return this.red.shl(this, num);
- };
-
- BN.prototype.redMul = function redMul (num) {
- assert(this.red, 'redMul works only with red numbers');
- this.red._verify2(this, num);
- return this.red.mul(this, num);
- };
-
- BN.prototype.redIMul = function redIMul (num) {
- assert(this.red, 'redMul works only with red numbers');
- this.red._verify2(this, num);
- return this.red.imul(this, num);
- };
-
- BN.prototype.redSqr = function redSqr () {
- assert(this.red, 'redSqr works only with red numbers');
- this.red._verify1(this);
- return this.red.sqr(this);
- };
-
- BN.prototype.redISqr = function redISqr () {
- assert(this.red, 'redISqr works only with red numbers');
- this.red._verify1(this);
- return this.red.isqr(this);
- };
-
- // Square root over p
- BN.prototype.redSqrt = function redSqrt () {
- assert(this.red, 'redSqrt works only with red numbers');
- this.red._verify1(this);
- return this.red.sqrt(this);
- };
-
- BN.prototype.redInvm = function redInvm () {
- assert(this.red, 'redInvm works only with red numbers');
- this.red._verify1(this);
- return this.red.invm(this);
- };
-
- // Return negative clone of `this` % `red modulo`
- BN.prototype.redNeg = function redNeg () {
- assert(this.red, 'redNeg works only with red numbers');
- this.red._verify1(this);
- return this.red.neg(this);
- };
-
- BN.prototype.redPow = function redPow (num) {
- assert(this.red && !num.red, 'redPow(normalNum)');
- this.red._verify1(this);
- return this.red.pow(this, num);
- };
-
- // Prime numbers with efficient reduction
- var primes = {
- k256: null,
- p224: null,
- p192: null,
- p25519: null
- };
-
- // Pseudo-Mersenne prime
- function MPrime (name, p) {
- // P = 2 ^ N - K
- this.name = name;
- this.p = new BN(p, 16);
- this.n = this.p.bitLength();
- this.k = new BN(1).iushln(this.n).isub(this.p);
-
- this.tmp = this._tmp();
- }
-
- MPrime.prototype._tmp = function _tmp () {
- var tmp = new BN(null);
- tmp.words = new Array(Math.ceil(this.n / 13));
- return tmp;
- };
-
- MPrime.prototype.ireduce = function ireduce (num) {
- // Assumes that `num` is less than `P^2`
- // num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P)
- var r = num;
- var rlen;
-
- do {
- this.split(r, this.tmp);
- r = this.imulK(r);
- r = r.iadd(this.tmp);
- rlen = r.bitLength();
- } while (rlen > this.n);
-
- var cmp = rlen < this.n ? -1 : r.ucmp(this.p);
- if (cmp === 0) {
- r.words[0] = 0;
- r.length = 1;
- } else if (cmp > 0) {
- r.isub(this.p);
- } else {
- r.strip();
- }
-
- return r;
- };
-
- MPrime.prototype.split = function split (input, out) {
- input.iushrn(this.n, 0, out);
- };
-
- MPrime.prototype.imulK = function imulK (num) {
- return num.imul(this.k);
- };
-
- function K256 () {
- MPrime.call(
- this,
- 'k256',
- 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f');
- }
- inherits(K256, MPrime);
-
- K256.prototype.split = function split (input, output) {
- // 256 = 9 * 26 + 22
- var mask = 0x3fffff;
-
- var outLen = Math.min(input.length, 9);
- for (var i = 0; i < outLen; i++) {
- output.words[i] = input.words[i];
- }
- output.length = outLen;
-
- if (input.length <= 9) {
- input.words[0] = 0;
- input.length = 1;
- return;
- }
-
- // Shift by 9 limbs
- var prev = input.words[9];
- output.words[output.length++] = prev & mask;
-
- for (i = 10; i < input.length; i++) {
- var next = input.words[i] | 0;
- input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22);
- prev = next;
- }
- prev >>>= 22;
- input.words[i - 10] = prev;
- if (prev === 0 && input.length > 10) {
- input.length -= 10;
- } else {
- input.length -= 9;
- }
- };
-
- K256.prototype.imulK = function imulK (num) {
- // K = 0x1000003d1 = [ 0x40, 0x3d1 ]
- num.words[num.length] = 0;
- num.words[num.length + 1] = 0;
- num.length += 2;
-
- // bounded at: 0x40 * 0x3ffffff + 0x3d0 = 0x100000390
- var lo = 0;
- for (var i = 0; i < num.length; i++) {
- var w = num.words[i] | 0;
- lo += w * 0x3d1;
- num.words[i] = lo & 0x3ffffff;
- lo = w * 0x40 + ((lo / 0x4000000) | 0);
- }
-
- // Fast length reduction
- if (num.words[num.length - 1] === 0) {
- num.length--;
- if (num.words[num.length - 1] === 0) {
- num.length--;
- }
- }
- return num;
- };
-
- function P224 () {
- MPrime.call(
- this,
- 'p224',
- 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001');
- }
- inherits(P224, MPrime);
-
- function P192 () {
- MPrime.call(
- this,
- 'p192',
- 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff');
- }
- inherits(P192, MPrime);
-
- function P25519 () {
- // 2 ^ 255 - 19
- MPrime.call(
- this,
- '25519',
- '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed');
- }
- inherits(P25519, MPrime);
-
- P25519.prototype.imulK = function imulK (num) {
- // K = 0x13
- var carry = 0;
- for (var i = 0; i < num.length; i++) {
- var hi = (num.words[i] | 0) * 0x13 + carry;
- var lo = hi & 0x3ffffff;
- hi >>>= 26;
-
- num.words[i] = lo;
- carry = hi;
- }
- if (carry !== 0) {
- num.words[num.length++] = carry;
- }
- return num;
- };
-
- // Exported mostly for testing purposes, use plain name instead
- BN._prime = function prime (name) {
- // Cached version of prime
- if (primes[name]) return primes[name];
-
- var prime;
- if (name === 'k256') {
- prime = new K256();
- } else if (name === 'p224') {
- prime = new P224();
- } else if (name === 'p192') {
- prime = new P192();
- } else if (name === 'p25519') {
- prime = new P25519();
- } else {
- throw new Error('Unknown prime ' + name);
- }
- primes[name] = prime;
-
- return prime;
- };
-
- //
- // Base reduction engine
- //
- function Red (m) {
- if (typeof m === 'string') {
- var prime = BN._prime(m);
- this.m = prime.p;
- this.prime = prime;
- } else {
- assert(m.gtn(1), 'modulus must be greater than 1');
- this.m = m;
- this.prime = null;
- }
- }
-
- Red.prototype._verify1 = function _verify1 (a) {
- assert(a.negative === 0, 'red works only with positives');
- assert(a.red, 'red works only with red numbers');
- };
-
- Red.prototype._verify2 = function _verify2 (a, b) {
- assert((a.negative | b.negative) === 0, 'red works only with positives');
- assert(a.red && a.red === b.red,
- 'red works only with red numbers');
- };
-
- Red.prototype.imod = function imod (a) {
- if (this.prime) return this.prime.ireduce(a)._forceRed(this);
- return a.umod(this.m)._forceRed(this);
- };
-
- Red.prototype.neg = function neg (a) {
- if (a.isZero()) {
- return a.clone();
- }
-
- return this.m.sub(a)._forceRed(this);
- };
-
- Red.prototype.add = function add (a, b) {
- this._verify2(a, b);
-
- var res = a.add(b);
- if (res.cmp(this.m) >= 0) {
- res.isub(this.m);
- }
- return res._forceRed(this);
- };
-
- Red.prototype.iadd = function iadd (a, b) {
- this._verify2(a, b);
-
- var res = a.iadd(b);
- if (res.cmp(this.m) >= 0) {
- res.isub(this.m);
- }
- return res;
- };
-
- Red.prototype.sub = function sub (a, b) {
- this._verify2(a, b);
-
- var res = a.sub(b);
- if (res.cmpn(0) < 0) {
- res.iadd(this.m);
- }
- return res._forceRed(this);
- };
-
- Red.prototype.isub = function isub (a, b) {
- this._verify2(a, b);
-
- var res = a.isub(b);
- if (res.cmpn(0) < 0) {
- res.iadd(this.m);
- }
- return res;
- };
-
- Red.prototype.shl = function shl (a, num) {
- this._verify1(a);
- return this.imod(a.ushln(num));
- };
-
- Red.prototype.imul = function imul (a, b) {
- this._verify2(a, b);
- return this.imod(a.imul(b));
- };
-
- Red.prototype.mul = function mul (a, b) {
- this._verify2(a, b);
- return this.imod(a.mul(b));
- };
-
- Red.prototype.isqr = function isqr (a) {
- return this.imul(a, a.clone());
- };
-
- Red.prototype.sqr = function sqr (a) {
- return this.mul(a, a);
- };
-
- Red.prototype.sqrt = function sqrt (a) {
- if (a.isZero()) return a.clone();
-
- var mod3 = this.m.andln(3);
- assert(mod3 % 2 === 1);
-
- // Fast case
- if (mod3 === 3) {
- var pow = this.m.add(new BN(1)).iushrn(2);
- return this.pow(a, pow);
- }
-
- // Tonelli-Shanks algorithm (Totally unoptimized and slow)
- //
- // Find Q and S, that Q * 2 ^ S = (P - 1)
- var q = this.m.subn(1);
- var s = 0;
- while (!q.isZero() && q.andln(1) === 0) {
- s++;
- q.iushrn(1);
- }
- assert(!q.isZero());
-
- var one = new BN(1).toRed(this);
- var nOne = one.redNeg();
-
- // Find quadratic non-residue
- // NOTE: Max is such because of generalized Riemann hypothesis.
- var lpow = this.m.subn(1).iushrn(1);
- var z = this.m.bitLength();
- z = new BN(2 * z * z).toRed(this);
-
- while (this.pow(z, lpow).cmp(nOne) !== 0) {
- z.redIAdd(nOne);
- }
-
- var c = this.pow(z, q);
- var r = this.pow(a, q.addn(1).iushrn(1));
- var t = this.pow(a, q);
- var m = s;
- while (t.cmp(one) !== 0) {
- var tmp = t;
- for (var i = 0; tmp.cmp(one) !== 0; i++) {
- tmp = tmp.redSqr();
- }
- assert(i < m);
- var b = this.pow(c, new BN(1).iushln(m - i - 1));
-
- r = r.redMul(b);
- c = b.redSqr();
- t = t.redMul(c);
- m = i;
- }
-
- return r;
- };
-
- Red.prototype.invm = function invm (a) {
- var inv = a._invmp(this.m);
- if (inv.negative !== 0) {
- inv.negative = 0;
- return this.imod(inv).redNeg();
- } else {
- return this.imod(inv);
- }
- };
-
- Red.prototype.pow = function pow (a, num) {
- if (num.isZero()) return new BN(1);
- if (num.cmpn(1) === 0) return a.clone();
-
- var windowSize = 4;
- var wnd = new Array(1 << windowSize);
- wnd[0] = new BN(1).toRed(this);
- wnd[1] = a;
- for (var i = 2; i < wnd.length; i++) {
- wnd[i] = this.mul(wnd[i - 1], a);
- }
-
- var res = wnd[0];
- var current = 0;
- var currentLen = 0;
- var start = num.bitLength() % 26;
- if (start === 0) {
- start = 26;
- }
-
- for (i = num.length - 1; i >= 0; i--) {
- var word = num.words[i];
- for (var j = start - 1; j >= 0; j--) {
- var bit = (word >> j) & 1;
- if (res !== wnd[0]) {
- res = this.sqr(res);
- }
-
- if (bit === 0 && current === 0) {
- currentLen = 0;
- continue;
- }
-
- current <<= 1;
- current |= bit;
- currentLen++;
- if (currentLen !== windowSize && (i !== 0 || j !== 0)) continue;
-
- res = this.mul(res, wnd[current]);
- currentLen = 0;
- current = 0;
- }
- start = 26;
- }
-
- return res;
- };
-
- Red.prototype.convertTo = function convertTo (num) {
- var r = num.umod(this.m);
-
- return r === num ? r.clone() : r;
- };
-
- Red.prototype.convertFrom = function convertFrom (num) {
- var res = num.clone();
- res.red = null;
- return res;
- };
-
- //
- // Montgomery method engine
- //
-
- BN.mont = function mont (num) {
- return new Mont(num);
- };
-
- function Mont (m) {
- Red.call(this, m);
-
- this.shift = this.m.bitLength();
- if (this.shift % 26 !== 0) {
- this.shift += 26 - (this.shift % 26);
- }
-
- this.r = new BN(1).iushln(this.shift);
- this.r2 = this.imod(this.r.sqr());
- this.rinv = this.r._invmp(this.m);
-
- this.minv = this.rinv.mul(this.r).isubn(1).div(this.m);
- this.minv = this.minv.umod(this.r);
- this.minv = this.r.sub(this.minv);
- }
- inherits(Mont, Red);
-
- Mont.prototype.convertTo = function convertTo (num) {
- return this.imod(num.ushln(this.shift));
- };
-
- Mont.prototype.convertFrom = function convertFrom (num) {
- var r = this.imod(num.mul(this.rinv));
- r.red = null;
- return r;
- };
-
- Mont.prototype.imul = function imul (a, b) {
- if (a.isZero() || b.isZero()) {
- a.words[0] = 0;
- a.length = 1;
- return a;
- }
-
- var t = a.imul(b);
- var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
- var u = t.isub(c).iushrn(this.shift);
- var res = u;
-
- if (u.cmp(this.m) >= 0) {
- res = u.isub(this.m);
- } else if (u.cmpn(0) < 0) {
- res = u.iadd(this.m);
- }
-
- return res._forceRed(this);
- };
-
- Mont.prototype.mul = function mul (a, b) {
- if (a.isZero() || b.isZero()) return new BN(0)._forceRed(this);
-
- var t = a.mul(b);
- var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
- var u = t.isub(c).iushrn(this.shift);
- var res = u;
- if (u.cmp(this.m) >= 0) {
- res = u.isub(this.m);
- } else if (u.cmpn(0) < 0) {
- res = u.iadd(this.m);
- }
-
- return res._forceRed(this);
- };
-
- Mont.prototype.invm = function invm (a) {
- // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
- var res = this.imod(a._invmp(this.m).mul(this.r2));
- return res._forceRed(this);
- };
-})(typeof module === 'undefined' || module, this);
-
-},{}],82:[function(require,module,exports){
-var r;
-
-module.exports = function rand(len) {
- if (!r)
- r = new Rand(null);
-
- return r.generate(len);
-};
-
-function Rand(rand) {
- this.rand = rand;
-}
-module.exports.Rand = Rand;
-
-Rand.prototype.generate = function generate(len) {
- return this._rand(len);
-};
-
-// Emulate crypto API using randy
-Rand.prototype._rand = function _rand(n) {
- if (this.rand.getBytes)
- return this.rand.getBytes(n);
-
- var res = new Uint8Array(n);
- for (var i = 0; i < res.length; i++)
- res[i] = this.rand.getByte();
- return res;
-};
-
-if (typeof self === 'object') {
- if (self.crypto && self.crypto.getRandomValues) {
- // Modern browsers
- Rand.prototype._rand = function _rand(n) {
- var arr = new Uint8Array(n);
- self.crypto.getRandomValues(arr);
- return arr;
- };
- } else if (self.msCrypto && self.msCrypto.getRandomValues) {
- // IE
- Rand.prototype._rand = function _rand(n) {
- var arr = new Uint8Array(n);
- self.msCrypto.getRandomValues(arr);
- return arr;
- };
-
- // Safari's WebWorkers do not have `crypto`
- } else if (typeof window === 'object') {
- // Old junk
- Rand.prototype._rand = function() {
- throw new Error('Not implemented yet');
- };
- }
-} else {
- // Node.js or Web worker with no crypto support
- try {
- var crypto = require('crypto');
- if (typeof crypto.randomBytes !== 'function')
- throw new Error('Not supported');
-
- Rand.prototype._rand = function _rand(n) {
- return crypto.randomBytes(n);
- };
- } catch (e) {
- }
-}
-
-},{"crypto":3}],83:[function(require,module,exports){
-var basex = require('base-x')
-var ALPHABET = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
-
-module.exports = basex(ALPHABET)
-
-},{"base-x":35}],84:[function(require,module,exports){
-(function (Buffer){
-'use strict'
-
-var base58 = require('bs58')
-
-module.exports = function (checksumFn) {
- // Encode a buffer as a base58-check encoded string
- function encode (payload) {
- var checksum = checksumFn(payload)
-
- return base58.encode(Buffer.concat([
- payload,
- checksum
- ], payload.length + 4))
- }
-
- function decodeRaw (buffer) {
- var payload = buffer.slice(0, -4)
- var checksum = buffer.slice(-4)
- var newChecksum = checksumFn(payload)
-
- if (checksum[0] ^ newChecksum[0] |
- checksum[1] ^ newChecksum[1] |
- checksum[2] ^ newChecksum[2] |
- checksum[3] ^ newChecksum[3]) return
-
- return payload
- }
-
- // Decode a base58-check encoded string to a buffer, no result if checksum is wrong
- function decodeUnsafe (string) {
- var buffer = base58.decodeUnsafe(string)
- if (!buffer) return
-
- return decodeRaw(buffer)
- }
-
- function decode (string) {
- var buffer = base58.decode(string)
- var payload = decodeRaw(buffer, checksumFn)
- if (!payload) throw new Error('Invalid checksum')
- return payload
- }
-
- return {
- encode: encode,
- decode: decode,
- decodeUnsafe: decodeUnsafe
- }
-}
-
-}).call(this,require("buffer").Buffer)
-},{"bs58":83,"buffer":5}],85:[function(require,module,exports){
-'use strict'
-
-var createHash = require('create-hash')
-var bs58checkBase = require('./base')
-
-// SHA256(SHA256(buffer))
-function sha256x2 (buffer) {
- var tmp = createHash('sha256').update(buffer).digest()
- return createHash('sha256').update(tmp).digest()
-}
-
-module.exports = bs58checkBase(sha256x2)
-
-},{"./base":84,"create-hash":87}],86:[function(require,module,exports){
-var Buffer = require('safe-buffer').Buffer
-var Transform = require('stream').Transform
-var StringDecoder = require('string_decoder').StringDecoder
-var inherits = require('inherits')
-
-function CipherBase (hashMode) {
- Transform.call(this)
- this.hashMode = typeof hashMode === 'string'
- if (this.hashMode) {
- this[hashMode] = this._finalOrDigest
- } else {
- this.final = this._finalOrDigest
- }
- if (this._final) {
- this.__final = this._final
- this._final = null
- }
- this._decoder = null
- this._encoding = null
-}
-inherits(CipherBase, Transform)
-
-CipherBase.prototype.update = function (data, inputEnc, outputEnc) {
- if (typeof data === 'string') {
- data = Buffer.from(data, inputEnc)
- }
-
- var outData = this._update(data)
- if (this.hashMode) return this
-
- if (outputEnc) {
- outData = this._toString(outData, outputEnc)
- }
-
- return outData
-}
-
-CipherBase.prototype.setAutoPadding = function () {}
-CipherBase.prototype.getAuthTag = function () {
- throw new Error('trying to get auth tag in unsupported state')
-}
-
-CipherBase.prototype.setAuthTag = function () {
- throw new Error('trying to set auth tag in unsupported state')
-}
-
-CipherBase.prototype.setAAD = function () {
- throw new Error('trying to set aad in unsupported state')
-}
-
-CipherBase.prototype._transform = function (data, _, next) {
- var err
- try {
- if (this.hashMode) {
- this._update(data)
- } else {
- this.push(this._update(data))
- }
- } catch (e) {
- err = e
- } finally {
- next(err)
- }
-}
-CipherBase.prototype._flush = function (done) {
- var err
- try {
- this.push(this.__final())
- } catch (e) {
- err = e
- }
-
- done(err)
-}
-CipherBase.prototype._finalOrDigest = function (outputEnc) {
- var outData = this.__final() || Buffer.alloc(0)
- if (outputEnc) {
- outData = this._toString(outData, outputEnc, true)
- }
- return outData
-}
-
-CipherBase.prototype._toString = function (value, enc, fin) {
- if (!this._decoder) {
- this._decoder = new StringDecoder(enc)
- this._encoding = enc
- }
-
- if (this._encoding !== enc) throw new Error('can\'t switch encodings')
-
- var out = this._decoder.write(value)
- if (fin) {
- out += this._decoder.end()
- }
-
- return out
-}
-
-module.exports = CipherBase
-
-},{"inherits":121,"safe-buffer":128,"stream":28,"string_decoder":29}],87:[function(require,module,exports){
-(function (Buffer){
-'use strict'
-var inherits = require('inherits')
-var md5 = require('./md5')
-var RIPEMD160 = require('ripemd160')
-var sha = require('sha.js')
-
-var Base = require('cipher-base')
-
-function HashNoConstructor (hash) {
- Base.call(this, 'digest')
-
- this._hash = hash
- this.buffers = []
-}
-
-inherits(HashNoConstructor, Base)
-
-HashNoConstructor.prototype._update = function (data) {
- this.buffers.push(data)
-}
-
-HashNoConstructor.prototype._final = function () {
- var buf = Buffer.concat(this.buffers)
- var r = this._hash(buf)
- this.buffers = null
-
- return r
-}
-
-function Hash (hash) {
- Base.call(this, 'digest')
-
- this._hash = hash
-}
-
-inherits(Hash, Base)
-
-Hash.prototype._update = function (data) {
- this._hash.update(data)
-}
-
-Hash.prototype._final = function () {
- return this._hash.digest()
-}
-
-module.exports = function createHash (alg) {
- alg = alg.toLowerCase()
- if (alg === 'md5') return new HashNoConstructor(md5)
- if (alg === 'rmd160' || alg === 'ripemd160') return new Hash(new RIPEMD160())
-
- return new Hash(sha(alg))
-}
-
-}).call(this,require("buffer").Buffer)
-},{"./md5":89,"buffer":5,"cipher-base":86,"inherits":121,"ripemd160":127,"sha.js":130}],88:[function(require,module,exports){
-(function (Buffer){
-'use strict'
-var intSize = 4
-var zeroBuffer = new Buffer(intSize)
-zeroBuffer.fill(0)
-
-var charSize = 8
-var hashSize = 16
-
-function toArray (buf) {
- if ((buf.length % intSize) !== 0) {
- var len = buf.length + (intSize - (buf.length % intSize))
- buf = Buffer.concat([buf, zeroBuffer], len)
- }
-
- var arr = new Array(buf.length >>> 2)
- for (var i = 0, j = 0; i < buf.length; i += intSize, j++) {
- arr[j] = buf.readInt32LE(i)
- }
-
- return arr
-}
-
-module.exports = function hash (buf, fn) {
- var arr = fn(toArray(buf), buf.length * charSize)
- buf = new Buffer(hashSize)
- for (var i = 0; i < arr.length; i++) {
- buf.writeInt32LE(arr[i], i << 2, true)
- }
- return buf
-}
-
-}).call(this,require("buffer").Buffer)
-},{"buffer":5}],89:[function(require,module,exports){
-'use strict'
-/*
- * A JavaScript implementation of the RSA Data Security, Inc. MD5 Message
- * Digest Algorithm, as defined in RFC 1321.
- * Version 2.1 Copyright (C) Paul Johnston 1999 - 2002.
- * Other contributors: Greg Holt, Andrew Kepert, Ydnar, Lostinet
- * Distributed under the BSD License
- * See http://pajhome.org.uk/crypt/md5 for more info.
- */
-
-var makeHash = require('./make-hash')
-
-/*
- * Calculate the MD5 of an array of little-endian words, and a bit length
- */
-function core_md5 (x, len) {
- /* append padding */
- x[len >> 5] |= 0x80 << ((len) % 32)
- x[(((len + 64) >>> 9) << 4) + 14] = len
-
- var a = 1732584193
- var b = -271733879
- var c = -1732584194
- var d = 271733878
-
- for (var i = 0; i < x.length; i += 16) {
- var olda = a
- var oldb = b
- var oldc = c
- var oldd = d
-
- a = md5_ff(a, b, c, d, x[i + 0], 7, -680876936)
- d = md5_ff(d, a, b, c, x[i + 1], 12, -389564586)
- c = md5_ff(c, d, a, b, x[i + 2], 17, 606105819)
- b = md5_ff(b, c, d, a, x[i + 3], 22, -1044525330)
- a = md5_ff(a, b, c, d, x[i + 4], 7, -176418897)
- d = md5_ff(d, a, b, c, x[i + 5], 12, 1200080426)
- c = md5_ff(c, d, a, b, x[i + 6], 17, -1473231341)
- b = md5_ff(b, c, d, a, x[i + 7], 22, -45705983)
- a = md5_ff(a, b, c, d, x[i + 8], 7, 1770035416)
- d = md5_ff(d, a, b, c, x[i + 9], 12, -1958414417)
- c = md5_ff(c, d, a, b, x[i + 10], 17, -42063)
- b = md5_ff(b, c, d, a, x[i + 11], 22, -1990404162)
- a = md5_ff(a, b, c, d, x[i + 12], 7, 1804603682)
- d = md5_ff(d, a, b, c, x[i + 13], 12, -40341101)
- c = md5_ff(c, d, a, b, x[i + 14], 17, -1502002290)
- b = md5_ff(b, c, d, a, x[i + 15], 22, 1236535329)
-
- a = md5_gg(a, b, c, d, x[i + 1], 5, -165796510)
- d = md5_gg(d, a, b, c, x[i + 6], 9, -1069501632)
- c = md5_gg(c, d, a, b, x[i + 11], 14, 643717713)
- b = md5_gg(b, c, d, a, x[i + 0], 20, -373897302)
- a = md5_gg(a, b, c, d, x[i + 5], 5, -701558691)
- d = md5_gg(d, a, b, c, x[i + 10], 9, 38016083)
- c = md5_gg(c, d, a, b, x[i + 15], 14, -660478335)
- b = md5_gg(b, c, d, a, x[i + 4], 20, -405537848)
- a = md5_gg(a, b, c, d, x[i + 9], 5, 568446438)
- d = md5_gg(d, a, b, c, x[i + 14], 9, -1019803690)
- c = md5_gg(c, d, a, b, x[i + 3], 14, -187363961)
- b = md5_gg(b, c, d, a, x[i + 8], 20, 1163531501)
- a = md5_gg(a, b, c, d, x[i + 13], 5, -1444681467)
- d = md5_gg(d, a, b, c, x[i + 2], 9, -51403784)
- c = md5_gg(c, d, a, b, x[i + 7], 14, 1735328473)
- b = md5_gg(b, c, d, a, x[i + 12], 20, -1926607734)
-
- a = md5_hh(a, b, c, d, x[i + 5], 4, -378558)
- d = md5_hh(d, a, b, c, x[i + 8], 11, -2022574463)
- c = md5_hh(c, d, a, b, x[i + 11], 16, 1839030562)
- b = md5_hh(b, c, d, a, x[i + 14], 23, -35309556)
- a = md5_hh(a, b, c, d, x[i + 1], 4, -1530992060)
- d = md5_hh(d, a, b, c, x[i + 4], 11, 1272893353)
- c = md5_hh(c, d, a, b, x[i + 7], 16, -155497632)
- b = md5_hh(b, c, d, a, x[i + 10], 23, -1094730640)
- a = md5_hh(a, b, c, d, x[i + 13], 4, 681279174)
- d = md5_hh(d, a, b, c, x[i + 0], 11, -358537222)
- c = md5_hh(c, d, a, b, x[i + 3], 16, -722521979)
- b = md5_hh(b, c, d, a, x[i + 6], 23, 76029189)
- a = md5_hh(a, b, c, d, x[i + 9], 4, -640364487)
- d = md5_hh(d, a, b, c, x[i + 12], 11, -421815835)
- c = md5_hh(c, d, a, b, x[i + 15], 16, 530742520)
- b = md5_hh(b, c, d, a, x[i + 2], 23, -995338651)
-
- a = md5_ii(a, b, c, d, x[i + 0], 6, -198630844)
- d = md5_ii(d, a, b, c, x[i + 7], 10, 1126891415)
- c = md5_ii(c, d, a, b, x[i + 14], 15, -1416354905)
- b = md5_ii(b, c, d, a, x[i + 5], 21, -57434055)
- a = md5_ii(a, b, c, d, x[i + 12], 6, 1700485571)
- d = md5_ii(d, a, b, c, x[i + 3], 10, -1894986606)
- c = md5_ii(c, d, a, b, x[i + 10], 15, -1051523)
- b = md5_ii(b, c, d, a, x[i + 1], 21, -2054922799)
- a = md5_ii(a, b, c, d, x[i + 8], 6, 1873313359)
- d = md5_ii(d, a, b, c, x[i + 15], 10, -30611744)
- c = md5_ii(c, d, a, b, x[i + 6], 15, -1560198380)
- b = md5_ii(b, c, d, a, x[i + 13], 21, 1309151649)
- a = md5_ii(a, b, c, d, x[i + 4], 6, -145523070)
- d = md5_ii(d, a, b, c, x[i + 11], 10, -1120210379)
- c = md5_ii(c, d, a, b, x[i + 2], 15, 718787259)
- b = md5_ii(b, c, d, a, x[i + 9], 21, -343485551)
-
- a = safe_add(a, olda)
- b = safe_add(b, oldb)
- c = safe_add(c, oldc)
- d = safe_add(d, oldd)
- }
-
- return [a, b, c, d]
-}
-
-/*
- * These functions implement the four basic operations the algorithm uses.
- */
-function md5_cmn (q, a, b, x, s, t) {
- return safe_add(bit_rol(safe_add(safe_add(a, q), safe_add(x, t)), s), b)
-}
-
-function md5_ff (a, b, c, d, x, s, t) {
- return md5_cmn((b & c) | ((~b) & d), a, b, x, s, t)
-}
-
-function md5_gg (a, b, c, d, x, s, t) {
- return md5_cmn((b & d) | (c & (~d)), a, b, x, s, t)
-}
-
-function md5_hh (a, b, c, d, x, s, t) {
- return md5_cmn(b ^ c ^ d, a, b, x, s, t)
-}
-
-function md5_ii (a, b, c, d, x, s, t) {
- return md5_cmn(c ^ (b | (~d)), a, b, x, s, t)
-}
-
-/*
- * Add integers, wrapping at 2^32. This uses 16-bit operations internally
- * to work around bugs in some JS interpreters.
- */
-function safe_add (x, y) {
- var lsw = (x & 0xFFFF) + (y & 0xFFFF)
- var msw = (x >> 16) + (y >> 16) + (lsw >> 16)
- return (msw << 16) | (lsw & 0xFFFF)
-}
-
-/*
- * Bitwise rotate a 32-bit number to the left.
- */
-function bit_rol (num, cnt) {
- return (num << cnt) | (num >>> (32 - cnt))
-}
-
-module.exports = function md5 (buf) {
- return makeHash(buf, core_md5)
-}
-
-},{"./make-hash":88}],90:[function(require,module,exports){
-'use strict'
-var inherits = require('inherits')
-var Legacy = require('./legacy')
-var Base = require('cipher-base')
-var Buffer = require('safe-buffer').Buffer
-var md5 = require('create-hash/md5')
-var RIPEMD160 = require('ripemd160')
-
-var sha = require('sha.js')
-
-var ZEROS = Buffer.alloc(128)
-
-function Hmac (alg, key) {
- Base.call(this, 'digest')
- if (typeof key === 'string') {
- key = Buffer.from(key)
- }
-
- var blocksize = (alg === 'sha512' || alg === 'sha384') ? 128 : 64
-
- this._alg = alg
- this._key = key
- if (key.length > blocksize) {
- var hash = alg === 'rmd160' ? new RIPEMD160() : sha(alg)
- key = hash.update(key).digest()
- } else if (key.length < blocksize) {
- key = Buffer.concat([key, ZEROS], blocksize)
- }
-
- var ipad = this._ipad = Buffer.allocUnsafe(blocksize)
- var opad = this._opad = Buffer.allocUnsafe(blocksize)
-
- for (var i = 0; i < blocksize; i++) {
- ipad[i] = key[i] ^ 0x36
- opad[i] = key[i] ^ 0x5C
- }
- this._hash = alg === 'rmd160' ? new RIPEMD160() : sha(alg)
- this._hash.update(ipad)
-}
-
-inherits(Hmac, Base)
-
-Hmac.prototype._update = function (data) {
- this._hash.update(data)
-}
-
-Hmac.prototype._final = function () {
- var h = this._hash.digest()
- var hash = this._alg === 'rmd160' ? new RIPEMD160() : sha(this._alg)
- return hash.update(this._opad).update(h).digest()
-}
-
-module.exports = function createHmac (alg, key) {
- alg = alg.toLowerCase()
- if (alg === 'rmd160' || alg === 'ripemd160') {
- return new Hmac('rmd160', key)
- }
- if (alg === 'md5') {
- return new Legacy(md5, key)
- }
- return new Hmac(alg, key)
-}
-
-},{"./legacy":91,"cipher-base":86,"create-hash/md5":89,"inherits":121,"ripemd160":127,"safe-buffer":128,"sha.js":130}],91:[function(require,module,exports){
-'use strict'
-var inherits = require('inherits')
-var Buffer = require('safe-buffer').Buffer
-
-var Base = require('cipher-base')
-
-var ZEROS = Buffer.alloc(128)
-var blocksize = 64
-
-function Hmac (alg, key) {
- Base.call(this, 'digest')
- if (typeof key === 'string') {
- key = Buffer.from(key)
- }
-
- this._alg = alg
- this._key = key
-
- if (key.length > blocksize) {
- key = alg(key)
- } else if (key.length < blocksize) {
- key = Buffer.concat([key, ZEROS], blocksize)
- }
-
- var ipad = this._ipad = Buffer.allocUnsafe(blocksize)
- var opad = this._opad = Buffer.allocUnsafe(blocksize)
-
- for (var i = 0; i < blocksize; i++) {
- ipad[i] = key[i] ^ 0x36
- opad[i] = key[i] ^ 0x5C
- }
-
- this._hash = [ipad]
-}
-
-inherits(Hmac, Base)
-
-Hmac.prototype._update = function (data) {
- this._hash.push(data)
-}
-
-Hmac.prototype._final = function () {
- var h = this._alg(Buffer.concat(this._hash))
- return this._alg(Buffer.concat([this._opad, h]))
-}
-module.exports = Hmac
-
-},{"cipher-base":86,"inherits":121,"safe-buffer":128}],92:[function(require,module,exports){
-var assert = require('assert')
-var BigInteger = require('bigi')
-
-var Point = require('./point')
-
-function Curve (p, a, b, Gx, Gy, n, h) {
- this.p = p
- this.a = a
- this.b = b
- this.G = Point.fromAffine(this, Gx, Gy)
- this.n = n
- this.h = h
-
- this.infinity = new Point(this, null, null, BigInteger.ZERO)
-
- // result caching
- this.pOverFour = p.add(BigInteger.ONE).shiftRight(2)
-
- // determine size of p in bytes
- this.pLength = Math.floor((this.p.bitLength() + 7) / 8)
-}
-
-Curve.prototype.pointFromX = function (isOdd, x) {
- var alpha = x.pow(3).add(this.a.multiply(x)).add(this.b).mod(this.p)
- var beta = alpha.modPow(this.pOverFour, this.p) // XXX: not compatible with all curves
-
- var y = beta
- if (beta.isEven() ^ !isOdd) {
- y = this.p.subtract(y) // -y % p
- }
-
- return Point.fromAffine(this, x, y)
-}
-
-Curve.prototype.isInfinity = function (Q) {
- if (Q === this.infinity) return true
-
- return Q.z.signum() === 0 && Q.y.signum() !== 0
-}
-
-Curve.prototype.isOnCurve = function (Q) {
- if (this.isInfinity(Q)) return true
-
- var x = Q.affineX
- var y = Q.affineY
- var a = this.a
- var b = this.b
- var p = this.p
-
- // Check that xQ and yQ are integers in the interval [0, p - 1]
- if (x.signum() < 0 || x.compareTo(p) >= 0) return false
- if (y.signum() < 0 || y.compareTo(p) >= 0) return false
-
- // and check that y^2 = x^3 + ax + b (mod p)
- var lhs = y.square().mod(p)
- var rhs = x.pow(3).add(a.multiply(x)).add(b).mod(p)
- return lhs.equals(rhs)
-}
-
-/**
- * Validate an elliptic curve point.
- *
- * See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive
- */
-Curve.prototype.validate = function (Q) {
- // Check Q != O
- assert(!this.isInfinity(Q), 'Point is at infinity')
- assert(this.isOnCurve(Q), 'Point is not on the curve')
-
- // Check nQ = O (where Q is a scalar multiple of G)
- var nQ = Q.multiply(this.n)
- assert(this.isInfinity(nQ), 'Point is not a scalar multiple of G')
-
- return true
-}
-
-module.exports = Curve
-
-},{"./point":96,"assert":1,"bigi":39}],93:[function(require,module,exports){
-module.exports={
- "secp128r1": {
- "p": "fffffffdffffffffffffffffffffffff",
- "a": "fffffffdfffffffffffffffffffffffc",
- "b": "e87579c11079f43dd824993c2cee5ed3",
- "n": "fffffffe0000000075a30d1b9038a115",
- "h": "01",
- "Gx": "161ff7528b899b2d0c28607ca52c5b86",
- "Gy": "cf5ac8395bafeb13c02da292dded7a83"
- },
- "secp160k1": {
- "p": "fffffffffffffffffffffffffffffffeffffac73",
- "a": "00",
- "b": "07",
- "n": "0100000000000000000001b8fa16dfab9aca16b6b3",
- "h": "01",
- "Gx": "3b4c382ce37aa192a4019e763036f4f5dd4d7ebb",
- "Gy": "938cf935318fdced6bc28286531733c3f03c4fee"
- },
- "secp160r1": {
- "p": "ffffffffffffffffffffffffffffffff7fffffff",
- "a": "ffffffffffffffffffffffffffffffff7ffffffc",
- "b": "1c97befc54bd7a8b65acf89f81d4d4adc565fa45",
- "n": "0100000000000000000001f4c8f927aed3ca752257",
- "h": "01",
- "Gx": "4a96b5688ef573284664698968c38bb913cbfc82",
- "Gy": "23a628553168947d59dcc912042351377ac5fb32"
- },
- "secp192k1": {
- "p": "fffffffffffffffffffffffffffffffffffffffeffffee37",
- "a": "00",
- "b": "03",
- "n": "fffffffffffffffffffffffe26f2fc170f69466a74defd8d",
- "h": "01",
- "Gx": "db4ff10ec057e9ae26b07d0280b7f4341da5d1b1eae06c7d",
- "Gy": "9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d"
- },
- "secp192r1": {
- "p": "fffffffffffffffffffffffffffffffeffffffffffffffff",
- "a": "fffffffffffffffffffffffffffffffefffffffffffffffc",
- "b": "64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1",
- "n": "ffffffffffffffffffffffff99def836146bc9b1b4d22831",
- "h": "01",
- "Gx": "188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012",
- "Gy": "07192b95ffc8da78631011ed6b24cdd573f977a11e794811"
- },
- "secp256k1": {
- "p": "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f",
- "a": "00",
- "b": "07",
- "n": "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141",
- "h": "01",
- "Gx": "79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
- "Gy": "483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8"
- },
- "secp256r1": {
- "p": "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
- "a": "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc",
- "b": "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b",
- "n": "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551",
- "h": "01",
- "Gx": "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296",
- "Gy": "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"
- }
-}
-
-},{}],94:[function(require,module,exports){
-var Point = require('./point')
-var Curve = require('./curve')
-
-var getCurveByName = require('./names')
-
-module.exports = {
- Curve: Curve,
- Point: Point,
- getCurveByName: getCurveByName
-}
-
-},{"./curve":92,"./names":95,"./point":96}],95:[function(require,module,exports){
-var BigInteger = require('bigi')
-
-var curves = require('./curves.json')
-var Curve = require('./curve')
-
-function getCurveByName (name) {
- var curve = curves[name]
- if (!curve) return null
-
- var p = new BigInteger(curve.p, 16)
- var a = new BigInteger(curve.a, 16)
- var b = new BigInteger(curve.b, 16)
- var n = new BigInteger(curve.n, 16)
- var h = new BigInteger(curve.h, 16)
- var Gx = new BigInteger(curve.Gx, 16)
- var Gy = new BigInteger(curve.Gy, 16)
-
- return new Curve(p, a, b, Gx, Gy, n, h)
-}
-
-module.exports = getCurveByName
-
-},{"./curve":92,"./curves.json":93,"bigi":39}],96:[function(require,module,exports){
-(function (Buffer){
-var assert = require('assert')
-var BigInteger = require('bigi')
-
-var THREE = BigInteger.valueOf(3)
-
-function Point (curve, x, y, z) {
- assert.notStrictEqual(z, undefined, 'Missing Z coordinate')
-
- this.curve = curve
- this.x = x
- this.y = y
- this.z = z
- this._zInv = null
-
- this.compressed = true
-}
-
-Object.defineProperty(Point.prototype, 'zInv', {
- get: function () {
- if (this._zInv === null) {
- this._zInv = this.z.modInverse(this.curve.p)
- }
-
- return this._zInv
- }
-})
-
-Object.defineProperty(Point.prototype, 'affineX', {
- get: function () {
- return this.x.multiply(this.zInv).mod(this.curve.p)
- }
-})
-
-Object.defineProperty(Point.prototype, 'affineY', {
- get: function () {
- return this.y.multiply(this.zInv).mod(this.curve.p)
- }
-})
-
-Point.fromAffine = function (curve, x, y) {
- return new Point(curve, x, y, BigInteger.ONE)
-}
-
-Point.prototype.equals = function (other) {
- if (other === this) return true
- if (this.curve.isInfinity(this)) return this.curve.isInfinity(other)
- if (this.curve.isInfinity(other)) return this.curve.isInfinity(this)
-
- // u = Y2 * Z1 - Y1 * Z2
- var u = other.y.multiply(this.z).subtract(this.y.multiply(other.z)).mod(this.curve.p)
-
- if (u.signum() !== 0) return false
-
- // v = X2 * Z1 - X1 * Z2
- var v = other.x.multiply(this.z).subtract(this.x.multiply(other.z)).mod(this.curve.p)
-
- return v.signum() === 0
-}
-
-Point.prototype.negate = function () {
- var y = this.curve.p.subtract(this.y)
-
- return new Point(this.curve, this.x, y, this.z)
-}
-
-Point.prototype.add = function (b) {
- if (this.curve.isInfinity(this)) return b
- if (this.curve.isInfinity(b)) return this
-
- var x1 = this.x
- var y1 = this.y
- var x2 = b.x
- var y2 = b.y
-
- // u = Y2 * Z1 - Y1 * Z2
- var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.p)
- // v = X2 * Z1 - X1 * Z2
- var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.p)
-
- if (v.signum() === 0) {
- if (u.signum() === 0) {
- return this.twice() // this == b, so double
- }
-
- return this.curve.infinity // this = -b, so infinity
- }
-
- var v2 = v.square()
- var v3 = v2.multiply(v)
- var x1v2 = x1.multiply(v2)
- var zu2 = u.square().multiply(this.z)
-
- // x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
- var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.p)
- // y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
- var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.p)
- // z3 = v^3 * z1 * z2
- var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.p)
-
- return new Point(this.curve, x3, y3, z3)
-}
-
-Point.prototype.twice = function () {
- if (this.curve.isInfinity(this)) return this
- if (this.y.signum() === 0) return this.curve.infinity
-
- var x1 = this.x
- var y1 = this.y
-
- var y1z1 = y1.multiply(this.z).mod(this.curve.p)
- var y1sqz1 = y1z1.multiply(y1).mod(this.curve.p)
- var a = this.curve.a
-
- // w = 3 * x1^2 + a * z1^2
- var w = x1.square().multiply(THREE)
-
- if (a.signum() !== 0) {
- w = w.add(this.z.square().multiply(a))
- }
-
- w = w.mod(this.curve.p)
- // x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
- var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.p)
- // y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
- var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.p)
- // z3 = 8 * (y1 * z1)^3
- var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.p)
-
- return new Point(this.curve, x3, y3, z3)
-}
-
-// Simple NAF (Non-Adjacent Form) multiplication algorithm
-// TODO: modularize the multiplication algorithm
-Point.prototype.multiply = function (k) {
- if (this.curve.isInfinity(this)) return this
- if (k.signum() === 0) return this.curve.infinity
-
- var e = k
- var h = e.multiply(THREE)
-
- var neg = this.negate()
- var R = this
-
- for (var i = h.bitLength() - 2; i > 0; --i) {
- var hBit = h.testBit(i)
- var eBit = e.testBit(i)
-
- R = R.twice()
-
- if (hBit !== eBit) {
- R = R.add(hBit ? this : neg)
- }
- }
-
- return R
-}
-
-// Compute this*j + x*k (simultaneous multiplication)
-Point.prototype.multiplyTwo = function (j, x, k) {
- var i = Math.max(j.bitLength(), k.bitLength()) - 1
- var R = this.curve.infinity
- var both = this.add(x)
-
- while (i >= 0) {
- var jBit = j.testBit(i)
- var kBit = k.testBit(i)
-
- R = R.twice()
-
- if (jBit) {
- if (kBit) {
- R = R.add(both)
- } else {
- R = R.add(this)
- }
- } else if (kBit) {
- R = R.add(x)
- }
- --i
- }
-
- return R
-}
-
-Point.prototype.getEncoded = function (compressed) {
- if (compressed == null) compressed = this.compressed
- if (this.curve.isInfinity(this)) return new Buffer('00', 'hex') // Infinity point encoded is simply '00'
-
- var x = this.affineX
- var y = this.affineY
- var byteLength = this.curve.pLength
- var buffer
-
- // 0x02/0x03 | X
- if (compressed) {
- buffer = new Buffer(1 + byteLength)
- buffer.writeUInt8(y.isEven() ? 0x02 : 0x03, 0)
-
- // 0x04 | X | Y
- } else {
- buffer = new Buffer(1 + byteLength + byteLength)
- buffer.writeUInt8(0x04, 0)
-
- y.toBuffer(byteLength).copy(buffer, 1 + byteLength)
- }
-
- x.toBuffer(byteLength).copy(buffer, 1)
-
- return buffer
-}
-
-Point.decodeFrom = function (curve, buffer) {
- var type = buffer.readUInt8(0)
- var compressed = (type !== 4)
-
- var byteLength = Math.floor((curve.p.bitLength() + 7) / 8)
- var x = BigInteger.fromBuffer(buffer.slice(1, 1 + byteLength))
-
- var Q
- if (compressed) {
- assert.equal(buffer.length, byteLength + 1, 'Invalid sequence length')
- assert(type === 0x02 || type === 0x03, 'Invalid sequence tag')
-
- var isOdd = (type === 0x03)
- Q = curve.pointFromX(isOdd, x)
- } else {
- assert.equal(buffer.length, 1 + byteLength + byteLength, 'Invalid sequence length')
-
- var y = BigInteger.fromBuffer(buffer.slice(1 + byteLength))
- Q = Point.fromAffine(curve, x, y)
- }
-
- Q.compressed = compressed
- return Q
-}
-
-Point.prototype.toString = function () {
- if (this.curve.isInfinity(this)) return '(INFINITY)'
-
- return '(' + this.affineX.toString() + ',' + this.affineY.toString() + ')'
-}
-
-module.exports = Point
-
-}).call(this,require("buffer").Buffer)
-},{"assert":1,"bigi":39,"buffer":5}],97:[function(require,module,exports){
-'use strict';
-
-var elliptic = exports;
-
-elliptic.version = require('../package.json').version;
-elliptic.utils = require('./elliptic/utils');
-elliptic.rand = require('brorand');
-elliptic.curve = require('./elliptic/curve');
-elliptic.curves = require('./elliptic/curves');
-
-// Protocols
-elliptic.ec = require('./elliptic/ec');
-elliptic.eddsa = require('./elliptic/eddsa');
-
-},{"../package.json":112,"./elliptic/curve":100,"./elliptic/curves":103,"./elliptic/ec":104,"./elliptic/eddsa":107,"./elliptic/utils":111,"brorand":82}],98:[function(require,module,exports){
-'use strict';
-
-var BN = require('bn.js');
-var elliptic = require('../../elliptic');
-var utils = elliptic.utils;
-var getNAF = utils.getNAF;
-var getJSF = utils.getJSF;
-var assert = utils.assert;
-
-function BaseCurve(type, conf) {
- this.type = type;
- this.p = new BN(conf.p, 16);
-
- // Use Montgomery, when there is no fast reduction for the prime
- this.red = conf.prime ? BN.red(conf.prime) : BN.mont(this.p);
-
- // Useful for many curves
- this.zero = new BN(0).toRed(this.red);
- this.one = new BN(1).toRed(this.red);
- this.two = new BN(2).toRed(this.red);
-
- // Curve configuration, optional
- this.n = conf.n && new BN(conf.n, 16);
- this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed);
-
- // Temporary arrays
- this._wnafT1 = new Array(4);
- this._wnafT2 = new Array(4);
- this._wnafT3 = new Array(4);
- this._wnafT4 = new Array(4);
-
- // Generalized Greg Maxwell's trick
- var adjustCount = this.n && this.p.div(this.n);
- if (!adjustCount || adjustCount.cmpn(100) > 0) {
- this.redN = null;
- } else {
- this._maxwellTrick = true;
- this.redN = this.n.toRed(this.red);
- }
-}
-module.exports = BaseCurve;
-
-BaseCurve.prototype.point = function point() {
- throw new Error('Not implemented');
-};
-
-BaseCurve.prototype.validate = function validate() {
- throw new Error('Not implemented');
-};
-
-BaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) {
- assert(p.precomputed);
- var doubles = p._getDoubles();
-
- var naf = getNAF(k, 1);
- var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);
- I /= 3;
-
- // Translate into more windowed form
- var repr = [];
- for (var j = 0; j < naf.length; j += doubles.step) {
- var nafW = 0;
- for (var k = j + doubles.step - 1; k >= j; k--)
- nafW = (nafW << 1) + naf[k];
- repr.push(nafW);
- }
-
- var a = this.jpoint(null, null, null);
- var b = this.jpoint(null, null, null);
- for (var i = I; i > 0; i--) {
- for (var j = 0; j < repr.length; j++) {
- var nafW = repr[j];
- if (nafW === i)
- b = b.mixedAdd(doubles.points[j]);
- else if (nafW === -i)
- b = b.mixedAdd(doubles.points[j].neg());
- }
- a = a.add(b);
- }
- return a.toP();
-};
-
-BaseCurve.prototype._wnafMul = function _wnafMul(p, k) {
- var w = 4;
-
- // Precompute window
- var nafPoints = p._getNAFPoints(w);
- w = nafPoints.wnd;
- var wnd = nafPoints.points;
-
- // Get NAF form
- var naf = getNAF(k, w);
-
- // Add `this`*(N+1) for every w-NAF index
- var acc = this.jpoint(null, null, null);
- for (var i = naf.length - 1; i >= 0; i--) {
- // Count zeroes
- for (var k = 0; i >= 0 && naf[i] === 0; i--)
- k++;
- if (i >= 0)
- k++;
- acc = acc.dblp(k);
-
- if (i < 0)
- break;
- var z = naf[i];
- assert(z !== 0);
- if (p.type === 'affine') {
- // J +- P
- if (z > 0)
- acc = acc.mixedAdd(wnd[(z - 1) >> 1]);
- else
- acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg());
- } else {
- // J +- J
- if (z > 0)
- acc = acc.add(wnd[(z - 1) >> 1]);
- else
- acc = acc.add(wnd[(-z - 1) >> 1].neg());
- }
- }
- return p.type === 'affine' ? acc.toP() : acc;
-};
-
-BaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW,
- points,
- coeffs,
- len,
- jacobianResult) {
- var wndWidth = this._wnafT1;
- var wnd = this._wnafT2;
- var naf = this._wnafT3;
-
- // Fill all arrays
- var max = 0;
- for (var i = 0; i < len; i++) {
- var p = points[i];
- var nafPoints = p._getNAFPoints(defW);
- wndWidth[i] = nafPoints.wnd;
- wnd[i] = nafPoints.points;
- }
-
- // Comb small window NAFs
- for (var i = len - 1; i >= 1; i -= 2) {
- var a = i - 1;
- var b = i;
- if (wndWidth[a] !== 1 || wndWidth[b] !== 1) {
- naf[a] = getNAF(coeffs[a], wndWidth[a]);
- naf[b] = getNAF(coeffs[b], wndWidth[b]);
- max = Math.max(naf[a].length, max);
- max = Math.max(naf[b].length, max);
- continue;
- }
-
- var comb = [
- points[a], /* 1 */
- null, /* 3 */
- null, /* 5 */
- points[b] /* 7 */
- ];
-
- // Try to avoid Projective points, if possible
- if (points[a].y.cmp(points[b].y) === 0) {
- comb[1] = points[a].add(points[b]);
- comb[2] = points[a].toJ().mixedAdd(points[b].neg());
- } else if (points[a].y.cmp(points[b].y.redNeg()) === 0) {
- comb[1] = points[a].toJ().mixedAdd(points[b]);
- comb[2] = points[a].add(points[b].neg());
- } else {
- comb[1] = points[a].toJ().mixedAdd(points[b]);
- comb[2] = points[a].toJ().mixedAdd(points[b].neg());
- }
-
- var index = [
- -3, /* -1 -1 */
- -1, /* -1 0 */
- -5, /* -1 1 */
- -7, /* 0 -1 */
- 0, /* 0 0 */
- 7, /* 0 1 */
- 5, /* 1 -1 */
- 1, /* 1 0 */
- 3 /* 1 1 */
- ];
-
- var jsf = getJSF(coeffs[a], coeffs[b]);
- max = Math.max(jsf[0].length, max);
- naf[a] = new Array(max);
- naf[b] = new Array(max);
- for (var j = 0; j < max; j++) {
- var ja = jsf[0][j] | 0;
- var jb = jsf[1][j] | 0;
-
- naf[a][j] = index[(ja + 1) * 3 + (jb + 1)];
- naf[b][j] = 0;
- wnd[a] = comb;
- }
- }
-
- var acc = this.jpoint(null, null, null);
- var tmp = this._wnafT4;
- for (var i = max; i >= 0; i--) {
- var k = 0;
-
- while (i >= 0) {
- var zero = true;
- for (var j = 0; j < len; j++) {
- tmp[j] = naf[j][i] | 0;
- if (tmp[j] !== 0)
- zero = false;
- }
- if (!zero)
- break;
- k++;
- i--;
- }
- if (i >= 0)
- k++;
- acc = acc.dblp(k);
- if (i < 0)
- break;
-
- for (var j = 0; j < len; j++) {
- var z = tmp[j];
- var p;
- if (z === 0)
- continue;
- else if (z > 0)
- p = wnd[j][(z - 1) >> 1];
- else if (z < 0)
- p = wnd[j][(-z - 1) >> 1].neg();
-
- if (p.type === 'affine')
- acc = acc.mixedAdd(p);
- else
- acc = acc.add(p);
- }
- }
- // Zeroify references
- for (var i = 0; i < len; i++)
- wnd[i] = null;
-
- if (jacobianResult)
- return acc;
- else
- return acc.toP();
-};
-
-function BasePoint(curve, type) {
- this.curve = curve;
- this.type = type;
- this.precomputed = null;
-}
-BaseCurve.BasePoint = BasePoint;
-
-BasePoint.prototype.eq = function eq(/*other*/) {
- throw new Error('Not implemented');
-};
-
-BasePoint.prototype.validate = function validate() {
- return this.curve.validate(this);
-};
-
-BaseCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
- bytes = utils.toArray(bytes, enc);
-
- var len = this.p.byteLength();
-
- // uncompressed, hybrid-odd, hybrid-even
- if ((bytes[0] === 0x04 || bytes[0] === 0x06 || bytes[0] === 0x07) &&
- bytes.length - 1 === 2 * len) {
- if (bytes[0] === 0x06)
- assert(bytes[bytes.length - 1] % 2 === 0);
- else if (bytes[0] === 0x07)
- assert(bytes[bytes.length - 1] % 2 === 1);
-
- var res = this.point(bytes.slice(1, 1 + len),
- bytes.slice(1 + len, 1 + 2 * len));
-
- return res;
- } else if ((bytes[0] === 0x02 || bytes[0] === 0x03) &&
- bytes.length - 1 === len) {
- return this.pointFromX(bytes.slice(1, 1 + len), bytes[0] === 0x03);
- }
- throw new Error('Unknown point format');
-};
-
-BasePoint.prototype.encodeCompressed = function encodeCompressed(enc) {
- return this.encode(enc, true);
-};
-
-BasePoint.prototype._encode = function _encode(compact) {
- var len = this.curve.p.byteLength();
- var x = this.getX().toArray('be', len);
-
- if (compact)
- return [ this.getY().isEven() ? 0x02 : 0x03 ].concat(x);
-
- return [ 0x04 ].concat(x, this.getY().toArray('be', len)) ;
-};
-
-BasePoint.prototype.encode = function encode(enc, compact) {
- return utils.encode(this._encode(compact), enc);
-};
-
-BasePoint.prototype.precompute = function precompute(power) {
- if (this.precomputed)
- return this;
-
- var precomputed = {
- doubles: null,
- naf: null,
- beta: null
- };
- precomputed.naf = this._getNAFPoints(8);
- precomputed.doubles = this._getDoubles(4, power);
- precomputed.beta = this._getBeta();
- this.precomputed = precomputed;
-
- return this;
-};
-
-BasePoint.prototype._hasDoubles = function _hasDoubles(k) {
- if (!this.precomputed)
- return false;
-
- var doubles = this.precomputed.doubles;
- if (!doubles)
- return false;
-
- return doubles.points.length >= Math.ceil((k.bitLength() + 1) / doubles.step);
-};
-
-BasePoint.prototype._getDoubles = function _getDoubles(step, power) {
- if (this.precomputed && this.precomputed.doubles)
- return this.precomputed.doubles;
-
- var doubles = [ this ];
- var acc = this;
- for (var i = 0; i < power; i += step) {
- for (var j = 0; j < step; j++)
- acc = acc.dbl();
- doubles.push(acc);
- }
- return {
- step: step,
- points: doubles
- };
-};
-
-BasePoint.prototype._getNAFPoints = function _getNAFPoints(wnd) {
- if (this.precomputed && this.precomputed.naf)
- return this.precomputed.naf;
-
- var res = [ this ];
- var max = (1 << wnd) - 1;
- var dbl = max === 1 ? null : this.dbl();
- for (var i = 1; i < max; i++)
- res[i] = res[i - 1].add(dbl);
- return {
- wnd: wnd,
- points: res
- };
-};
-
-BasePoint.prototype._getBeta = function _getBeta() {
- return null;
-};
-
-BasePoint.prototype.dblp = function dblp(k) {
- var r = this;
- for (var i = 0; i < k; i++)
- r = r.dbl();
- return r;
-};
-
-},{"../../elliptic":97,"bn.js":81}],99:[function(require,module,exports){
-'use strict';
-
-var curve = require('../curve');
-var elliptic = require('../../elliptic');
-var BN = require('bn.js');
-var inherits = require('inherits');
-var Base = curve.base;
-
-var assert = elliptic.utils.assert;
-
-function EdwardsCurve(conf) {
- // NOTE: Important as we are creating point in Base.call()
- this.twisted = (conf.a | 0) !== 1;
- this.mOneA = this.twisted && (conf.a | 0) === -1;
- this.extended = this.mOneA;
-
- Base.call(this, 'edwards', conf);
-
- this.a = new BN(conf.a, 16).umod(this.red.m);
- this.a = this.a.toRed(this.red);
- this.c = new BN(conf.c, 16).toRed(this.red);
- this.c2 = this.c.redSqr();
- this.d = new BN(conf.d, 16).toRed(this.red);
- this.dd = this.d.redAdd(this.d);
-
- assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);
- this.oneC = (conf.c | 0) === 1;
-}
-inherits(EdwardsCurve, Base);
-module.exports = EdwardsCurve;
-
-EdwardsCurve.prototype._mulA = function _mulA(num) {
- if (this.mOneA)
- return num.redNeg();
- else
- return this.a.redMul(num);
-};
-
-EdwardsCurve.prototype._mulC = function _mulC(num) {
- if (this.oneC)
- return num;
- else
- return this.c.redMul(num);
-};
-
-// Just for compatibility with Short curve
-EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {
- return this.point(x, y, z, t);
-};
-
-EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {
- x = new BN(x, 16);
- if (!x.red)
- x = x.toRed(this.red);
-
- var x2 = x.redSqr();
- var rhs = this.c2.redSub(this.a.redMul(x2));
- var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));
-
- var y2 = rhs.redMul(lhs.redInvm());
- var y = y2.redSqrt();
- if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
- throw new Error('invalid point');
-
- var isOdd = y.fromRed().isOdd();
- if (odd && !isOdd || !odd && isOdd)
- y = y.redNeg();
-
- return this.point(x, y);
-};
-
-EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {
- y = new BN(y, 16);
- if (!y.red)
- y = y.toRed(this.red);
-
- // x^2 = (y^2 - 1) / (d y^2 + 1)
- var y2 = y.redSqr();
- var lhs = y2.redSub(this.one);
- var rhs = y2.redMul(this.d).redAdd(this.one);
- var x2 = lhs.redMul(rhs.redInvm());
-
- if (x2.cmp(this.zero) === 0) {
- if (odd)
- throw new Error('invalid point');
- else
- return this.point(this.zero, y);
- }
-
- var x = x2.redSqrt();
- if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)
- throw new Error('invalid point');
-
- if (x.isOdd() !== odd)
- x = x.redNeg();
-
- return this.point(x, y);
-};
-
-EdwardsCurve.prototype.validate = function validate(point) {
- if (point.isInfinity())
- return true;
-
- // Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
- point.normalize();
-
- var x2 = point.x.redSqr();
- var y2 = point.y.redSqr();
- var lhs = x2.redMul(this.a).redAdd(y2);
- var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));
-
- return lhs.cmp(rhs) === 0;
-};
-
-function Point(curve, x, y, z, t) {
- Base.BasePoint.call(this, curve, 'projective');
- if (x === null && y === null && z === null) {
- this.x = this.curve.zero;
- this.y = this.curve.one;
- this.z = this.curve.one;
- this.t = this.curve.zero;
- this.zOne = true;
- } else {
- this.x = new BN(x, 16);
- this.y = new BN(y, 16);
- this.z = z ? new BN(z, 16) : this.curve.one;
- this.t = t && new BN(t, 16);
- if (!this.x.red)
- this.x = this.x.toRed(this.curve.red);
- if (!this.y.red)
- this.y = this.y.toRed(this.curve.red);
- if (!this.z.red)
- this.z = this.z.toRed(this.curve.red);
- if (this.t && !this.t.red)
- this.t = this.t.toRed(this.curve.red);
- this.zOne = this.z === this.curve.one;
-
- // Use extended coordinates
- if (this.curve.extended && !this.t) {
- this.t = this.x.redMul(this.y);
- if (!this.zOne)
- this.t = this.t.redMul(this.z.redInvm());
- }
- }
-}
-inherits(Point, Base.BasePoint);
-
-EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
- return Point.fromJSON(this, obj);
-};
-
-EdwardsCurve.prototype.point = function point(x, y, z, t) {
- return new Point(this, x, y, z, t);
-};
-
-Point.fromJSON = function fromJSON(curve, obj) {
- return new Point(curve, obj[0], obj[1], obj[2]);
-};
-
-Point.prototype.inspect = function inspect() {
- if (this.isInfinity())
- return '<EC Point Infinity>';
- return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
- ' y: ' + this.y.fromRed().toString(16, 2) +
- ' z: ' + this.z.fromRed().toString(16, 2) + '>';
-};
-
-Point.prototype.isInfinity = function isInfinity() {
- // XXX This code assumes that zero is always zero in red
- return this.x.cmpn(0) === 0 &&
- this.y.cmp(this.z) === 0;
-};
-
-Point.prototype._extDbl = function _extDbl() {
- // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
- // #doubling-dbl-2008-hwcd
- // 4M + 4S
-
- // A = X1^2
- var a = this.x.redSqr();
- // B = Y1^2
- var b = this.y.redSqr();
- // C = 2 * Z1^2
- var c = this.z.redSqr();
- c = c.redIAdd(c);
- // D = a * A
- var d = this.curve._mulA(a);
- // E = (X1 + Y1)^2 - A - B
- var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);
- // G = D + B
- var g = d.redAdd(b);
- // F = G - C
- var f = g.redSub(c);
- // H = D - B
- var h = d.redSub(b);
- // X3 = E * F
- var nx = e.redMul(f);
- // Y3 = G * H
- var ny = g.redMul(h);
- // T3 = E * H
- var nt = e.redMul(h);
- // Z3 = F * G
- var nz = f.redMul(g);
- return this.curve.point(nx, ny, nz, nt);
-};
-
-Point.prototype._projDbl = function _projDbl() {
- // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
- // #doubling-dbl-2008-bbjlp
- // #doubling-dbl-2007-bl
- // and others
- // Generally 3M + 4S or 2M + 4S
-
- // B = (X1 + Y1)^2
- var b = this.x.redAdd(this.y).redSqr();
- // C = X1^2
- var c = this.x.redSqr();
- // D = Y1^2
- var d = this.y.redSqr();
-
- var nx;
- var ny;
- var nz;
- if (this.curve.twisted) {
- // E = a * C
- var e = this.curve._mulA(c);
- // F = E + D
- var f = e.redAdd(d);
- if (this.zOne) {
- // X3 = (B - C - D) * (F - 2)
- nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));
- // Y3 = F * (E - D)
- ny = f.redMul(e.redSub(d));
- // Z3 = F^2 - 2 * F
- nz = f.redSqr().redSub(f).redSub(f);
- } else {
- // H = Z1^2
- var h = this.z.redSqr();
- // J = F - 2 * H
- var j = f.redSub(h).redISub(h);
- // X3 = (B-C-D)*J
- nx = b.redSub(c).redISub(d).redMul(j);
- // Y3 = F * (E - D)
- ny = f.redMul(e.redSub(d));
- // Z3 = F * J
- nz = f.redMul(j);
- }
- } else {
- // E = C + D
- var e = c.redAdd(d);
- // H = (c * Z1)^2
- var h = this.curve._mulC(this.c.redMul(this.z)).redSqr();
- // J = E - 2 * H
- var j = e.redSub(h).redSub(h);
- // X3 = c * (B - E) * J
- nx = this.curve._mulC(b.redISub(e)).redMul(j);
- // Y3 = c * E * (C - D)
- ny = this.curve._mulC(e).redMul(c.redISub(d));
- // Z3 = E * J
- nz = e.redMul(j);
- }
- return this.curve.point(nx, ny, nz);
-};
-
-Point.prototype.dbl = function dbl() {
- if (this.isInfinity())
- return this;
-
- // Double in extended coordinates
- if (this.curve.extended)
- return this._extDbl();
- else
- return this._projDbl();
-};
-
-Point.prototype._extAdd = function _extAdd(p) {
- // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
- // #addition-add-2008-hwcd-3
- // 8M
-
- // A = (Y1 - X1) * (Y2 - X2)
- var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));
- // B = (Y1 + X1) * (Y2 + X2)
- var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));
- // C = T1 * k * T2
- var c = this.t.redMul(this.curve.dd).redMul(p.t);
- // D = Z1 * 2 * Z2
- var d = this.z.redMul(p.z.redAdd(p.z));
- // E = B - A
- var e = b.redSub(a);
- // F = D - C
- var f = d.redSub(c);
- // G = D + C
- var g = d.redAdd(c);
- // H = B + A
- var h = b.redAdd(a);
- // X3 = E * F
- var nx = e.redMul(f);
- // Y3 = G * H
- var ny = g.redMul(h);
- // T3 = E * H
- var nt = e.redMul(h);
- // Z3 = F * G
- var nz = f.redMul(g);
- return this.curve.point(nx, ny, nz, nt);
-};
-
-Point.prototype._projAdd = function _projAdd(p) {
- // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
- // #addition-add-2008-bbjlp
- // #addition-add-2007-bl
- // 10M + 1S
-
- // A = Z1 * Z2
- var a = this.z.redMul(p.z);
- // B = A^2
- var b = a.redSqr();
- // C = X1 * X2
- var c = this.x.redMul(p.x);
- // D = Y1 * Y2
- var d = this.y.redMul(p.y);
- // E = d * C * D
- var e = this.curve.d.redMul(c).redMul(d);
- // F = B - E
- var f = b.redSub(e);
- // G = B + E
- var g = b.redAdd(e);
- // X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
- var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);
- var nx = a.redMul(f).redMul(tmp);
- var ny;
- var nz;
- if (this.curve.twisted) {
- // Y3 = A * G * (D - a * C)
- ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));
- // Z3 = F * G
- nz = f.redMul(g);
- } else {
- // Y3 = A * G * (D - C)
- ny = a.redMul(g).redMul(d.redSub(c));
- // Z3 = c * F * G
- nz = this.curve._mulC(f).redMul(g);
- }
- return this.curve.point(nx, ny, nz);
-};
-
-Point.prototype.add = function add(p) {
- if (this.isInfinity())
- return p;
- if (p.isInfinity())
- return this;
-
- if (this.curve.extended)
- return this._extAdd(p);
- else
- return this._projAdd(p);
-};
-
-Point.prototype.mul = function mul(k) {
- if (this._hasDoubles(k))
- return this.curve._fixedNafMul(this, k);
- else
- return this.curve._wnafMul(this, k);
-};
-
-Point.prototype.mulAdd = function mulAdd(k1, p, k2) {
- return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, false);
-};
-
-Point.prototype.jmulAdd = function jmulAdd(k1, p, k2) {
- return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, true);
-};
-
-Point.prototype.normalize = function normalize() {
- if (this.zOne)
- return this;
-
- // Normalize coordinates
- var zi = this.z.redInvm();
- this.x = this.x.redMul(zi);
- this.y = this.y.redMul(zi);
- if (this.t)
- this.t = this.t.redMul(zi);
- this.z = this.curve.one;
- this.zOne = true;
- return this;
-};
-
-Point.prototype.neg = function neg() {
- return this.curve.point(this.x.redNeg(),
- this.y,
- this.z,
- this.t && this.t.redNeg());
-};
-
-Point.prototype.getX = function getX() {
- this.normalize();
- return this.x.fromRed();
-};
-
-Point.prototype.getY = function getY() {
- this.normalize();
- return this.y.fromRed();
-};
-
-Point.prototype.eq = function eq(other) {
- return this === other ||
- this.getX().cmp(other.getX()) === 0 &&
- this.getY().cmp(other.getY()) === 0;
-};
-
-Point.prototype.eqXToP = function eqXToP(x) {
- var rx = x.toRed(this.curve.red).redMul(this.z);
- if (this.x.cmp(rx) === 0)
- return true;
-
- var xc = x.clone();
- var t = this.curve.redN.redMul(this.z);
- for (;;) {
- xc.iadd(this.curve.n);
- if (xc.cmp(this.curve.p) >= 0)
- return false;
-
- rx.redIAdd(t);
- if (this.x.cmp(rx) === 0)
- return true;
- }
- return false;
-};
-
-// Compatibility with BaseCurve
-Point.prototype.toP = Point.prototype.normalize;
-Point.prototype.mixedAdd = Point.prototype.add;
-
-},{"../../elliptic":97,"../curve":100,"bn.js":81,"inherits":121}],100:[function(require,module,exports){
-'use strict';
-
-var curve = exports;
-
-curve.base = require('./base');
-curve.short = require('./short');
-curve.mont = require('./mont');
-curve.edwards = require('./edwards');
-
-},{"./base":98,"./edwards":99,"./mont":101,"./short":102}],101:[function(require,module,exports){
-'use strict';
-
-var curve = require('../curve');
-var BN = require('bn.js');
-var inherits = require('inherits');
-var Base = curve.base;
-
-var elliptic = require('../../elliptic');
-var utils = elliptic.utils;
-
-function MontCurve(conf) {
- Base.call(this, 'mont', conf);
-
- this.a = new BN(conf.a, 16).toRed(this.red);
- this.b = new BN(conf.b, 16).toRed(this.red);
- this.i4 = new BN(4).toRed(this.red).redInvm();
- this.two = new BN(2).toRed(this.red);
- this.a24 = this.i4.redMul(this.a.redAdd(this.two));
-}
-inherits(MontCurve, Base);
-module.exports = MontCurve;
-
-MontCurve.prototype.validate = function validate(point) {
- var x = point.normalize().x;
- var x2 = x.redSqr();
- var rhs = x2.redMul(x).redAdd(x2.redMul(this.a)).redAdd(x);
- var y = rhs.redSqrt();
-
- return y.redSqr().cmp(rhs) === 0;
-};
-
-function Point(curve, x, z) {
- Base.BasePoint.call(this, curve, 'projective');
- if (x === null && z === null) {
- this.x = this.curve.one;
- this.z = this.curve.zero;
- } else {
- this.x = new BN(x, 16);
- this.z = new BN(z, 16);
- if (!this.x.red)
- this.x = this.x.toRed(this.curve.red);
- if (!this.z.red)
- this.z = this.z.toRed(this.curve.red);
- }
-}
-inherits(Point, Base.BasePoint);
-
-MontCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
- return this.point(utils.toArray(bytes, enc), 1);
-};
-
-MontCurve.prototype.point = function point(x, z) {
- return new Point(this, x, z);
-};
-
-MontCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
- return Point.fromJSON(this, obj);
-};
-
-Point.prototype.precompute = function precompute() {
- // No-op
-};
-
-Point.prototype._encode = function _encode() {
- return this.getX().toArray('be', this.curve.p.byteLength());
-};
-
-Point.fromJSON = function fromJSON(curve, obj) {
- return new Point(curve, obj[0], obj[1] || curve.one);
-};
-
-Point.prototype.inspect = function inspect() {
- if (this.isInfinity())
- return '<EC Point Infinity>';
- return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
- ' z: ' + this.z.fromRed().toString(16, 2) + '>';
-};
-
-Point.prototype.isInfinity = function isInfinity() {
- // XXX This code assumes that zero is always zero in red
- return this.z.cmpn(0) === 0;
-};
-
-Point.prototype.dbl = function dbl() {
- // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3
- // 2M + 2S + 4A
-
- // A = X1 + Z1
- var a = this.x.redAdd(this.z);
- // AA = A^2
- var aa = a.redSqr();
- // B = X1 - Z1
- var b = this.x.redSub(this.z);
- // BB = B^2
- var bb = b.redSqr();
- // C = AA - BB
- var c = aa.redSub(bb);
- // X3 = AA * BB
- var nx = aa.redMul(bb);
- // Z3 = C * (BB + A24 * C)
- var nz = c.redMul(bb.redAdd(this.curve.a24.redMul(c)));
- return this.curve.point(nx, nz);
-};
-
-Point.prototype.add = function add() {
- throw new Error('Not supported on Montgomery curve');
-};
-
-Point.prototype.diffAdd = function diffAdd(p, diff) {
- // http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3
- // 4M + 2S + 6A
-
- // A = X2 + Z2
- var a = this.x.redAdd(this.z);
- // B = X2 - Z2
- var b = this.x.redSub(this.z);
- // C = X3 + Z3
- var c = p.x.redAdd(p.z);
- // D = X3 - Z3
- var d = p.x.redSub(p.z);
- // DA = D * A
- var da = d.redMul(a);
- // CB = C * B
- var cb = c.redMul(b);
- // X5 = Z1 * (DA + CB)^2
- var nx = diff.z.redMul(da.redAdd(cb).redSqr());
- // Z5 = X1 * (DA - CB)^2
- var nz = diff.x.redMul(da.redISub(cb).redSqr());
- return this.curve.point(nx, nz);
-};
-
-Point.prototype.mul = function mul(k) {
- var t = k.clone();
- var a = this; // (N / 2) * Q + Q
- var b = this.curve.point(null, null); // (N / 2) * Q
- var c = this; // Q
-
- for (var bits = []; t.cmpn(0) !== 0; t.iushrn(1))
- bits.push(t.andln(1));
-
- for (var i = bits.length - 1; i >= 0; i--) {
- if (bits[i] === 0) {
- // N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q
- a = a.diffAdd(b, c);
- // N * Q = 2 * ((N / 2) * Q + Q))
- b = b.dbl();
- } else {
- // N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)
- b = a.diffAdd(b, c);
- // N * Q + Q = 2 * ((N / 2) * Q + Q)
- a = a.dbl();
- }
- }
- return b;
-};
-
-Point.prototype.mulAdd = function mulAdd() {
- throw new Error('Not supported on Montgomery curve');
-};
-
-Point.prototype.jumlAdd = function jumlAdd() {
- throw new Error('Not supported on Montgomery curve');
-};
-
-Point.prototype.eq = function eq(other) {
- return this.getX().cmp(other.getX()) === 0;
-};
-
-Point.prototype.normalize = function normalize() {
- this.x = this.x.redMul(this.z.redInvm());
- this.z = this.curve.one;
- return this;
-};
-
-Point.prototype.getX = function getX() {
- // Normalize coordinates
- this.normalize();
-
- return this.x.fromRed();
-};
-
-},{"../../elliptic":97,"../curve":100,"bn.js":81,"inherits":121}],102:[function(require,module,exports){
-'use strict';
-
-var curve = require('../curve');
-var elliptic = require('../../elliptic');
-var BN = require('bn.js');
-var inherits = require('inherits');
-var Base = curve.base;
-
-var assert = elliptic.utils.assert;
-
-function ShortCurve(conf) {
- Base.call(this, 'short', conf);
-
- this.a = new BN(conf.a, 16).toRed(this.red);
- this.b = new BN(conf.b, 16).toRed(this.red);
- this.tinv = this.two.redInvm();
-
- this.zeroA = this.a.fromRed().cmpn(0) === 0;
- this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;
-
- // If the curve is endomorphic, precalculate beta and lambda
- this.endo = this._getEndomorphism(conf);
- this._endoWnafT1 = new Array(4);
- this._endoWnafT2 = new Array(4);
-}
-inherits(ShortCurve, Base);
-module.exports = ShortCurve;
-
-ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {
- // No efficient endomorphism
- if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)
- return;
-
- // Compute beta and lambda, that lambda * P = (beta * Px; Py)
- var beta;
- var lambda;
- if (conf.beta) {
- beta = new BN(conf.beta, 16).toRed(this.red);
- } else {
- var betas = this._getEndoRoots(this.p);
- // Choose the smallest beta
- beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];
- beta = beta.toRed(this.red);
- }
- if (conf.lambda) {
- lambda = new BN(conf.lambda, 16);
- } else {
- // Choose the lambda that is matching selected beta
- var lambdas = this._getEndoRoots(this.n);
- if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {
- lambda = lambdas[0];
- } else {
- lambda = lambdas[1];
- assert(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);
- }
- }
-
- // Get basis vectors, used for balanced length-two representation
- var basis;
- if (conf.basis) {
- basis = conf.basis.map(function(vec) {
- return {
- a: new BN(vec.a, 16),
- b: new BN(vec.b, 16)
- };
- });
- } else {
- basis = this._getEndoBasis(lambda);
- }
-
- return {
- beta: beta,
- lambda: lambda,
- basis: basis
- };
-};
-
-ShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {
- // Find roots of for x^2 + x + 1 in F
- // Root = (-1 +- Sqrt(-3)) / 2
- //
- var red = num === this.p ? this.red : BN.mont(num);
- var tinv = new BN(2).toRed(red).redInvm();
- var ntinv = tinv.redNeg();
-
- var s = new BN(3).toRed(red).redNeg().redSqrt().redMul(tinv);
-
- var l1 = ntinv.redAdd(s).fromRed();
- var l2 = ntinv.redSub(s).fromRed();
- return [ l1, l2 ];
-};
-
-ShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {
- // aprxSqrt >= sqrt(this.n)
- var aprxSqrt = this.n.ushrn(Math.floor(this.n.bitLength() / 2));
-
- // 3.74
- // Run EGCD, until r(L + 1) < aprxSqrt
- var u = lambda;
- var v = this.n.clone();
- var x1 = new BN(1);
- var y1 = new BN(0);
- var x2 = new BN(0);
- var y2 = new BN(1);
-
- // NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)
- var a0;
- var b0;
- // First vector
- var a1;
- var b1;
- // Second vector
- var a2;
- var b2;
-
- var prevR;
- var i = 0;
- var r;
- var x;
- while (u.cmpn(0) !== 0) {
- var q = v.div(u);
- r = v.sub(q.mul(u));
- x = x2.sub(q.mul(x1));
- var y = y2.sub(q.mul(y1));
-
- if (!a1 && r.cmp(aprxSqrt) < 0) {
- a0 = prevR.neg();
- b0 = x1;
- a1 = r.neg();
- b1 = x;
- } else if (a1 && ++i === 2) {
- break;
- }
- prevR = r;
-
- v = u;
- u = r;
- x2 = x1;
- x1 = x;
- y2 = y1;
- y1 = y;
- }
- a2 = r.neg();
- b2 = x;
-
- var len1 = a1.sqr().add(b1.sqr());
- var len2 = a2.sqr().add(b2.sqr());
- if (len2.cmp(len1) >= 0) {
- a2 = a0;
- b2 = b0;
- }
-
- // Normalize signs
- if (a1.negative) {
- a1 = a1.neg();
- b1 = b1.neg();
- }
- if (a2.negative) {
- a2 = a2.neg();
- b2 = b2.neg();
- }
-
- return [
- { a: a1, b: b1 },
- { a: a2, b: b2 }
- ];
-};
-
-ShortCurve.prototype._endoSplit = function _endoSplit(k) {
- var basis = this.endo.basis;
- var v1 = basis[0];
- var v2 = basis[1];
-
- var c1 = v2.b.mul(k).divRound(this.n);
- var c2 = v1.b.neg().mul(k).divRound(this.n);
-
- var p1 = c1.mul(v1.a);
- var p2 = c2.mul(v2.a);
- var q1 = c1.mul(v1.b);
- var q2 = c2.mul(v2.b);
-
- // Calculate answer
- var k1 = k.sub(p1).sub(p2);
- var k2 = q1.add(q2).neg();
- return { k1: k1, k2: k2 };
-};
-
-ShortCurve.prototype.pointFromX = function pointFromX(x, odd) {
- x = new BN(x, 16);
- if (!x.red)
- x = x.toRed(this.red);
-
- var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
- var y = y2.redSqrt();
- if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
- throw new Error('invalid point');
-
- // XXX Is there any way to tell if the number is odd without converting it
- // to non-red form?
- var isOdd = y.fromRed().isOdd();
- if (odd && !isOdd || !odd && isOdd)
- y = y.redNeg();
-
- return this.point(x, y);
-};
-
-ShortCurve.prototype.validate = function validate(point) {
- if (point.inf)
- return true;
-
- var x = point.x;
- var y = point.y;
-
- var ax = this.a.redMul(x);
- var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);
- return y.redSqr().redISub(rhs).cmpn(0) === 0;
-};
-
-ShortCurve.prototype._endoWnafMulAdd =
- function _endoWnafMulAdd(points, coeffs, jacobianResult) {
- var npoints = this._endoWnafT1;
- var ncoeffs = this._endoWnafT2;
- for (var i = 0; i < points.length; i++) {
- var split = this._endoSplit(coeffs[i]);
- var p = points[i];
- var beta = p._getBeta();
-
- if (split.k1.negative) {
- split.k1.ineg();
- p = p.neg(true);
- }
- if (split.k2.negative) {
- split.k2.ineg();
- beta = beta.neg(true);
- }
-
- npoints[i * 2] = p;
- npoints[i * 2 + 1] = beta;
- ncoeffs[i * 2] = split.k1;
- ncoeffs[i * 2 + 1] = split.k2;
- }
- var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2, jacobianResult);
-
- // Clean-up references to points and coefficients
- for (var j = 0; j < i * 2; j++) {
- npoints[j] = null;
- ncoeffs[j] = null;
- }
- return res;
-};
-
-function Point(curve, x, y, isRed) {
- Base.BasePoint.call(this, curve, 'affine');
- if (x === null && y === null) {
- this.x = null;
- this.y = null;
- this.inf = true;
- } else {
- this.x = new BN(x, 16);
- this.y = new BN(y, 16);
- // Force redgomery representation when loading from JSON
- if (isRed) {
- this.x.forceRed(this.curve.red);
- this.y.forceRed(this.curve.red);
- }
- if (!this.x.red)
- this.x = this.x.toRed(this.curve.red);
- if (!this.y.red)
- this.y = this.y.toRed(this.curve.red);
- this.inf = false;
- }
-}
-inherits(Point, Base.BasePoint);
-
-ShortCurve.prototype.point = function point(x, y, isRed) {
- return new Point(this, x, y, isRed);
-};
-
-ShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {
- return Point.fromJSON(this, obj, red);
-};
-
-Point.prototype._getBeta = function _getBeta() {
- if (!this.curve.endo)
- return;
-
- var pre = this.precomputed;
- if (pre && pre.beta)
- return pre.beta;
-
- var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);
- if (pre) {
- var curve = this.curve;
- var endoMul = function(p) {
- return curve.point(p.x.redMul(curve.endo.beta), p.y);
- };
- pre.beta = beta;
- beta.precomputed = {
- beta: null,
- naf: pre.naf && {
- wnd: pre.naf.wnd,
- points: pre.naf.points.map(endoMul)
- },
- doubles: pre.doubles && {
- step: pre.doubles.step,
- points: pre.doubles.points.map(endoMul)
- }
- };
- }
- return beta;
-};
-
-Point.prototype.toJSON = function toJSON() {
- if (!this.precomputed)
- return [ this.x, this.y ];
-
- return [ this.x, this.y, this.precomputed && {
- doubles: this.precomputed.doubles && {
- step: this.precomputed.doubles.step,
- points: this.precomputed.doubles.points.slice(1)
- },
- naf: this.precomputed.naf && {
- wnd: this.precomputed.naf.wnd,
- points: this.precomputed.naf.points.slice(1)
- }
- } ];
-};
-
-Point.fromJSON = function fromJSON(curve, obj, red) {
- if (typeof obj === 'string')
- obj = JSON.parse(obj);
- var res = curve.point(obj[0], obj[1], red);
- if (!obj[2])
- return res;
-
- function obj2point(obj) {
- return curve.point(obj[0], obj[1], red);
- }
-
- var pre = obj[2];
- res.precomputed = {
- beta: null,
- doubles: pre.doubles && {
- step: pre.doubles.step,
- points: [ res ].concat(pre.doubles.points.map(obj2point))
- },
- naf: pre.naf && {
- wnd: pre.naf.wnd,
- points: [ res ].concat(pre.naf.points.map(obj2point))
- }
- };
- return res;
-};
-
-Point.prototype.inspect = function inspect() {
- if (this.isInfinity())
- return '<EC Point Infinity>';
- return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
- ' y: ' + this.y.fromRed().toString(16, 2) + '>';
-};
-
-Point.prototype.isInfinity = function isInfinity() {
- return this.inf;
-};
-
-Point.prototype.add = function add(p) {
- // O + P = P
- if (this.inf)
- return p;
-
- // P + O = P
- if (p.inf)
- return this;
-
- // P + P = 2P
- if (this.eq(p))
- return this.dbl();
-
- // P + (-P) = O
- if (this.neg().eq(p))
- return this.curve.point(null, null);
-
- // P + Q = O
- if (this.x.cmp(p.x) === 0)
- return this.curve.point(null, null);
-
- var c = this.y.redSub(p.y);
- if (c.cmpn(0) !== 0)
- c = c.redMul(this.x.redSub(p.x).redInvm());
- var nx = c.redSqr().redISub(this.x).redISub(p.x);
- var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
- return this.curve.point(nx, ny);
-};
-
-Point.prototype.dbl = function dbl() {
- if (this.inf)
- return this;
-
- // 2P = O
- var ys1 = this.y.redAdd(this.y);
- if (ys1.cmpn(0) === 0)
- return this.curve.point(null, null);
-
- var a = this.curve.a;
-
- var x2 = this.x.redSqr();
- var dyinv = ys1.redInvm();
- var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);
-
- var nx = c.redSqr().redISub(this.x.redAdd(this.x));
- var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
- return this.curve.point(nx, ny);
-};
-
-Point.prototype.getX = function getX() {
- return this.x.fromRed();
-};
-
-Point.prototype.getY = function getY() {
- return this.y.fromRed();
-};
-
-Point.prototype.mul = function mul(k) {
- k = new BN(k, 16);
-
- if (this._hasDoubles(k))
- return this.curve._fixedNafMul(this, k);
- else if (this.curve.endo)
- return this.curve._endoWnafMulAdd([ this ], [ k ]);
- else
- return this.curve._wnafMul(this, k);
-};
-
-Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {
- var points = [ this, p2 ];
- var coeffs = [ k1, k2 ];
- if (this.curve.endo)
- return this.curve._endoWnafMulAdd(points, coeffs);
- else
- return this.curve._wnafMulAdd(1, points, coeffs, 2);
-};
-
-Point.prototype.jmulAdd = function jmulAdd(k1, p2, k2) {
- var points = [ this, p2 ];
- var coeffs = [ k1, k2 ];
- if (this.curve.endo)
- return this.curve._endoWnafMulAdd(points, coeffs, true);
- else
- return this.curve._wnafMulAdd(1, points, coeffs, 2, true);
-};
-
-Point.prototype.eq = function eq(p) {
- return this === p ||
- this.inf === p.inf &&
- (this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);
-};
-
-Point.prototype.neg = function neg(_precompute) {
- if (this.inf)
- return this;
-
- var res = this.curve.point(this.x, this.y.redNeg());
- if (_precompute && this.precomputed) {
- var pre = this.precomputed;
- var negate = function(p) {
- return p.neg();
- };
- res.precomputed = {
- naf: pre.naf && {
- wnd: pre.naf.wnd,
- points: pre.naf.points.map(negate)
- },
- doubles: pre.doubles && {
- step: pre.doubles.step,
- points: pre.doubles.points.map(negate)
- }
- };
- }
- return res;
-};
-
-Point.prototype.toJ = function toJ() {
- if (this.inf)
- return this.curve.jpoint(null, null, null);
-
- var res = this.curve.jpoint(this.x, this.y, this.curve.one);
- return res;
-};
-
-function JPoint(curve, x, y, z) {
- Base.BasePoint.call(this, curve, 'jacobian');
- if (x === null && y === null && z === null) {
- this.x = this.curve.one;
- this.y = this.curve.one;
- this.z = new BN(0);
- } else {
- this.x = new BN(x, 16);
- this.y = new BN(y, 16);
- this.z = new BN(z, 16);
- }
- if (!this.x.red)
- this.x = this.x.toRed(this.curve.red);
- if (!this.y.red)
- this.y = this.y.toRed(this.curve.red);
- if (!this.z.red)
- this.z = this.z.toRed(this.curve.red);
-
- this.zOne = this.z === this.curve.one;
-}
-inherits(JPoint, Base.BasePoint);
-
-ShortCurve.prototype.jpoint = function jpoint(x, y, z) {
- return new JPoint(this, x, y, z);
-};
-
-JPoint.prototype.toP = function toP() {
- if (this.isInfinity())
- return this.curve.point(null, null);
-
- var zinv = this.z.redInvm();
- var zinv2 = zinv.redSqr();
- var ax = this.x.redMul(zinv2);
- var ay = this.y.redMul(zinv2).redMul(zinv);
-
- return this.curve.point(ax, ay);
-};
-
-JPoint.prototype.neg = function neg() {
- return this.curve.jpoint(this.x, this.y.redNeg(), this.z);
-};
-
-JPoint.prototype.add = function add(p) {
- // O + P = P
- if (this.isInfinity())
- return p;
-
- // P + O = P
- if (p.isInfinity())
- return this;
-
- // 12M + 4S + 7A
- var pz2 = p.z.redSqr();
- var z2 = this.z.redSqr();
- var u1 = this.x.redMul(pz2);
- var u2 = p.x.redMul(z2);
- var s1 = this.y.redMul(pz2.redMul(p.z));
- var s2 = p.y.redMul(z2.redMul(this.z));
-
- var h = u1.redSub(u2);
- var r = s1.redSub(s2);
- if (h.cmpn(0) === 0) {
- if (r.cmpn(0) !== 0)
- return this.curve.jpoint(null, null, null);
- else
- return this.dbl();
- }
-
- var h2 = h.redSqr();
- var h3 = h2.redMul(h);
- var v = u1.redMul(h2);
-
- var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
- var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
- var nz = this.z.redMul(p.z).redMul(h);
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype.mixedAdd = function mixedAdd(p) {
- // O + P = P
- if (this.isInfinity())
- return p.toJ();
-
- // P + O = P
- if (p.isInfinity())
- return this;
-
- // 8M + 3S + 7A
- var z2 = this.z.redSqr();
- var u1 = this.x;
- var u2 = p.x.redMul(z2);
- var s1 = this.y;
- var s2 = p.y.redMul(z2).redMul(this.z);
-
- var h = u1.redSub(u2);
- var r = s1.redSub(s2);
- if (h.cmpn(0) === 0) {
- if (r.cmpn(0) !== 0)
- return this.curve.jpoint(null, null, null);
- else
- return this.dbl();
- }
-
- var h2 = h.redSqr();
- var h3 = h2.redMul(h);
- var v = u1.redMul(h2);
-
- var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
- var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
- var nz = this.z.redMul(h);
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype.dblp = function dblp(pow) {
- if (pow === 0)
- return this;
- if (this.isInfinity())
- return this;
- if (!pow)
- return this.dbl();
-
- if (this.curve.zeroA || this.curve.threeA) {
- var r = this;
- for (var i = 0; i < pow; i++)
- r = r.dbl();
- return r;
- }
-
- // 1M + 2S + 1A + N * (4S + 5M + 8A)
- // N = 1 => 6M + 6S + 9A
- var a = this.curve.a;
- var tinv = this.curve.tinv;
-
- var jx = this.x;
- var jy = this.y;
- var jz = this.z;
- var jz4 = jz.redSqr().redSqr();
-
- // Reuse results
- var jyd = jy.redAdd(jy);
- for (var i = 0; i < pow; i++) {
- var jx2 = jx.redSqr();
- var jyd2 = jyd.redSqr();
- var jyd4 = jyd2.redSqr();
- var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
-
- var t1 = jx.redMul(jyd2);
- var nx = c.redSqr().redISub(t1.redAdd(t1));
- var t2 = t1.redISub(nx);
- var dny = c.redMul(t2);
- dny = dny.redIAdd(dny).redISub(jyd4);
- var nz = jyd.redMul(jz);
- if (i + 1 < pow)
- jz4 = jz4.redMul(jyd4);
-
- jx = nx;
- jz = nz;
- jyd = dny;
- }
-
- return this.curve.jpoint(jx, jyd.redMul(tinv), jz);
-};
-
-JPoint.prototype.dbl = function dbl() {
- if (this.isInfinity())
- return this;
-
- if (this.curve.zeroA)
- return this._zeroDbl();
- else if (this.curve.threeA)
- return this._threeDbl();
- else
- return this._dbl();
-};
-
-JPoint.prototype._zeroDbl = function _zeroDbl() {
- var nx;
- var ny;
- var nz;
- // Z = 1
- if (this.zOne) {
- // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
- // #doubling-mdbl-2007-bl
- // 1M + 5S + 14A
-
- // XX = X1^2
- var xx = this.x.redSqr();
- // YY = Y1^2
- var yy = this.y.redSqr();
- // YYYY = YY^2
- var yyyy = yy.redSqr();
- // S = 2 * ((X1 + YY)^2 - XX - YYYY)
- var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
- s = s.redIAdd(s);
- // M = 3 * XX + a; a = 0
- var m = xx.redAdd(xx).redIAdd(xx);
- // T = M ^ 2 - 2*S
- var t = m.redSqr().redISub(s).redISub(s);
-
- // 8 * YYYY
- var yyyy8 = yyyy.redIAdd(yyyy);
- yyyy8 = yyyy8.redIAdd(yyyy8);
- yyyy8 = yyyy8.redIAdd(yyyy8);
-
- // X3 = T
- nx = t;
- // Y3 = M * (S - T) - 8 * YYYY
- ny = m.redMul(s.redISub(t)).redISub(yyyy8);
- // Z3 = 2*Y1
- nz = this.y.redAdd(this.y);
- } else {
- // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
- // #doubling-dbl-2009-l
- // 2M + 5S + 13A
-
- // A = X1^2
- var a = this.x.redSqr();
- // B = Y1^2
- var b = this.y.redSqr();
- // C = B^2
- var c = b.redSqr();
- // D = 2 * ((X1 + B)^2 - A - C)
- var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);
- d = d.redIAdd(d);
- // E = 3 * A
- var e = a.redAdd(a).redIAdd(a);
- // F = E^2
- var f = e.redSqr();
-
- // 8 * C
- var c8 = c.redIAdd(c);
- c8 = c8.redIAdd(c8);
- c8 = c8.redIAdd(c8);
-
- // X3 = F - 2 * D
- nx = f.redISub(d).redISub(d);
- // Y3 = E * (D - X3) - 8 * C
- ny = e.redMul(d.redISub(nx)).redISub(c8);
- // Z3 = 2 * Y1 * Z1
- nz = this.y.redMul(this.z);
- nz = nz.redIAdd(nz);
- }
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype._threeDbl = function _threeDbl() {
- var nx;
- var ny;
- var nz;
- // Z = 1
- if (this.zOne) {
- // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
- // #doubling-mdbl-2007-bl
- // 1M + 5S + 15A
-
- // XX = X1^2
- var xx = this.x.redSqr();
- // YY = Y1^2
- var yy = this.y.redSqr();
- // YYYY = YY^2
- var yyyy = yy.redSqr();
- // S = 2 * ((X1 + YY)^2 - XX - YYYY)
- var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
- s = s.redIAdd(s);
- // M = 3 * XX + a
- var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);
- // T = M^2 - 2 * S
- var t = m.redSqr().redISub(s).redISub(s);
- // X3 = T
- nx = t;
- // Y3 = M * (S - T) - 8 * YYYY
- var yyyy8 = yyyy.redIAdd(yyyy);
- yyyy8 = yyyy8.redIAdd(yyyy8);
- yyyy8 = yyyy8.redIAdd(yyyy8);
- ny = m.redMul(s.redISub(t)).redISub(yyyy8);
- // Z3 = 2 * Y1
- nz = this.y.redAdd(this.y);
- } else {
- // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
- // 3M + 5S
-
- // delta = Z1^2
- var delta = this.z.redSqr();
- // gamma = Y1^2
- var gamma = this.y.redSqr();
- // beta = X1 * gamma
- var beta = this.x.redMul(gamma);
- // alpha = 3 * (X1 - delta) * (X1 + delta)
- var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));
- alpha = alpha.redAdd(alpha).redIAdd(alpha);
- // X3 = alpha^2 - 8 * beta
- var beta4 = beta.redIAdd(beta);
- beta4 = beta4.redIAdd(beta4);
- var beta8 = beta4.redAdd(beta4);
- nx = alpha.redSqr().redISub(beta8);
- // Z3 = (Y1 + Z1)^2 - gamma - delta
- nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);
- // Y3 = alpha * (4 * beta - X3) - 8 * gamma^2
- var ggamma8 = gamma.redSqr();
- ggamma8 = ggamma8.redIAdd(ggamma8);
- ggamma8 = ggamma8.redIAdd(ggamma8);
- ggamma8 = ggamma8.redIAdd(ggamma8);
- ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);
- }
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype._dbl = function _dbl() {
- var a = this.curve.a;
-
- // 4M + 6S + 10A
- var jx = this.x;
- var jy = this.y;
- var jz = this.z;
- var jz4 = jz.redSqr().redSqr();
-
- var jx2 = jx.redSqr();
- var jy2 = jy.redSqr();
-
- var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
-
- var jxd4 = jx.redAdd(jx);
- jxd4 = jxd4.redIAdd(jxd4);
- var t1 = jxd4.redMul(jy2);
- var nx = c.redSqr().redISub(t1.redAdd(t1));
- var t2 = t1.redISub(nx);
-
- var jyd8 = jy2.redSqr();
- jyd8 = jyd8.redIAdd(jyd8);
- jyd8 = jyd8.redIAdd(jyd8);
- jyd8 = jyd8.redIAdd(jyd8);
- var ny = c.redMul(t2).redISub(jyd8);
- var nz = jy.redAdd(jy).redMul(jz);
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype.trpl = function trpl() {
- if (!this.curve.zeroA)
- return this.dbl().add(this);
-
- // hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl
- // 5M + 10S + ...
-
- // XX = X1^2
- var xx = this.x.redSqr();
- // YY = Y1^2
- var yy = this.y.redSqr();
- // ZZ = Z1^2
- var zz = this.z.redSqr();
- // YYYY = YY^2
- var yyyy = yy.redSqr();
- // M = 3 * XX + a * ZZ2; a = 0
- var m = xx.redAdd(xx).redIAdd(xx);
- // MM = M^2
- var mm = m.redSqr();
- // E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM
- var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
- e = e.redIAdd(e);
- e = e.redAdd(e).redIAdd(e);
- e = e.redISub(mm);
- // EE = E^2
- var ee = e.redSqr();
- // T = 16*YYYY
- var t = yyyy.redIAdd(yyyy);
- t = t.redIAdd(t);
- t = t.redIAdd(t);
- t = t.redIAdd(t);
- // U = (M + E)^2 - MM - EE - T
- var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);
- // X3 = 4 * (X1 * EE - 4 * YY * U)
- var yyu4 = yy.redMul(u);
- yyu4 = yyu4.redIAdd(yyu4);
- yyu4 = yyu4.redIAdd(yyu4);
- var nx = this.x.redMul(ee).redISub(yyu4);
- nx = nx.redIAdd(nx);
- nx = nx.redIAdd(nx);
- // Y3 = 8 * Y1 * (U * (T - U) - E * EE)
- var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));
- ny = ny.redIAdd(ny);
- ny = ny.redIAdd(ny);
- ny = ny.redIAdd(ny);
- // Z3 = (Z1 + E)^2 - ZZ - EE
- var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);
-
- return this.curve.jpoint(nx, ny, nz);
-};
-
-JPoint.prototype.mul = function mul(k, kbase) {
- k = new BN(k, kbase);
-
- return this.curve._wnafMul(this, k);
-};
-
-JPoint.prototype.eq = function eq(p) {
- if (p.type === 'affine')
- return this.eq(p.toJ());
-
- if (this === p)
- return true;
-
- // x1 * z2^2 == x2 * z1^2
- var z2 = this.z.redSqr();
- var pz2 = p.z.redSqr();
- if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)
- return false;
-
- // y1 * z2^3 == y2 * z1^3
- var z3 = z2.redMul(this.z);
- var pz3 = pz2.redMul(p.z);
- return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;
-};
-
-JPoint.prototype.eqXToP = function eqXToP(x) {
- var zs = this.z.redSqr();
- var rx = x.toRed(this.curve.red).redMul(zs);
- if (this.x.cmp(rx) === 0)
- return true;
-
- var xc = x.clone();
- var t = this.curve.redN.redMul(zs);
- for (;;) {
- xc.iadd(this.curve.n);
- if (xc.cmp(this.curve.p) >= 0)
- return false;
-
- rx.redIAdd(t);
- if (this.x.cmp(rx) === 0)
- return true;
- }
- return false;
-};
-
-JPoint.prototype.inspect = function inspect() {
- if (this.isInfinity())
- return '<EC JPoint Infinity>';
- return '<EC JPoint x: ' + this.x.toString(16, 2) +
- ' y: ' + this.y.toString(16, 2) +
- ' z: ' + this.z.toString(16, 2) + '>';
-};
-
-JPoint.prototype.isInfinity = function isInfinity() {
- // XXX This code assumes that zero is always zero in red
- return this.z.cmpn(0) === 0;
-};
-
-},{"../../elliptic":97,"../curve":100,"bn.js":81,"inherits":121}],103:[function(require,module,exports){
-'use strict';
-
-var curves = exports;
-
-var hash = require('hash.js');
-var elliptic = require('../elliptic');
-
-var assert = elliptic.utils.assert;
-
-function PresetCurve(options) {
- if (options.type === 'short')
- this.curve = new elliptic.curve.short(options);
- else if (options.type === 'edwards')
- this.curve = new elliptic.curve.edwards(options);
- else
- this.curve = new elliptic.curve.mont(options);
- this.g = this.curve.g;
- this.n = this.curve.n;
- this.hash = options.hash;
-
- assert(this.g.validate(), 'Invalid curve');
- assert(this.g.mul(this.n).isInfinity(), 'Invalid curve, G*N != O');
-}
-curves.PresetCurve = PresetCurve;
-
-function defineCurve(name, options) {
- Object.defineProperty(curves, name, {
- configurable: true,
- enumerable: true,
- get: function() {
- var curve = new PresetCurve(options);
- Object.defineProperty(curves, name, {
- configurable: true,
- enumerable: true,
- value: curve
- });
- return curve;
- }
- });
-}
-
-defineCurve('p192', {
- type: 'short',
- prime: 'p192',
- p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',
- a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',
- b: '64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1',
- n: 'ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831',
- hash: hash.sha256,
- gRed: false,
- g: [
- '188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012',
- '07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811'
- ]
-});
-
-defineCurve('p224', {
- type: 'short',
- prime: 'p224',
- p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',
- a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',
- b: 'b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4',
- n: 'ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d',
- hash: hash.sha256,
- gRed: false,
- g: [
- 'b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21',
- 'bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34'
- ]
-});
-
-defineCurve('p256', {
- type: 'short',
- prime: null,
- p: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff',
- a: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc',
- b: '5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b',
- n: 'ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551',
- hash: hash.sha256,
- gRed: false,
- g: [
- '6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296',
- '4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5'
- ]
-});
-
-defineCurve('p384', {
- type: 'short',
- prime: null,
- p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'fffffffe ffffffff 00000000 00000000 ffffffff',
- a: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'fffffffe ffffffff 00000000 00000000 fffffffc',
- b: 'b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f ' +
- '5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef',
- n: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 ' +
- 'f4372ddf 581a0db2 48b0a77a ecec196a ccc52973',
- hash: hash.sha384,
- gRed: false,
- g: [
- 'aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 ' +
- '5502f25d bf55296c 3a545e38 72760ab7',
- '3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 ' +
- '0a60b1ce 1d7e819d 7a431d7c 90ea0e5f'
- ]
-});
-
-defineCurve('p521', {
- type: 'short',
- prime: null,
- p: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'ffffffff ffffffff ffffffff ffffffff ffffffff',
- a: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'ffffffff ffffffff ffffffff ffffffff fffffffc',
- b: '00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b ' +
- '99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd ' +
- '3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00',
- n: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
- 'ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 ' +
- 'f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409',
- hash: hash.sha512,
- gRed: false,
- g: [
- '000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 ' +
- '053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 ' +
- 'a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66',
- '00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 ' +
- '579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 ' +
- '3fad0761 353c7086 a272c240 88be9476 9fd16650'
- ]
-});
-
-defineCurve('curve25519', {
- type: 'mont',
- prime: 'p25519',
- p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
- a: '76d06',
- b: '1',
- n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
- hash: hash.sha256,
- gRed: false,
- g: [
- '9'
- ]
-});
-
-defineCurve('ed25519', {
- type: 'edwards',
- prime: 'p25519',
- p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
- a: '-1',
- c: '1',
- // -121665 * (121666^(-1)) (mod P)
- d: '52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3',
- n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
- hash: hash.sha256,
- gRed: false,
- g: [
- '216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a',
-
- // 4/5
- '6666666666666666666666666666666666666666666666666666666666666658'
- ]
-});
-
-var pre;
-try {
- pre = require('./precomputed/secp256k1');
-} catch (e) {
- pre = undefined;
-}
-
-defineCurve('secp256k1', {
- type: 'short',
- prime: 'k256',
- p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f',
- a: '0',
- b: '7',
- n: 'ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141',
- h: '1',
- hash: hash.sha256,
-
- // Precomputed endomorphism
- beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',
- lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',
- basis: [
- {
- a: '3086d221a7d46bcde86c90e49284eb15',
- b: '-e4437ed6010e88286f547fa90abfe4c3'
- },
- {
- a: '114ca50f7a8e2f3f657c1108d9d44cfd8',
- b: '3086d221a7d46bcde86c90e49284eb15'
- }
- ],
-
- gRed: false,
- g: [
- '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
- '483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',
- pre
- ]
-});
-
-},{"../elliptic":97,"./precomputed/secp256k1":110,"hash.js":114}],104:[function(require,module,exports){
-'use strict';
-
-var BN = require('bn.js');
-var HmacDRBG = require('hmac-drbg');
-var elliptic = require('../../elliptic');
-var utils = elliptic.utils;
-var assert = utils.assert;
-
-var KeyPair = require('./key');
-var Signature = require('./signature');
-
-function EC(options) {
- if (!(this instanceof EC))
- return new EC(options);
-
- // Shortcut `elliptic.ec(curve-name)`
- if (typeof options === 'string') {
- assert(elliptic.curves.hasOwnProperty(options), 'Unknown curve ' + options);
-
- options = elliptic.curves[options];
- }
-
- // Shortcut for `elliptic.ec(elliptic.curves.curveName)`
- if (options instanceof elliptic.curves.PresetCurve)
- options = { curve: options };
-
- this.curve = options.curve.curve;
- this.n = this.curve.n;
- this.nh = this.n.ushrn(1);
- this.g = this.curve.g;
-
- // Point on curve
- this.g = options.curve.g;
- this.g.precompute(options.curve.n.bitLength() + 1);
-
- // Hash for function for DRBG
- this.hash = options.hash || options.curve.hash;
-}
-module.exports = EC;
-
-EC.prototype.keyPair = function keyPair(options) {
- return new KeyPair(this, options);
-};
-
-EC.prototype.keyFromPrivate = function keyFromPrivate(priv, enc) {
- return KeyPair.fromPrivate(this, priv, enc);
-};
-
-EC.prototype.keyFromPublic = function keyFromPublic(pub, enc) {
- return KeyPair.fromPublic(this, pub, enc);
-};
-
-EC.prototype.genKeyPair = function genKeyPair(options) {
- if (!options)
- options = {};
-
- // Instantiate Hmac_DRBG
- var drbg = new HmacDRBG({
- hash: this.hash,
- pers: options.pers,
- persEnc: options.persEnc || 'utf8',
- entropy: options.entropy || elliptic.rand(this.hash.hmacStrength),
- entropyEnc: options.entropy && options.entropyEnc || 'utf8',
- nonce: this.n.toArray()
- });
-
- var bytes = this.n.byteLength();
- var ns2 = this.n.sub(new BN(2));
- do {
- var priv = new BN(drbg.generate(bytes));
- if (priv.cmp(ns2) > 0)
- continue;
-
- priv.iaddn(1);
- return this.keyFromPrivate(priv);
- } while (true);
-};
-
-EC.prototype._truncateToN = function truncateToN(msg, truncOnly) {
- var delta = msg.byteLength() * 8 - this.n.bitLength();
- if (delta > 0)
- msg = msg.ushrn(delta);
- if (!truncOnly && msg.cmp(this.n) >= 0)
- return msg.sub(this.n);
- else
- return msg;
-};
-
-EC.prototype.sign = function sign(msg, key, enc, options) {
- if (typeof enc === 'object') {
- options = enc;
- enc = null;
- }
- if (!options)
- options = {};
-
- key = this.keyFromPrivate(key, enc);
- msg = this._truncateToN(new BN(msg, 16));
-
- // Zero-extend key to provide enough entropy
- var bytes = this.n.byteLength();
- var bkey = key.getPrivate().toArray('be', bytes);
-
- // Zero-extend nonce to have the same byte size as N
- var nonce = msg.toArray('be', bytes);
-
- // Instantiate Hmac_DRBG
- var drbg = new HmacDRBG({
- hash: this.hash,
- entropy: bkey,
- nonce: nonce,
- pers: options.pers,
- persEnc: options.persEnc || 'utf8'
- });
-
- // Number of bytes to generate
- var ns1 = this.n.sub(new BN(1));
-
- for (var iter = 0; true; iter++) {
- var k = options.k ?
- options.k(iter) :
- new BN(drbg.generate(this.n.byteLength()));
- k = this._truncateToN(k, true);
- if (k.cmpn(1) <= 0 || k.cmp(ns1) >= 0)
- continue;
-
- var kp = this.g.mul(k);
- if (kp.isInfinity())
- continue;
-
- var kpX = kp.getX();
- var r = kpX.umod(this.n);
- if (r.cmpn(0) === 0)
- continue;
-
- var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg));
- s = s.umod(this.n);
- if (s.cmpn(0) === 0)
- continue;
-
- var recoveryParam = (kp.getY().isOdd() ? 1 : 0) |
- (kpX.cmp(r) !== 0 ? 2 : 0);
-
- // Use complement of `s`, if it is > `n / 2`
- if (options.canonical && s.cmp(this.nh) > 0) {
- s = this.n.sub(s);
- recoveryParam ^= 1;
- }
-
- return new Signature({ r: r, s: s, recoveryParam: recoveryParam });
- }
-};
-
-EC.prototype.verify = function verify(msg, signature, key, enc) {
- msg = this._truncateToN(new BN(msg, 16));
- key = this.keyFromPublic(key, enc);
- signature = new Signature(signature, 'hex');
-
- // Perform primitive values validation
- var r = signature.r;
- var s = signature.s;
- if (r.cmpn(1) < 0 || r.cmp(this.n) >= 0)
- return false;
- if (s.cmpn(1) < 0 || s.cmp(this.n) >= 0)
- return false;
-
- // Validate signature
- var sinv = s.invm(this.n);
- var u1 = sinv.mul(msg).umod(this.n);
- var u2 = sinv.mul(r).umod(this.n);
-
- if (!this.curve._maxwellTrick) {
- var p = this.g.mulAdd(u1, key.getPublic(), u2);
- if (p.isInfinity())
- return false;
-
- return p.getX().umod(this.n).cmp(r) === 0;
- }
-
- // NOTE: Greg Maxwell's trick, inspired by:
- // https://git.io/vad3K
-
- var p = this.g.jmulAdd(u1, key.getPublic(), u2);
- if (p.isInfinity())
- return false;
-
- // Compare `p.x` of Jacobian point with `r`,
- // this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the
- // inverse of `p.z^2`
- return p.eqXToP(r);
-};
-
-EC.prototype.recoverPubKey = function(msg, signature, j, enc) {
- assert((3 & j) === j, 'The recovery param is more than two bits');
- signature = new Signature(signature, enc);
-
- var n = this.n;
- var e = new BN(msg);
- var r = signature.r;
- var s = signature.s;
-
- // A set LSB signifies that the y-coordinate is odd
- var isYOdd = j & 1;
- var isSecondKey = j >> 1;
- if (r.cmp(this.curve.p.umod(this.curve.n)) >= 0 && isSecondKey)
- throw new Error('Unable to find sencond key candinate');
-
- // 1.1. Let x = r + jn.
- if (isSecondKey)
- r = this.curve.pointFromX(r.add(this.curve.n), isYOdd);
- else
- r = this.curve.pointFromX(r, isYOdd);
-
- var rInv = signature.r.invm(n);
- var s1 = n.sub(e).mul(rInv).umod(n);
- var s2 = s.mul(rInv).umod(n);
-
- // 1.6.1 Compute Q = r^-1 (sR - eG)
- // Q = r^-1 (sR + -eG)
- return this.g.mulAdd(s1, r, s2);
-};
-
-EC.prototype.getKeyRecoveryParam = function(e, signature, Q, enc) {
- signature = new Signature(signature, enc);
- if (signature.recoveryParam !== null)
- return signature.recoveryParam;
-
- for (var i = 0; i < 4; i++) {
- var Qprime;
- try {
- Qprime = this.recoverPubKey(e, signature, i);
- } catch (e) {
- continue;
- }
-
- if (Qprime.eq(Q))
- return i;
- }
- throw new Error('Unable to find valid recovery factor');
-};
-
-},{"../../elliptic":97,"./key":105,"./signature":106,"bn.js":81,"hmac-drbg":120}],105:[function(require,module,exports){
-'use strict';
-
-var BN = require('bn.js');
-var elliptic = require('../../elliptic');
-var utils = elliptic.utils;
-var assert = utils.assert;
-
-function KeyPair(ec, options) {
- this.ec = ec;
- this.priv = null;
- this.pub = null;
-
- // KeyPair(ec, { priv: ..., pub: ... })
- if (options.priv)
- this._importPrivate(options.priv, options.privEnc);
- if (options.pub)
- this._importPublic(options.pub, options.pubEnc);
-}
-module.exports = KeyPair;
-
-KeyPair.fromPublic = function fromPublic(ec, pub, enc) {
- if (pub instanceof KeyPair)
- return pub;
-
- return new KeyPair(ec, {
- pub: pub,
- pubEnc: enc
- });
-};
-
-KeyPair.fromPrivate = function fromPrivate(ec, priv, enc) {
- if (priv instanceof KeyPair)
- return priv;
-
- return new KeyPair(ec, {
- priv: priv,
- privEnc: enc
- });
-};
-
-KeyPair.prototype.validate = function validate() {
- var pub = this.getPublic();
-
- if (pub.isInfinity())
- return { result: false, reason: 'Invalid public key' };
- if (!pub.validate())
- return { result: false, reason: 'Public key is not a point' };
- if (!pub.mul(this.ec.curve.n).isInfinity())
- return { result: false, reason: 'Public key * N != O' };
-
- return { result: true, reason: null };
-};
-
-KeyPair.prototype.getPublic = function getPublic(compact, enc) {
- // compact is optional argument
- if (typeof compact === 'string') {
- enc = compact;
- compact = null;
- }
-
- if (!this.pub)
- this.pub = this.ec.g.mul(this.priv);
-
- if (!enc)
- return this.pub;
-
- return this.pub.encode(enc, compact);
-};
-
-KeyPair.prototype.getPrivate = function getPrivate(enc) {
- if (enc === 'hex')
- return this.priv.toString(16, 2);
- else
- return this.priv;
-};
-
-KeyPair.prototype._importPrivate = function _importPrivate(key, enc) {
- this.priv = new BN(key, enc || 16);
-
- // Ensure that the priv won't be bigger than n, otherwise we may fail
- // in fixed multiplication method
- this.priv = this.priv.umod(this.ec.curve.n);
-};
-
-KeyPair.prototype._importPublic = function _importPublic(key, enc) {
- if (key.x || key.y) {
- // Montgomery points only have an `x` coordinate.
- // Weierstrass/Edwards points on the other hand have both `x` and
- // `y` coordinates.
- if (this.ec.curve.type === 'mont') {
- assert(key.x, 'Need x coordinate');
- } else if (this.ec.curve.type === 'short' ||
- this.ec.curve.type === 'edwards') {
- assert(key.x && key.y, 'Need both x and y coordinate');
- }
- this.pub = this.ec.curve.point(key.x, key.y);
- return;
- }
- this.pub = this.ec.curve.decodePoint(key, enc);
-};
-
-// ECDH
-KeyPair.prototype.derive = function derive(pub) {
- return pub.mul(this.priv).getX();
-};
-
-// ECDSA
-KeyPair.prototype.sign = function sign(msg, enc, options) {
- return this.ec.sign(msg, this, enc, options);
-};
-
-KeyPair.prototype.verify = function verify(msg, signature) {
- return this.ec.verify(msg, signature, this);
-};
-
-KeyPair.prototype.inspect = function inspect() {
- return '<Key priv: ' + (this.priv && this.priv.toString(16, 2)) +
- ' pub: ' + (this.pub && this.pub.inspect()) + ' >';
-};
-
-},{"../../elliptic":97,"bn.js":81}],106:[function(require,module,exports){
-'use strict';
-
-var BN = require('bn.js');
-
-var elliptic = require('../../elliptic');
-var utils = elliptic.utils;
-var assert = utils.assert;
-
-function Signature(options, enc) {
- if (options instanceof Signature)
- return options;
-
- if (this._importDER(options, enc))
- return;
-
- assert(options.r && options.s, 'Signature without r or s');
- this.r = new BN(options.r, 16);
- this.s = new BN(options.s, 16);
- if (options.recoveryParam === undefined)
- this.recoveryParam = null;
- else
- this.recoveryParam = options.recoveryParam;
-}
-module.exports = Signature;
-
-function Position() {
- this.place = 0;
-}
-
-function getLength(buf, p) {
- var initial = buf[p.place++];
- if (!(initial & 0x80)) {
- return initial;
- }
- var octetLen = initial & 0xf;
- var val = 0;
- for (var i = 0, off = p.place; i < octetLen; i++, off++) {
- val <<= 8;
- val |= buf[off];