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(x.isNeg != y.isNeg) { y.isNeg = !y.isNeg; result = biSubtract(x, y); y.isNeg = !y.isNeg; } else { result = new BigInt(); var c = 0; var n; for (var i = 0; i < x.digits.length; ++i) { n = x.digits[i] + y.digits[i] + c; result.digits[i] = n % biRadix; c = Number(n >= biRadix); } result.isNeg = x.isNeg; } return result; } function biSubtract(x, y) { var result; if (x.isNeg != y.isNeg) { y.isNeg = !y.isNeg; result = biAdd(x, y); y.isNeg = !y.isNeg; } else { result = new BigInt(); var n, c; c = 0; for (var i = 0; i < x.digits.length; ++i) { n = x.digits[i] - y.digits[i] + c; result.digits[i] = n % biRadix; // Stupid non-conforming modulus operation. if (result.digits[i] < 0) result.digits[i] += biRadix; c = 0 - Number(n < 0); } // Fix up the negative sign, if any. if (c == -1) { c = 0; for (var i = 0; i < x.digits.length; ++i) { n = 0 - result.digits[i] + c; result.digits[i] = n % biRadix; // Stupid non-conforming modulus operation. if (result.digits[i] < 0) result.digits[i] += biRadix; c = 0 - Number(n < 0); } // Result is opposite sign of arguments. result.isNeg = !x.isNeg; } else { // Result is same sign. result.isNeg = x.isNeg; } } return result; } function biHighIndex(x) { var result = x.digits.length - 1; while (result > 0 && x.digits[result] == 0) --result; return result; } function biNumBits(x) { var n = biHighIndex(x); var d = x.digits[n]; var m = (n + 1) * bitsPerDigit; var result; for (result = m; result > m - bitsPerDigit; --result) { if ((d & 0x8000) != 0) break; d <<= 1; } return result; } function biMultiply(x, y) { var result = new BigInt(); var c; var n = biHighIndex(x); var t = biHighIndex(y); var u, uv, k; for (var i = 0; i <= t; ++i) { c = 0; k = i; for (j = 0; j <= n; ++j, ++k) { uv = result.digits[k] + x.digits[j] * y.digits[i] + c; result.digits[k] = uv & maxDigitVal; c = uv >>> biRadixBits; //c = Math.floor(uv / biRadix); } result.digits[i + n + 1] = c; } // Someone give me a logical xor, please. result.isNeg = x.isNeg != y.isNeg; return result; } function biMultiplyDigit(x, y) { var n, c, uv; result = new BigInt(); n = biHighIndex(x); c = 0; for (var j = 0; j <= n; ++j) { uv = result.digits[j] + x.digits[j] * y + c; result.digits[j] = uv & maxDigitVal; c = uv >>> biRadixBits; //c = Math.floor(uv / biRadix); } result.digits[1 + n] = c; return result; } function arrayCopy(src, srcStart, dest, destStart, n) { var m = Math.min(srcStart + n, src.length); for (var i = srcStart, j = destStart; i < m; ++i, ++j) { dest[j] = src[i]; } } var highBitMasks = new Array(0x0000, 0x8000, 0xC000, 0xE000, 0xF000, 0xF800, 0xFC00, 0xFE00, 0xFF00, 0xFF80, 0xFFC0, 0xFFE0, 0xFFF0, 0xFFF8, 0xFFFC, 0xFFFE, 0xFFFF); function biShiftLeft(x, n) { var digitCount = Math.floor(n / bitsPerDigit); var result = new BigInt(); arrayCopy(x.digits, 0, result.digits, digitCount, result.digits.length - digitCount); var bits = n % bitsPerDigit; var rightBits = bitsPerDigit - bits; for (var i = result.digits.length - 1, i1 = i - 1; i > 0; --i, --i1) { result.digits[i] = ((result.digits[i] << bits) & maxDigitVal) | ((result.digits[i1] & highBitMasks[bits]) >>> (rightBits)); } result.digits[0] = ((result.digits[i] << bits) & maxDigitVal); result.isNeg = x.isNeg; return result; } var lowBitMasks = new Array(0x0000, 0x0001, 0x0003, 0x0007, 0x000F, 0x001F, 0x003F, 0x007F, 0x00FF, 0x01FF, 0x03FF, 0x07FF, 0x0FFF, 0x1FFF, 0x3FFF, 0x7FFF, 0xFFFF); function biShiftRight(x, n) { var digitCount = Math.floor(n / bitsPerDigit); var result = new BigInt(); arrayCopy(x.digits, digitCount, result.digits, 0, x.digits.length - digitCount); var bits = n % bitsPerDigit; var leftBits = bitsPerDigit - bits; for (var i = 0, i1 = i + 1; i < result.digits.length - 1; ++i, ++i1) { result.digits[i] = (result.digits[i] >>> bits) | ((result.digits[i1] & lowBitMasks[bits]) << leftBits); } result.digits[result.digits.length - 1] >>>= bits; result.isNeg = x.isNeg; return result; } function biMultiplyByRadixPower(x, n) { var result = new BigInt(); arrayCopy(x.digits, 0, result.digits, n, result.digits.length - n); return result; } function biDivideByRadixPower(x, n) { var result = new BigInt(); arrayCopy(x.digits, n, result.digits, 0, result.digits.length - n); return result; } function biModuloByRadixPower(x, n) { var result = new BigInt(); arrayCopy(x.digits, 0, result.digits, 0, n); return result; } function biCompare(x, y) { if (x.isNeg != y.isNeg) { return 1 - 2 * Number(x.isNeg); } for (var i = x.digits.length - 1; i >= 0; --i) { if (x.digits[i] != y.digits[i]) { if (x.isNeg) { return 1 - 2 * Number(x.digits[i] > y.digits[i]); } else { return 1 - 2 * Number(x.digits[i] < y.digits[i]); } } } return 0; } function biDivideModulo(x, y) { var nb = biNumBits(x); var tb = biNumBits(y); var origYIsNeg = y.isNeg; var q, r; if (nb < tb) { // |x| < |y| if (x.isNeg) { q = biCopy(bigOne); q.isNeg = !y.isNeg; x.isNeg = false; y.isNeg = false; r = biSubtract(y, x); // Restore signs, 'cause they're references. x.isNeg = true; y.isNeg = origYIsNeg; } else { q = new BigInt(); r = biCopy(x); } return new Array(q, r); } q = new BigInt(); r = x; // Normalize Y. var t = Math.ceil(tb / bitsPerDigit) - 1; var lambda = 0; while (y.digits[t] < biHalfRadix) { y = biShiftLeft(y, 1); ++lambda; ++tb; t = Math.ceil(tb / bitsPerDigit) - 1; } r = biShiftLeft(r, lambda); nb += lambda; // Update the bit count for x. var n = Math.ceil(nb / bitsPerDigit) - 1; var b = biMultiplyByRadixPower(y, n - t); while (biCompare(r, b) != -1) { ++q.digits[n - t]; r = biSubtract(r, b); } for (var i = n; i > t; --i) { var ri = (i >= r.digits.length) ? 0 : r.digits[i]; var ri1 = (i - 1 >= r.digits.length) ? 0 : r.digits[i - 1]; var ri2 = (i - 2 >= r.digits.length) ? 0 : r.digits[i - 2]; var yt = (t >= y.digits.length) ? 0 : y.digits[t]; var yt1 = (t - 1 >= y.digits.length) ? 0 : y.digits[t - 1]; if (ri == yt) { q.digits[i - t - 1] = maxDigitVal; } else { q.digits[i - t - 1] = Math.floor((ri * biRadix + ri1) / yt); } var c1 = q.digits[i - t - 1] * ((yt * biRadix) + yt1); var c2 = (ri * biRadixSquared) + ((ri1 * biRadix) + ri2); while (c1 > c2) { --q.digits[i - t - 1]; c1 = q.digits[i - t - 1] * ((yt * biRadix) | yt1); c2 = (ri * biRadix * biRadix) + ((ri1 * biRadix) + ri2); } b = biMultiplyByRadixPower(y, i - t - 1); r = biSubtract(r, biMultiplyDigit(b, q.digits[i - t - 1])); if (r.isNeg) { r = biAdd(r, b); --q.digits[i - t - 1]; } } r = biShiftRight(r, lambda); // Fiddle with the signs and stuff to make sure that 0 <= r < y. q.isNeg = x.isNeg != origYIsNeg; if (x.isNeg) { if (origYIsNeg) { q = biAdd(q, bigOne); } else { q = biSubtract(q, bigOne); } y = biShiftRight(y, lambda); r = biSubtract(y, r); } // Check for the unbelievably stupid degenerate case of r == -0. if (r.digits[0] == 0 && biHighIndex(r) == 0) r.isNeg = false; return new Array(q, r); } function biDivide(x, y) { return biDivideModulo(x, y)[0]; } function biModulo(x, y) { return biDivideModulo(x, y)[1]; } function biMultiplyMod(x, y, m) { return biModulo(biMultiply(x, y), m); } function biPow(x, y) { var result = bigOne; var a = x; while (true) { if ((y & 1) != 0) result = biMultiply(result, a); y >>= 1; if (y == 0) break; a = biMultiply(a, a); } return result; } function biPowMod(x, y, m) { var result = bigOne; var a = x; var k = y; while (true) { if ((k.digits[0] & 1) != 0) result = biMultiplyMod(result, a, m); k = biShiftRight(k, 1); if (k.digits[0] == 0 && biHighIndex(k) == 0) break; a = biMultiplyMod(a, a, m); } return result; } // ----------------------------- /* RSA */ function RSAKeyPair(encryptionExponent, decryptionExponent, modulus) { this.e = biFromHex(encryptionExponent); this.d = biFromHex(decryptionExponent); this.m = biFromHex(modulus); this.digitSize = 2 * biHighIndex(this.m) + 2; this.chunkSize = this.digitSize - 11; this.radix = 16; this.barrett = new BarrettMu(this.m); } function twoDigit(n) { return (n < 10 ? "0" : "") + String(n); } function encryptedString(key, s) { if (key.chunkSize > key.digitSize - 11) { return "Error"; } var a = new Array(); var sl = s.length; var i = 0; while (i < sl) { a[i] = s.charCodeAt(i); i++; } var al = a.length; var result = ""; var j, k, block; for (i = 0; i < al; i += key.chunkSize) { block = new BigInt(); j = 0; var x; var msgLength = (i+key.chunkSize)>al ? al%key.chunkSize : key.chunkSize; var b = new Array(); for (x=0; x<msgLength; x++) { b[x] = a[i+msgLength-1-x]; } b[msgLength] = 0; // marker var paddedSize = Math.max(8, key.digitSize - 3 - msgLength); for (x=0; x<paddedSize; x++) { b[msgLength+1+x] = Math.floor(Math.random()*254) + 1; // [1,255] } // It can be asserted that msgLength+paddedSize == key.digitSize-3 b[key.digitSize-2] = 2; // marker b[key.digitSize-1] = 0; // marker for (k = 0; k < key.digitSize; ++j) { block.digits[j] = b[k++]; block.digits[j] += b[k++] << 8; } var crypt = key.barrett.powMod(block, key.e); var text = key.radix == 16 ? biToHex(crypt) : biToString(crypt, key.radix); result += text + " "; } return result.substring(0, result.length - 1); // Remove last space. } function decryptedString(key, s) { var blocks = s.split(" "); var result = ""; var i, j, block; for (i = 0; i < blocks.length; ++i) { var bi; if (key.radix == 16) { bi = biFromHex(blocks[i]); } else { bi