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Many thanks to its contributors: * * https://github.com/dchest/tweetnacl-js */ var forge = require('./forge'); require('./jsbn'); require('./random'); require('./sha512'); require('./util'); var asn1Validator = require('./asn1-validator'); var publicKeyValidator = asn1Validator.publicKeyValidator; var privateKeyValidator = asn1Validator.privateKeyValidator; if(typeof BigInteger === 'undefined') { var BigInteger = forge.jsbn.BigInteger; } var ByteBuffer = forge.util.ByteBuffer; var NativeBuffer = typeof Buffer === 'undefined' ? Uint8Array : Buffer; /* * Ed25519 algorithms, see RFC 8032: * https://tools.ietf.org/html/rfc8032 */ forge.pki = forge.pki || {}; module.exports = forge.pki.ed25519 = forge.ed25519 = forge.ed25519 || {}; var ed25519 = forge.ed25519; ed25519.constants = {}; ed25519.constants.PUBLIC_KEY_BYTE_LENGTH = 32; ed25519.constants.PRIVATE_KEY_BYTE_LENGTH = 64; ed25519.constants.SEED_BYTE_LENGTH = 32; ed25519.constants.SIGN_BYTE_LENGTH = 64; ed25519.constants.HASH_BYTE_LENGTH = 64; ed25519.generateKeyPair = function(options) { options = options || {}; var seed = options.seed; if(seed === undefined) { // generate seed seed = forge.random.getBytesSync(ed25519.constants.SEED_BYTE_LENGTH); } else if(typeof seed === 'string') { if(seed.length !== ed25519.constants.SEED_BYTE_LENGTH) { throw new TypeError( '"seed" must be ' + ed25519.constants.SEED_BYTE_LENGTH + ' bytes in length.'); } } else if(!(seed instanceof Uint8Array)) { throw new TypeError( '"seed" must be a node.js Buffer, Uint8Array, or a binary string.'); } seed = messageToNativeBuffer({message: seed, encoding: 'binary'}); var pk = new NativeBuffer(ed25519.constants.PUBLIC_KEY_BYTE_LENGTH); var sk = new NativeBuffer(ed25519.constants.PRIVATE_KEY_BYTE_LENGTH); for(var i = 0; i < 32; ++i) { sk[i] = seed[i]; } crypto_sign_keypair(pk, sk); return {publicKey: pk, privateKey: sk}; }; /** * Converts a private key from a RFC8410 ASN.1 encoding. * * @param obj - The asn1 representation of a private key. * * @returns {Object} keyInfo - The key information. * @returns {Buffer|Uint8Array} keyInfo.privateKeyBytes - 32 private key bytes. */ ed25519.privateKeyFromAsn1 = function(obj) { var capture = {}; var errors = []; var valid = forge.asn1.validate(obj, privateKeyValidator, capture, errors); if(!valid) { var error = new Error('Invalid Key.'); error.errors = errors; throw error; } var oid = forge.asn1.derToOid(capture.privateKeyOid); var ed25519Oid = forge.oids.EdDSA25519; if(oid !== ed25519Oid) { throw new Error('Invalid OID "' + oid + '"; OID must be "' + ed25519Oid + '".'); } var privateKey = capture.privateKey; // manually extract the private key bytes from nested octet string, see FIXME: // https://github.com/digitalbazaar/forge/blob/master/lib/asn1.js#L542 var privateKeyBytes = messageToNativeBuffer({ message: forge.asn1.fromDer(privateKey).value, encoding: 'binary' }); // TODO: RFC8410 specifies a format for encoding the public key bytes along // with the private key bytes. `publicKeyBytes` can be returned in the // future. https://tools.ietf.org/html/rfc8410#section-10.3 return {privateKeyBytes: privateKeyBytes}; }; /** * Converts a public key from a RFC8410 ASN.1 encoding. * * @param obj - The asn1 representation of a public key. * * @return {Buffer|Uint8Array} - 32 public key bytes. */ ed25519.publicKeyFromAsn1 = function(obj) { // get SubjectPublicKeyInfo var capture = {}; var errors = []; var valid = forge.asn1.validate(obj, publicKeyValidator, capture, errors); if(!valid) { var error = new Error('Invalid Key.'); error.errors = errors; throw error; } var oid = forge.asn1.derToOid(capture.publicKeyOid); var ed25519Oid = forge.oids.EdDSA25519; if(oid !== ed25519Oid) { throw new Error('Invalid OID "' + oid + '"; OID must be "' + ed25519Oid + '".'); } var publicKeyBytes = capture.ed25519PublicKey; if(publicKeyBytes.length !== ed25519.constants.PUBLIC_KEY_BYTE_LENGTH) { throw new Error('Key length is invalid.'); } return messageToNativeBuffer({ message: publicKeyBytes, encoding: 'binary' }); }; ed25519.publicKeyFromPrivateKey = function(options) { options = options || {}; var privateKey = messageToNativeBuffer({ message: options.privateKey, encoding: 'binary' }); if(privateKey.length !== ed25519.constants.PRIVATE_KEY_BYTE_LENGTH) { throw new TypeError( '"options.privateKey" must have a byte length of ' + ed25519.constants.PRIVATE_KEY_BYTE_LENGTH); } var pk = new NativeBuffer(ed25519.constants.PUBLIC_KEY_BYTE_LENGTH); for(var i = 0; i < pk.length; ++i) { pk[i] = privateKey[32 + i]; } return pk; }; ed25519.sign = function(options) { options = options || {}; var msg = messageToNativeBuffer(options); var privateKey = messageToNativeBuffer({ message: options.privateKey, encoding: 'binary' }); if(privateKey.length === ed25519.constants.SEED_BYTE_LENGTH) { var keyPair = ed25519.generateKeyPair({seed: privateKey}); privateKey = keyPair.privateKey; } else if(privateKey.length !== ed25519.constants.PRIVATE_KEY_BYTE_LENGTH) { throw new TypeError( '"options.privateKey" must have a byte length of ' + ed25519.constants.SEED_BYTE_LENGTH + ' or ' + ed25519.constants.PRIVATE_KEY_BYTE_LENGTH); } var signedMsg = new NativeBuffer( ed25519.constants.SIGN_BYTE_LENGTH + msg.length); crypto_sign(signedMsg, msg, msg.length, privateKey); var sig = new NativeBuffer(ed25519.constants.SIGN_BYTE_LENGTH); for(var i = 0; i < sig.length; ++i) { sig[i] = signedMsg[i]; } return sig; }; ed25519.verify = function(options) { options = options || {}; var msg = messageToNativeBuffer(options); if(options.signature === undefined) { throw new TypeError( '"options.signature" must be a node.js Buffer, a Uint8Array, a forge ' + 'ByteBuffer, or a binary string.'); } var sig = messageToNativeBuffer({ message: options.signature, encoding: 'binary' }); if(sig.length !== ed25519.constants.SIGN_BYTE_LENGTH) { throw new TypeError( '"options.signature" must have a byte length of ' + ed25519.constants.SIGN_BYTE_LENGTH); } var publicKey = messageToNativeBuffer({ message: options.publicKey, encoding: 'binary' }); if(publicKey.length !== ed25519.constants.PUBLIC_KEY_BYTE_LENGTH) { throw new TypeError( '"options.publicKey" must have a byte length of ' + ed25519.constants.PUBLIC_KEY_BYTE_LENGTH); } var sm = new NativeBuffer(ed25519.constants.SIGN_BYTE_LENGTH + msg.length); var m = new NativeBuffer(ed25519.constants.SIGN_BYTE_LENGTH + msg.length); var i; for(i = 0; i < ed25519.constants.SIGN_BYTE_LENGTH; ++i) { sm[i] = sig[i]; } for(i = 0; i < msg.length; ++i) { sm[i + ed25519.constants.SIGN_BYTE_LENGTH] = msg[i]; } return (crypto_sign_open(m, sm, sm.length, publicKey) >= 0); }; function messageToNativeBuffer(options) { var message = options.message; if(message instanceof Uint8Array || message instanceof NativeBuffer) { return message; } var encoding = options.encoding; if(message === undefined) { if(options.md) { // TODO: more rigorous validation that `md` is a MessageDigest message = options.md.digest().getBytes(); encoding = 'binary'; } else { throw new TypeError('"options.message" or "options.md" not specified.'); } } if(typeof message === 'string' && !encoding) { throw new TypeError('"options.encoding" must be "binary" or "utf8".'); } if(typeof message === 'string') { if(typeof Buffer !== 'undefined') { return Buffer.from(message, encoding); } message = new ByteBuffer(message, encoding); } else if(!(message instanceof ByteBuffer)) { throw new TypeError( '"options.message" must be a node.js Buffer, a Uint8Array, a forge ' + 'ByteBuffer, or a string with "options.encoding" specifying its ' + 'encoding.'); } // convert to native buffer var buffer = new NativeBuffer(message.length()); for(var i = 0; i < buffer.length; ++i) { buffer[i] = message.at(i); } return buffer; } var gf0 = gf(); var gf1 = gf([1]); var D = gf([ 0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab, 0x4141, 0x0a4d, 0x0070, 0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203]); var D2 = gf([ 0xf159, 0x26b2, 0x9b94, 0xebd6, 0xb156, 0x8283, 0x149a, 0x00e0, 0xd130, 0xeef3, 0x80f2, 0x198e, 0xfce7, 0x56df, 0xd9dc, 0x2406]); var X = gf([ 0xd51a, 0x8f25, 0x2d60, 0xc956, 0xa7b2, 0x9525, 0xc760, 0x692c, 0xdc5c, 0xfdd6, 0xe231, 0xc0a4, 0x53fe, 0xcd6e, 0x36d3, 0x2169]); var Y = gf([ 0x6658, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666]); var L = new Float64Array([ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0x10]); var I = gf([ 0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43, 0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83]); // TODO: update forge buffer implementation to use `Buffer` or `Uint8Array`, // whichever is available, to improve performance function sha512(msg, msgLen) { // Note: `out` and `msg` are NativeBuffer var md = forge.md.sha512.create(); var buffer = new ByteBuffer(msg); md.update(buffer.getBytes(msgLen), 'binary'); var hash = md.digest().getBytes(); if(typeof Buffer !== 'undefined') { return Buffer.from(hash, 'binary'); } var out = new NativeBuffer(ed25519.constants.HASH_BYTE_LENGTH); for(var i = 0; i < 64; ++i) { out[i] = hash.charCodeAt(i); } return out; } function crypto_sign_keypair(pk, sk) { var p = [gf(), gf(), gf(), gf()]; var i; var d = sha512(sk, 32); d[0] &= 248; d[31] &= 127; d[31] |= 64; scalarbase(p, d); pack(pk, p); for(i = 0; i < 32; ++i) { sk[i + 32] = pk[i]; } return 0; } // Note: difference from C - smlen returned, not passed as argument. function crypto_sign(sm, m, n, sk) { var i, j, x = new Float64Array(64); var p = [gf(), gf(), gf(), gf()]; var d = sha512(sk, 32); d[0] &= 248; d[31] &= 127; d[31] |= 64; var smlen = n + 64; for(i = 0; i < n; ++i) { sm[64 + i] = m[i]; } for(i = 0; i < 32; ++i) { sm[32 + i] = d[32 + i]; } var r = sha512(sm.subarray(32), n + 32); reduce(r); scalarbase(p, r); pack(sm, p); for(i = 32; i < 64; ++i) { sm[i] = sk[i]; } var h = sha512(sm, n + 64); reduce(h); for(i = 32; i < 64; ++i) { x[i] = 0; } for(i = 0; i < 32; ++i) { x[i] = r[i]; } for(i = 0; i < 32; ++i) { for(j = 0; j < 32; j++) { x[i + j] += h[i] * d[j]; } } modL(sm.subarray(32), x); return smlen; } function crypto_sign_open(m, sm, n, pk) { var i, mlen; var t = new NativeBuffer(32); var p = [gf(), gf(), gf(), gf()], q = [gf(), gf(), gf(), gf()]; mlen = -1; if(n < 64) { return -1; } if(unpackneg(q, pk)) { return -1; } for(i = 0; i < n; ++i) { m[i] = sm[i]; } for(i = 0; i < 32; ++i) { m[i + 32] = pk[i]; } var h = sha512(m, n); reduce(h); scalarmult(p, q, h); scalarbase(q, sm.subarray(32)); add(p, q); pack(t, p); n -= 64; if(crypto_verify_32(sm, 0, t, 0)) { for(i = 0; i < n; ++i) { m[i] = 0; } return -1; } for(i = 0; i < n; ++i) { m[i] = sm[i + 64]; } mlen = n; return mlen; } function modL(r, x) { var carry, i, j, k; for(i = 63; i >= 32; --i) { carry = 0; for(j = i - 32, k = i - 12; j < k; ++j) { x[j] += carry - 16 * x[i] * L[j - (i - 32)]; carry = (x[j] + 128) >> 8; x[j] -= carry * 256; } x[j] += carry; x[i] = 0; } carry = 0; for(j = 0; j < 32; ++j) { x[j] += carry - (x[31] >> 4) * L[j]; carry = x[j] >> 8; x[j] &= 255; } for(j = 0; j < 32; ++j) { x[j] -= carry * L[j]; } for(i = 0; i < 32; ++i) { x[i + 1] += x[i] >> 8; r[i] = x[i] & 255; } } function reduce(r) { var x = new Float64Array(64); for(var i = 0; i < 64; ++i) { x[i] = r[i]; r[i] = 0; } modL(r, x); } function add(p, q) { var a = gf(), b = gf(), c = gf(), d = gf(), e = gf(), f = gf(), g = gf(), h = gf(), t = gf(); Z(a, p[1], p[0]); Z(t, q[1], q[0]); M(a, a, t); A(b, p[0], p[1]); A(t, q[0], q[1]); M(b, b, t); M(c, p[3], q[3]); M(c, c, D2); M(d, p[2], q[2]); A(d, d, d); Z(e, b, a); Z(f, d, c); A(g, d, c); A(h, b, a); M(p[0], e, f); M(p[1], h, g); M(p[2], g, f); M(p[3], e, h); } function cswap(p, q, b) { for(var i = 0; i < 4; ++i) { sel25519(p[i], q[i], b); } } function pack(r, p) { var tx = gf(), ty = gf(), zi = gf(); inv25519(zi, p[2]); M(tx, p[0], zi); M(ty, p[1], zi); pack25519(r, ty); r[31] ^= par25519(tx) << 7; } function pack25519(o, n) { var i, j, b; var m = gf(), t = gf(); for(i = 0; i < 16; ++i) { t[i] = n[i]; } car25519(t); car25519(t); car25519(t); for(j = 0; j < 2; ++j) { m[0] = t[0] - 0xffed; for(i = 1; i < 15; ++i) { m[i] = t[i] - 0xffff - ((m[i - 1] >> 16) & 1); m[i-1] &= 0xffff; } m[15] = t[15] - 0x7fff - ((m[14] >> 16) & 1); b = (m[15] >> 16) & 1; m[14] &= 0xffff; sel25519(t, m, 1 - b); } for (i = 0; i < 16; i++) { o[2 * i] = t[i] & 0xff; o[2 * i + 1] = t[i] >> 8; } } function unpackneg(r, p) { var t = gf(), chk = gf(), num = gf(), den = gf(), den2 = gf(), den4 = gf(), den6 = gf(); set25519(r[2], gf1); unpack25519(r[1], p); S(num, r[1]); M(den, num, D); Z(num, num, r[2]); A(den, r[2], den); S(den2, den); S(den4, den2); M(den6, den4, den2); M(t, den6, num); M(t, t, den); pow2523(t, t); M(t, t, num); M(t, t, den); M(t, t, den); M(r[0], t, den); S(chk, r[0]); M(chk, chk, den); if(neq25519(chk, num)) { M(r[0], r[0], I); } S(chk, r[0]); M(chk, chk, den); if(neq25519(chk, num)) { return -1; } if(par25519(r[0]) === (p[31] >> 7)) { Z(r[0], gf0, r[0]); } M(r[3], r[0], r[1]); return 0; } function unpack25519(o, n) { var i; for(i = 0; i < 16; ++i) { o[i] = n[2 * i] + (n[2 * i + 1] << 8); } o[15] &= 0x7fff; } function pow2523(o, i) { var c = gf(); var a; for(a = 0; a < 16; ++a) { c[a] = i[a]; } for(a = 250; a >= 0; --a) { S(c, c); if(a !== 1) { M(c, c, i); } } for(a = 0; a < 16; ++a) { o[a] = c[a]; } } function neq25519(a, b) { var c = new NativeBuffer(32); var d = new NativeBuffer(32); pack25519(c, a); pack25519(d, b); return crypto_verify_32(c, 0, d, 0); } function crypto_verify_32(x, xi, y, yi) { return vn(x, xi, y, yi, 32); } function vn(x, xi, y, yi, n) { var i, d = 0; for(i = 0; i < n; ++i) { d |= x[xi + i] ^ y[yi + i]; } return (1 & ((d - 1) >>> 8)) - 1; } function par25519(a) { var d = new NativeBuffer(32); pack25519(d, a); return d[0] & 1; } function scalarmult(p, q, s) { var b, i; set25519(p[0], gf0); set25519(p[1], gf1); set25519(p[2], gf1); set25519(p[3], gf0); for(i = 255; i >= 0; --i) { b = (s[(i / 8)|0] >> (i & 7)) & 1; cswap(p, q, b); add(q, p); add(p, p); cswap(p, q, b); } } function scalarbase(p, s) { var q = [gf(), gf(), gf(), gf()]; set25519(q[0], X); set25519(q[1], Y); set25519(q[2], gf1); M(q[3], X, Y); scalarmult(p, q, s); } function set25519(r, a) { var i; for(i = 0; i < 16; i++) { r[i] = a[i] | 0; } } function inv25519(o, i) { var c = gf(); var a; for(a = 0; a < 16; ++a) { c[a] = i[a]; } for(a = 253; a >= 0; --a) { S(c, c); if(a !== 2 && a !== 4) { M(c, c, i); } } for(a = 0; a < 16; ++a) { o[a] = c[a]; } } function car25519(o) { var i, v, c = 1; for(i = 0; i < 16; ++i) { v = o[i] + c + 65535; c = Math.floor(v / 65536); o[i] = v - c * 65536; } o[0] += c - 1 + 37 * (c - 1); } function sel25519(p, q, b) { var t, c = ~(b - 1); for(var i = 0; i < 16; ++i) { t = c & (p[i] ^ q[i]); p[i] ^= t; q[i] ^= t; } } function gf(init) { var i, r = new Float64Array(16); if(init) { for(i = 0; i < init.length; ++i) { r[i] = init[i]; } } return r; } function A(o, a, b) { for(var i = 0; i < 16; ++i) { o[i] = a[i] + b[i]; } } function Z(o, a, b) { for(var i = 0; i < 16; ++i) { o[i] = a[i] - b[i]; } } function S(o, a) { M(o, a, a); } function M(o, a, b) { var v, c, t0 = 0, t1 = 0, t2 = 0, t3 = 0, t4 = 0, t5 = 0, t6 = 0, t7 = 0, t8 = 0, t9 = 0, t10 = 0, t11 = 0, t12 = 0, t13 = 0, t14 = 0, t15 = 0, t16 = 0, t17 = 0, t18 = 0, t19 = 0, t20 = 0, t21 = 0, t22 = 0, t23 = 0, t24 = 0, t25 = 0, t26 = 0, t27 = 0, t28 = 0, t29 = 0, t30 = 0, b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5], b6 = b[6], b7 = b[7], b8 = b[8], b9 = b[9], b10 = b[10], b11 = b[11], b12 = b[12], b13 = b[13], b14 = b[14], b15 = b[15]; v = a[0]; t0 += v * b0; t1 += v * b1; t2 += v * b2; t3 += v * b3; t4 += v * b4; t5 += v * b5; t6 += v * b6; t7 += v * b7; t8 += v * b8; t9 += v * b9; t10 += v * b10; t11 += v * b11; t12 += v * b12; t13 += v * b13; t14 += v * b14; t15 += v * b15; v = a[1]; t1 += v * b0; t2 += v * b1; t3 += v * b2; t4 += v * b3; t5 += v * b4; t6 += v * b5; t7 += v * b6; t8 += v * b7; t9 += v * b8; t10 += v * b9; t11 += v * b10; t12 += v * b11; t13 += v * b12; t14 += v * b13; t15 += v * b14; t16 += v * b15; v = a[2]; t2 += v * b0; t3 += v * b1; t4 += v * b2; t5 += v * b3; t6 += v * b4; t7 += v * b5; t8 += v * b6; t9 += v * b7; t10 += v * b8; t11 += v * b9; t12 += v * b10; t13 += v * b11; t14 += v * b12; t15 += v * b13; t16 += v * b14; t17 += v * b15; v = a[3]; t3 += v * b0; t4 += v * b1; t5 += v * b2; t6 += v * b3; t7 += v * b4; t8 += v * b5; t9 += v * b6; t10 += v * b7; t11 += v * b8; t12 += v * b9; t13 += v * b10; t14 += v * b11; t15 += v * b12; t16 += v * b13; t17 += v * b14; t18 += v * b15; v = a[4]; t4 += v * b0; t5 += v * b1; t6 += v * b2; t7 += v * b3; t8 += v * b4; t9 += v * b5; t10 += v * b6; t11 += v * b7; t12 += v * b8; t13 += v * b9; t14 += v * b10; t15 += v * b11; t16 += v * b12; t17 += v * b13; t18 += v * b14; t19 += v * b15; v = a[5]; t5 += v * b0; t6 += v * b1; t7 += v * b2; t8 += v * b3; t9 += v * b4; t10 += v * b5; t11 += v * b6; t12 += v * b7; t13 += v * b8; t14 += v * b9; t15 += v * b10; t16 += v * b11; t17 += v * b12; t18 += v * b13; t19 += v * b14; t20 += v * b15; v = a[6]; t6 += v * b0; t7 += v * b1; t8 += v * b2; t9 += v * b3; t10 += v * b4; t11 += v * b5; t12 += v * b6; t13 += v * b7; t14 += v * b8; t15 += v * b9; t16 += v * b10; t17 += v * b11; t18 += v * b12; t19 += v * b13; t20 += v * b14; t21 += v * b15; v = a[7]; t7 += v * b0; t8 += v * b1; t9 += v * b2; t10 += v * b3; t11 += v * b4; t12 += v * b5; t13 += v * b6; t14 += v * b7; t15 += v * b8; t16 += v * b9; t17 += v * b10; t18 += v * b11; t19 += v * b12; t20 += v * b13; t21 += v * b14; t22 += v * b15; v = a[8]; t8 += v * b0; t9 += v * b1; t10 += v * b2; t11 += v * b3; t12 += v * b4; t13 += v * b5; t14 += v * b6; t15 += v * b7; t16 += v * b8; t17 += v * b9; t18 += v * b10; t19 += v * b11; t20 += v * b12; t21 += v * b13; t22 += v * b14; t23 += v * b15; v = a[9]; t9 += v * b0; t10 += v * b1; t11 += v * b2; t12 += v * b3; t13 += v * b4; t14 += v * b5; t15 += v * b6; t16 += v * b7; t17 += v * b8; t18 += v * b9; t19 += v * b10; t20 += v * b11; t21 += v * b12; t22 += v * b13; t23 += v * b14; t24 += v * b15; v = a[10]; t10 += v * b0; t11 += v * b1; t12 += v * b2; t13 += v * b3; t14 += v * b4; t15 += v * b5; t16 += v * b6; t17 += v * b7; t18 += v * b8; t19 += v * b9; t20 += v * b10; t21 += v * b11; t22 += v * b12; t23 += v * b13; t24 += v * b14; t25 += v * b15; v = a[11]; t11 += v * b0; t12 += v * b1; t13 += v * b2; t14 += v * b3; t15 += v * b4; t16 += v * b5; t17 += v * b6; t18 += v * b7; t19 += v * b8; t20 += v * b9; t21 += v * b10; t22 += v * b11; t23 += v * b12; t24 += v * b13; t25 += v * b14; t26 += v * b15; v = a[12]; t12 += v * b0; t13 += v * b1; t14 += v * b2; t15 += v * b3; t16 += v * b4; t17 += v * b5; t18 += v * b6; t19 += v * b7; t20 += v * b8; t21 += v * b9; t22 += v * b10; t23 += v * b11; t24 += v * b12; t25 += v * b13; t26 += v * b14; t27 += v * b15; v = a[13]; t13 += v * b0; t14 += v * b1; t15 += v * b2; t16 += v * b3; t17 += v * b4; t18 += v * b5; t19 += v * b6; t20 += v * b7; t21 += v * b8; t22 += v * b9; t23 += v * b10; t24 += v * b11; t25 += v * b12; t26 += v * b13; t27 += v * b14; t28 += v * b15; v = a[14]; t14 += v * b0; t15 += v * b1; t16 += v * b2; t17 += v * b3; t18 += v * b4; t19 += v * b5; t20 += v * b6; t21 += v * b7; t22 += v * b8; t23 += v * b9; t24 += v * b10; t25 += v * b11; t26 += v * b12; t27 += v * b13; t28 += v * b14; t29 += v * b15; v = a[15]; t15 += v * b0; t16 += v * b1; t17 += v * b2; t18 += v * b3; t19 += v * b4; t20 += v * b5; t21 += v * b6; t22 += v * b7; t23 += v * b8; t24 += v * b9; t25 += v * b10; t26 += v * b11; t27 += v * b12; t28 += v * b13; t29 += v * b14; t30 += v * b15; t0 += 38 * t16; t1 += 38 * t17; t2 += 38 * t18; t3 += 38 * t19; t4 += 38 * t20; t5 += 38 * t21; t6 += 38 * t22; t7 += 38 * t23; t8 += 38 * t24; t9 += 38 * t25; t10 += 38 * t26; t11 += 38 * t27; t12 += 38 * t28; t13 += 38 * t29; t14 += 38 * t30; // t15 left as is // first car c = 1; v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536; v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536; v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536; v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536; v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536; v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536; v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536; v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536; v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536; v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536; v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536; v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536; v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536; v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536; v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536; v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536; t0 += c-1 + 37 * (c-1); // second car c = 1; v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536; v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536; v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536; v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536; v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536; v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536; v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536; v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536; v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536; v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536; v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536; v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536; v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536; v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536; v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536; v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536; t0 += c-1 + 37 * (c-1); o[ 0] = t0; o[ 1] = t1; o[ 2] = t2; o[ 3] = t3; o[ 4] = t4; o[ 5] = t5; o[ 6] = t6; o[ 7] = t7; o[ 8] = t8; o[ 9] = t9; o[10] = t10; o[11] = t11; o[12] = t12; o[13] = t13; o[14] = t14; o[15] = t15; }