CasperSecurity
/**
* JavaScript implementation of Ed25519.
*
* Copyright (c) 2017-2019 Digital Bazaar, Inc.
*
* This implementation is based on the most excellent TweetNaCl which is
* in the public domain. 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;
}