"use strict";
/**
* @fileOverview
* Digital signature scheme based on Curve25519 (Ed25519 or EdDSA).
*/
/*
* Copyright (c) 2011, 2012, 2014 Ron Garret
* Copyright (c) 2014 Mega Limited
* under the MIT License.
*
* Authors: Guy K. Kloss, Ron Garret
*
* You should have received a copy of the license along with this program.
*/
var core = require('./core');
var curve255 = require('./curve255');
var utils = require('./utils');
var BigInteger = require('jsbn').BigInteger;
var crypto = require('crypto');
/**
* @exports jodid25519/eddsa
* Digital signature scheme based on Curve25519 (Ed25519 or EdDSA).
*
* @description
* Digital signature scheme based on Curve25519 (Ed25519 or EdDSA).
*
* <p>
* This code is adapted from fast-djbec.js, a faster but more complicated
* version of the Ed25519 encryption scheme (as compared to djbec.js).
* It uses two different representations for big integers: The jsbn
* BigInteger class, which can represent arbitrary-length numbers, and a
* special fixed-length representation optimised for 256-bit integers.
* The reason both are needed is that the Ed25519 algorithm requires some
* 512-bit numbers.</p>
*/
var ns = {};
function _bi255(value) {
if (!(this instanceof _bi255)) {
return new _bi255(value);
}
if (typeof value === 'undefined') {
return _ZERO;
}
var c = value.constructor;
if ((c === Array || c === Uint16Array || c === Uint32Array) && (value.length === 16)) {
this.n = value;
} else if ((c === Array) && (value.length === 32)) {
this.n = _bytes2bi255(value).n;
} else if (c === String) {
this.n = utils.hexDecode(value);
} else if (c === Number) {
this.n = [value & 0xffff,
value >> 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
} else if (value instanceof _bi255) {
this.n = value.n.slice(0); // Copy constructor
} else {
throw "Bad argument for bignum: " + value;
}
}
_bi255.prototype = {
'toString' : function() {
return utils.hexEncode(this.n);
},
'toSource' : function() {
return '_' + utils.hexEncode(this.n);
},
'plus' : function(n1) {
return _bi255(core.bigintadd(this.n, n1.n));
},
'minus' : function(n1) {
return _bi255(core.bigintsub(this.n, n1.n)).modq();
},
'times' : function(n1) {
return _bi255(core.mulmodp(this.n, n1.n));
},
'divide' : function(n1) {
return this.times(n1.inv());
},
'sqr' : function() {
return _bi255(core.sqrmodp(this.n));
},
'cmp' : function(n1) {
return core.bigintcmp(this.n, n1.n);
},
'equals' : function(n1) {
return this.cmp(n1) === 0;
},
'isOdd' : function() {
return (this.n[0] & 1) === 1;
},
'shiftLeft' : function(cnt) {
_shiftL(this.n, cnt);
return this;
},
'shiftRight' : function(cnt) {
_shiftR(this.n, cnt);
return this;
},
'inv' : function() {
return _bi255(core.invmodp(this.n));
},
'pow' : function(e) {
return _bi255(_pow(this.n, e.n));
},
'modq' : function() {
return _modq(this);
},
'bytes' : function() {
return _bi255_bytes(this);
}
};
function _shiftL(n, cnt) {
var lastcarry = 0;
for (var i = 0; i < 16; i++) {
var carry = n[i] >> (16 - cnt);
n[i] = (n[i] << cnt) & 0xffff | lastcarry;
lastcarry = carry;
}
return n;
}
function _shiftR(n, cnt) {
var lastcarry = 0;
for (var i = 15; i >= 0; i--) {
var carry = n[i] << (16 - cnt) & 0xffff;
n[i] = (n[i] >> cnt) | lastcarry;
lastcarry = carry;
}
return n;
}
function _bi255_bytes(n) {
n = _bi255(n); // Make a copy because shiftRight is destructive
var a = new Array(32);
for (var i = 31; i >= 0; i--) {
a[i] = n.n[0] & 0xff;
n.shiftRight(8);
}
return a;
}
function _bytes2bi255(a) {
var n = _ZERO;
for (var i = 0; i < 32; i++) {
n.shiftLeft(8);
n = n.plus(_bi255(a[i]));
}
return n;
}
function _pow(n, e) {
var result = core.ONE();
for (var i = 0; i < 256; i++) {
if (core.getbit(e, i) === 1) {
result = core.mulmodp(result, n);
}
n = core.sqrmodp(n);
}
return result;
}
var _ZERO = _bi255(0);
var _ONE = _bi255(1);
var _TWO = _bi255(2);
// This is the core prime.
var _Q = _bi255([0xffff - 18, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff, 0xffff,
0xffff, 0xffff, 0x7fff]);
function _modq(n) {
core.reduce(n.n);
if (n.cmp(_Q) >= 0) {
return _modq(n.minus(_Q));
}
if (n.cmp(_ZERO) === -1) {
return _modq(n.plus(_Q));
} else {
return n;
}
}
// _RECOVERY_EXPONENT = _Q.plus(_bi255(3)).divide(_bi255(8));
var _RECOVERY_EXPONENT = _bi255('0ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe');
// _D = _Q.minus(_bi255(121665)).divide(_bi255(121666));
var _D = _bi255('52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3');
// _I = _TWO.pow(_Q.minus(_ONE).divide(_bi255(4)));
var _I = _bi255('2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0');
// _L = _TWO.pow(_bi255(252)).plus(_bi255('14def9dea2f79cd65812631a5cf5d3ed'));
var _L = _bi255('1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed');
var _L_BI = _bi('1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed', 16);
// ////////////////////////////////////////////////////////////
function _isoncurve(p) {
var x = p[0];
var y = p[1];
var xsqr = x.sqr();
var ysqr = y.sqr();
var v = _D.times(xsqr).times(ysqr);
return ysqr.minus(xsqr).minus(_ONE).minus(v).modq().equals(_ZERO);
}
function _xrecover(y) {
var ysquared = y.sqr();
var xx = ysquared.minus(_ONE).divide(_ONE.plus(_D.times(ysquared)));
var x = xx.pow(_RECOVERY_EXPONENT);
if (!(x.times(x).minus(xx).equals(_ZERO))) {
x = x.times(_I);
}
if (x.isOdd()) {
x = _Q.minus(x);
}
return x;
}
function _x_pt_add(pt1, pt2) {
var x1 = pt1[0];
var y1 = pt1[1];
var z1 = pt1[2];
var t1 = pt1[3];
var x2 = pt2[0];
var y2 = pt2[1];
var z2 = pt2[2];
var t2 = pt2[3];
var A = y1.minus(x1).times(y2.plus(x2));
var B = y1.plus(x1).times(y2.minus(x2));
var C = z1.times(_TWO).times(t2);
var D = t1.times(_TWO).times(z2);
var E = D.plus(C);
var F = B.minus(A);
var G = B.plus(A);
var H = D.minus(C);
return [E.times(F), G.times(H), F.times(G), E.times(H)];
}
function _xpt_double(pt1) {
var x1 = pt1[0];
var y1 = pt1[1];
var z1 = pt1[2];
var A = x1.times(x1);
var B = y1.times(y1);
var C = _TWO.times(z1).times(z1);
var D = _Q.minus(A);
var J = x1.plus(y1);
var E = J.times(J).minus(A).minus(B);
var G = D.plus(B);
var F = G.minus(C);
var H = D.minus(B);
return [E.times(F), G.times(H), F.times(G), E.times(H)];
}
function _xpt_mult(pt, n) {
if (n.equals(_ZERO)) {
return [_ZERO, _ONE, _ONE, _ZERO];
}
var odd = n.isOdd();
n.shiftRight(1);
var value = _xpt_double(_xpt_mult(pt, n));
return odd ? _x_pt_add(value, pt) : value;
}
function _pt_xform(pt) {
var x = pt[0];
var y = pt[1];
return [x, y, _ONE, x.times(y)];
}
function _pt_unxform(pt) {
var x = pt[0];
var y = pt[1];
var z = pt[2];
var invz = z.inv();
return [x.times(invz), y.times(invz)];
}
function _scalarmult(pt, n) {
return _pt_unxform(_xpt_mult(_pt_xform(pt), n));
}
function _bytesgetbit(bytes, n) {
return (bytes[bytes.length - (n >>> 3) - 1] >> (n & 7)) & 1;
}
function _xpt_mult_bytes(pt, bytes) {
var r = [_ZERO, _ONE, _ONE, _ZERO];
for (var i = (bytes.length << 3) - 1; i >= 0; i--) {
r = _xpt_double(r);
if (_bytesgetbit(bytes, i) === 1) {
r = _x_pt_add(r, pt);
}
}
return r;
}
function _scalarmultBytes(pt, bytes) {
return _pt_unxform(_xpt_mult_bytes(_pt_xform(pt), bytes));
}
var _by = _bi255(4).divide(_bi255(5));
var _bx = _xrecover(_by);
var _bp = [_bx, _by];
function _encodeint(n) {
return n.bytes(32).reverse();
}
function _decodeint(b) {
return _bi255(b.slice(0).reverse());
}
function _encodepoint(p) {
var v = _encodeint(p[1]);
if (p[0].isOdd()) {
v[31] |= 0x80;
}
return v;
}
function _decodepoint(v) {
v = v.slice(0);
var signbit = v[31] >> 7;
v[31] &= 127;
var y = _decodeint(v);
var x = _xrecover(y);
if ((x.n[0] & 1) !== signbit) {
x = _Q.minus(x);
}
var p = [x, y];
if (!_isoncurve(p)) {
throw ('Point is not on curve');
}
return p;
}
// //////////////////////////////////////////////////
/**
* Factory function to create a suitable BigInteger.
*
* @param value
* The value for the big integer.
* @param base {integer}
* Base of the conversion of elements in ``value``.
* @returns
* A BigInteger object.
*/
function _bi(value, base) {
if (base !== undefined) {
if (base === 256) {
return _bi(utils.string2bytes(value));
}
return new BigInteger(value, base);
} else if (typeof value === 'string') {
return new BigInteger(value, 10);
} else if ((value instanceof Array) || (value instanceof Uint8Array)
|| Buffer.isBuffer(value)) {
return new BigInteger(value);
} else if (typeof value === 'number') {
return new BigInteger(value.toString(), 10);
} else {
throw "Can't convert " + value + " to BigInteger";
}
}
function _bi2bytes(n, cnt) {
if (cnt === undefined) {
cnt = (n.bitLength() + 7) >>> 3;
}
var bytes = new Array(cnt);
for (var i = cnt - 1; i >= 0; i--) {
bytes[i] = n[0] & 255; // n.and(0xff);
n = n.shiftRight(8);
}
return bytes;
}
BigInteger.prototype.bytes = function(n) {
return _bi2bytes(this, n);
};
// /////////////////////////////////////////////////////////
function _bytehash(s) {
var sha = crypto.createHash('sha512').update(s).digest();
return _bi2bytes(_bi(sha), 64).reverse();
}
function _stringhash(s) {
var sha = crypto.createHash('sha512').update(s).digest();
return _map(_chr, _bi2bytes(_bi(sha), 64)).join('');
}
function _inthash(s) {
// Need a leading 0 to prevent sign extension
return _bi([0].concat(_bytehash(s)));
}
function _inthash_lo(s) {
return _bi255(_bytehash(s).slice(32, 64));
}
function _inthash_mod_l(s) {
return _inthash(s).mod(_L_BI);
}
function _get_a(sk) {
var a = _inthash_lo(sk);
a.n[0] &= 0xfff8;
a.n[15] &= 0x3fff;
a.n[15] |= 0x4000;
return a;
}
function _publickey(sk) {
return _encodepoint(_scalarmult(_bp, _get_a(sk)));
}
function _map(f, l) {
var result = new Array(l.length);
for (var i = 0; i < l.length; i++) {
result[i] = f(l[i]);
}
return result;
}
function _chr(n) {
return String.fromCharCode(n);
}
function _ord(c) {
return c.charCodeAt(0);
}
function _pt_add(p1, p2) {
return _pt_unxform(_x_pt_add(_pt_xform(p1), _pt_xform(p2)));
}
// Exports for the API.
/**
* Checks whether a point is on the curve.
*
* @function
* @param point {string}
* The point to check for in a byte string representation.
* @returns {boolean}
* true if the point is on the curve, false otherwise.
*/
ns.isOnCurve = function(point) {
try {
_isoncurve(_decodepoint(utils.string2bytes(point)));
} catch(e) {
if (e === 'Point is not on curve') {
return false;
} else {
throw e;
}
}
return true;
};
/**
* Computes the EdDSA public key.
*
* <p>Note: Seeds should be a byte string, not a unicode string containing
* multi-byte characters.</p>
*
* @function
* @param keySeed {string}
* Private key seed in the form of a byte string.
* @returns {string}
* Public key as byte string computed from the private key seed
* (32 bytes).
*/
ns.publicKey = function(keySeed) {
return utils.bytes2string(_publickey(keySeed));
};
/**
* Computes an EdDSA signature of a message.
*
* <p>Notes:</p>
*
* <ul>
* <li>Unicode messages need to be converted to a byte representation
* (e. g. UTF-8).</li>
* <li>If `publicKey` is given, and it is *not* a point of the curve,
* the signature will be faulty, but no error will be thrown.</li>
* </ul>
*
* @function
* @param message {string}
* Message in the form of a byte string.
* @param keySeed {string}
* Private key seed in the form of a byte string.
* @param publicKey {string}
* Public key as byte string (if not present, it will be computed from
* the private key seed).
* @returns {string}
* Detached message signature in the form of a byte string (64 bytes).
*/
ns.sign = function(message, keySeed, publicKey) {
if (publicKey === undefined) {
publicKey = _publickey(keySeed);
} else {
publicKey = utils.string2bytes(publicKey);
}
var a = _bi(_get_a(keySeed).toString(), 16);
var hs = _stringhash(keySeed);
var r = _bytehash(hs.slice(32, 64) + message);
var rp = _scalarmultBytes(_bp, r);
var erp = _encodepoint(rp);
r = _bi(r).mod(_bi(1, 10).shiftLeft(512));
var s = _map(_chr, erp).join('') + _map(_chr, publicKey).join('') + message;
s = _inthash_mod_l(s).multiply(a).add(r).mod(_L_BI);
return utils.bytes2string(erp.concat(_encodeint(s)));
};
/**
* Verifies an EdDSA signature of a message with the public key.
*
* <p>Note: Unicode messages need to be converted to a byte representation
* (e. g. UTF-8).</p>
*
* @function
* @param signature {string}
* Message signature in the form of a byte string. Can be detached
* (64 bytes), or attached to be sliced off.
* @param message {string}
* Message in the form of a byte string.
* @param publicKey {string}
* Public key as byte string (if not present, it will be computed from
* the private key seed).
* @returns {boolean}
* true, if the signature verifies.
*/
ns.verify = function(signature, message, publicKey) {
signature = utils.string2bytes(signature.slice(0, 64));
publicKey = utils.string2bytes(publicKey);
var rpe = signature.slice(0, 32);
var rp = _decodepoint(rpe);
var a = _decodepoint(publicKey);
var s = _decodeint(signature.slice(32, 64));
var h = _inthash(utils.bytes2string(rpe.concat(publicKey)) + message);
var v1 = _scalarmult(_bp, s);
var value = _scalarmultBytes(a, _bi2bytes(h));
var v2 = _pt_add(rp, value);
return v1[0].equals(v2[0]) && v1[1].equals(v2[1]);
};
/**
* Generates a new random private key seed of 32 bytes length (256 bit).
*
* @function
* @returns {string}
* Byte string containing a new random private key seed.
*/
ns.generateKeySeed = function() {
return core.generateKey(false);
};
module.exports = ns;
