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