482 lines
20 KiB
JavaScript
482 lines
20 KiB
JavaScript
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"use strict";
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/**
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* @fileOverview
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* Core operations on curve 25519 required for the higher level modules.
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*/
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/*
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* Copyright (c) 2007, 2013, 2014 Michele Bini
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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, Michele Bini
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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 crypto = require('crypto');
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/**
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* @exports jodid25519/core
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* Core operations on curve 25519 required for the higher level modules.
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*
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* @description
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* Core operations on curve 25519 required for the higher level modules.
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*
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* <p>
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* This core code is extracted from Michele Bini's curve255.js implementation,
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* which is used as a base for Curve25519 ECDH and Ed25519 EdDSA operations.
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* </p>
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*/
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var ns = {};
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function _setbit(n, c, v) {
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var i = c >> 4;
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var a = n[i];
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a = a + (1 << (c & 0xf)) * v;
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n[i] = a;
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}
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function _getbit(n, c) {
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return (n[c >> 4] >> (c & 0xf)) & 1;
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}
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function _ZERO() {
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return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
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}
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function _ONE() {
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return [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
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}
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// Basepoint.
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function _BASE() {
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return [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
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}
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// return -1, 0, +1 when a is less than, equal, or greater than b
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function _bigintcmp(a, b) {
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// The following code is a bit tricky to avoid code branching
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var c, abs_r, mask;
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var r = 0;
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for (c = 15; c >= 0; c--) {
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var x = a[c];
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var y = b[c];
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r = r + (x - y) * (1 - r * r);
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// http://graphics.stanford.edu/~seander/bithacks.html#IntegerAbs
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// correct for [-294967295, 294967295]
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mask = r >> 31;
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abs_r = (r + mask) ^ mask;
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// http://stackoverflow.com/questions/596467/how-do-i-convert-a-number-to-an-integer-in-javascript
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// this rounds towards zero
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r = ~~((r << 1) / (abs_r + 1));
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}
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return r;
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}
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function _bigintadd(a, b) {
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var r = [];
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var v;
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r[0] = (v = a[0] + b[0]) & 0xffff;
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r[1] = (v = (v >>> 16) + a[1] + b[1]) & 0xffff;
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r[2] = (v = (v >>> 16) + a[2] + b[2]) & 0xffff;
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r[3] = (v = (v >>> 16) + a[3] + b[3]) & 0xffff;
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r[4] = (v = (v >>> 16) + a[4] + b[4]) & 0xffff;
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r[5] = (v = (v >>> 16) + a[5] + b[5]) & 0xffff;
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r[6] = (v = (v >>> 16) + a[6] + b[6]) & 0xffff;
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r[7] = (v = (v >>> 16) + a[7] + b[7]) & 0xffff;
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r[8] = (v = (v >>> 16) + a[8] + b[8]) & 0xffff;
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r[9] = (v = (v >>> 16) + a[9] + b[9]) & 0xffff;
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r[10] = (v = (v >>> 16) + a[10] + b[10]) & 0xffff;
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r[11] = (v = (v >>> 16) + a[11] + b[11]) & 0xffff;
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r[12] = (v = (v >>> 16) + a[12] + b[12]) & 0xffff;
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r[13] = (v = (v >>> 16) + a[13] + b[13]) & 0xffff;
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r[14] = (v = (v >>> 16) + a[14] + b[14]) & 0xffff;
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r[15] = (v >>> 16) + a[15] + b[15];
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return r;
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}
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function _bigintsub(a, b) {
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var r = [];
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var v;
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r[0] = (v = 0x80000 + a[0] - b[0]) & 0xffff;
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r[1] = (v = (v >>> 16) + 0x7fff8 + a[1] - b[1]) & 0xffff;
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r[2] = (v = (v >>> 16) + 0x7fff8 + a[2] - b[2]) & 0xffff;
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r[3] = (v = (v >>> 16) + 0x7fff8 + a[3] - b[3]) & 0xffff;
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r[4] = (v = (v >>> 16) + 0x7fff8 + a[4] - b[4]) & 0xffff;
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r[5] = (v = (v >>> 16) + 0x7fff8 + a[5] - b[5]) & 0xffff;
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r[6] = (v = (v >>> 16) + 0x7fff8 + a[6] - b[6]) & 0xffff;
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r[7] = (v = (v >>> 16) + 0x7fff8 + a[7] - b[7]) & 0xffff;
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r[8] = (v = (v >>> 16) + 0x7fff8 + a[8] - b[8]) & 0xffff;
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r[9] = (v = (v >>> 16) + 0x7fff8 + a[9] - b[9]) & 0xffff;
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r[10] = (v = (v >>> 16) + 0x7fff8 + a[10] - b[10]) & 0xffff;
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r[11] = (v = (v >>> 16) + 0x7fff8 + a[11] - b[11]) & 0xffff;
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r[12] = (v = (v >>> 16) + 0x7fff8 + a[12] - b[12]) & 0xffff;
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r[13] = (v = (v >>> 16) + 0x7fff8 + a[13] - b[13]) & 0xffff;
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r[14] = (v = (v >>> 16) + 0x7fff8 + a[14] - b[14]) & 0xffff;
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r[15] = (v >>> 16) - 8 + a[15] - b[15];
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return r;
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}
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function _sqr8h(a7, a6, a5, a4, a3, a2, a1, a0) {
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// 'division by 0x10000' can not be replaced by '>> 16' because
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// more than 32 bits of precision are needed similarly
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// 'multiplication by 2' cannot be replaced by '<< 1'
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var r = [];
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var v;
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r[0] = (v = a0 * a0) & 0xffff;
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r[1] = (v = (0 | (v / 0x10000)) + 2 * a0 * a1) & 0xffff;
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r[2] = (v = (0 | (v / 0x10000)) + 2 * a0 * a2 + a1 * a1) & 0xffff;
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r[3] = (v = (0 | (v / 0x10000)) + 2 * a0 * a3 + 2 * a1 * a2) & 0xffff;
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r[4] = (v = (0 | (v / 0x10000)) + 2 * a0 * a4 + 2 * a1 * a3 + a2
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* a2) & 0xffff;
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r[5] = (v = (0 | (v / 0x10000)) + 2 * a0 * a5 + 2 * a1 * a4 + 2
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* a2 * a3) & 0xffff;
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r[6] = (v = (0 | (v / 0x10000)) + 2 * a0 * a6 + 2 * a1 * a5 + 2
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* a2 * a4 + a3 * a3) & 0xffff;
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r[7] = (v = (0 | (v / 0x10000)) + 2 * a0 * a7 + 2 * a1 * a6 + 2
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* a2 * a5 + 2 * a3 * a4) & 0xffff;
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r[8] = (v = (0 | (v / 0x10000)) + 2 * a1 * a7 + 2 * a2 * a6 + 2
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* a3 * a5 + a4 * a4) & 0xffff;
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r[9] = (v = (0 | (v / 0x10000)) + 2 * a2 * a7 + 2 * a3 * a6 + 2
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* a4 * a5) & 0xffff;
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r[10] = (v = (0 | (v / 0x10000)) + 2 * a3 * a7 + 2 * a4 * a6
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+ a5 * a5) & 0xffff;
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r[11] = (v = (0 | (v / 0x10000)) + 2 * a4 * a7 + 2 * a5 * a6) & 0xffff;
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r[12] = (v = (0 | (v / 0x10000)) + 2 * a5 * a7 + a6 * a6) & 0xffff;
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r[13] = (v = (0 | (v / 0x10000)) + 2 * a6 * a7) & 0xffff;
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r[14] = (v = (0 | (v / 0x10000)) + a7 * a7) & 0xffff;
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r[15] = 0 | (v / 0x10000);
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return r;
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}
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function _sqrmodp(a) {
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var x = _sqr8h(a[15], a[14], a[13], a[12], a[11], a[10], a[9],
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a[8]);
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var z = _sqr8h(a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0]);
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var y = _sqr8h(a[15] + a[7], a[14] + a[6], a[13] + a[5], a[12]
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+ a[4],
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a[11] + a[3], a[10] + a[2], a[9] + a[1], a[8]
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+ a[0]);
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var r = [];
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var v;
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r[0] = (v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80)
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* 38) & 0xffff;
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r[1] = (v = 0x7fff80 + (v >>> 16) + z[1]
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+ (y[9] - x[9] - z[9] + x[1]) * 38) & 0xffff;
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r[2] = (v = 0x7fff80 + (v >>> 16) + z[2]
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+ (y[10] - x[10] - z[10] + x[2]) * 38) & 0xffff;
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r[3] = (v = 0x7fff80 + (v >>> 16) + z[3]
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+ (y[11] - x[11] - z[11] + x[3]) * 38) & 0xffff;
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r[4] = (v = 0x7fff80 + (v >>> 16) + z[4]
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+ (y[12] - x[12] - z[12] + x[4]) * 38) & 0xffff;
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r[5] = (v = 0x7fff80 + (v >>> 16) + z[5]
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+ (y[13] - x[13] - z[13] + x[5]) * 38) & 0xffff;
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r[6] = (v = 0x7fff80 + (v >>> 16) + z[6]
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+ (y[14] - x[14] - z[14] + x[6]) * 38) & 0xffff;
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r[7] = (v = 0x7fff80 + (v >>> 16) + z[7]
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+ (y[15] - x[15] - z[15] + x[7]) * 38) & 0xffff;
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r[8] = (v = 0x7fff80 + (v >>> 16) + z[8] + y[0] - x[0] - z[0]
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+ x[8] * 38) & 0xffff;
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r[9] = (v = 0x7fff80 + (v >>> 16) + z[9] + y[1] - x[1] - z[1]
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+ x[9] * 38) & 0xffff;
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r[10] = (v = 0x7fff80 + (v >>> 16) + z[10] + y[2] - x[2] - z[2]
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+ x[10] * 38) & 0xffff;
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r[11] = (v = 0x7fff80 + (v >>> 16) + z[11] + y[3] - x[3] - z[3]
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+ x[11] * 38) & 0xffff;
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r[12] = (v = 0x7fff80 + (v >>> 16) + z[12] + y[4] - x[4] - z[4]
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+ x[12] * 38) & 0xffff;
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r[13] = (v = 0x7fff80 + (v >>> 16) + z[13] + y[5] - x[5] - z[5]
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+ x[13] * 38) & 0xffff;
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r[14] = (v = 0x7fff80 + (v >>> 16) + z[14] + y[6] - x[6] - z[6]
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+ x[14] * 38) & 0xffff;
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r[15] = 0x7fff80 + (v >>> 16) + z[15] + y[7] - x[7] - z[7]
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+ x[15] * 38;
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_reduce(r);
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return r;
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}
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function _mul8h(a7, a6, a5, a4, a3, a2, a1, a0, b7, b6, b5, b4, b3,
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b2, b1, b0) {
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// 'division by 0x10000' can not be replaced by '>> 16' because
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// more than 32 bits of precision are needed
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var r = [];
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var v;
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r[0] = (v = a0 * b0) & 0xffff;
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r[1] = (v = (0 | (v / 0x10000)) + a0 * b1 + a1 * b0) & 0xffff;
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r[2] = (v = (0 | (v / 0x10000)) + a0 * b2 + a1 * b1 + a2 * b0) & 0xffff;
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r[3] = (v = (0 | (v / 0x10000)) + a0 * b3 + a1 * b2 + a2 * b1
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+ a3 * b0) & 0xffff;
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r[4] = (v = (0 | (v / 0x10000)) + a0 * b4 + a1 * b3 + a2 * b2
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+ a3 * b1 + a4 * b0) & 0xffff;
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r[5] = (v = (0 | (v / 0x10000)) + a0 * b5 + a1 * b4 + a2 * b3
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+ a3 * b2 + a4 * b1 + a5 * b0) & 0xffff;
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r[6] = (v = (0 | (v / 0x10000)) + a0 * b6 + a1 * b5 + a2 * b4
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+ a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0) & 0xffff;
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r[7] = (v = (0 | (v / 0x10000)) + a0 * b7 + a1 * b6 + a2 * b5
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+ a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0) & 0xffff;
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r[8] = (v = (0 | (v / 0x10000)) + a1 * b7 + a2 * b6 + a3 * b5
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+ a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1) & 0xffff;
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r[9] = (v = (0 | (v / 0x10000)) + a2 * b7 + a3 * b6 + a4 * b5
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+ a5 * b4 + a6 * b3 + a7 * b2) & 0xffff;
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r[10] = (v = (0 | (v / 0x10000)) + a3 * b7 + a4 * b6 + a5 * b5
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+ a6 * b4 + a7 * b3) & 0xffff;
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r[11] = (v = (0 | (v / 0x10000)) + a4 * b7 + a5 * b6 + a6 * b5
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+ a7 * b4) & 0xffff;
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r[12] = (v = (0 | (v / 0x10000)) + a5 * b7 + a6 * b6 + a7 * b5) & 0xffff;
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r[13] = (v = (0 | (v / 0x10000)) + a6 * b7 + a7 * b6) & 0xffff;
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r[14] = (v = (0 | (v / 0x10000)) + a7 * b7) & 0xffff;
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r[15] = (0 | (v / 0x10000));
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return r;
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}
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function _mulmodp(a, b) {
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// Karatsuba multiplication scheme: x*y = (b^2+b)*x1*y1 -
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// b*(x1-x0)*(y1-y0) + (b+1)*x0*y0
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var x = _mul8h(a[15], a[14], a[13], a[12], a[11], a[10], a[9],
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a[8], b[15], b[14], b[13], b[12], b[11], b[10],
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b[9], b[8]);
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var z = _mul8h(a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0],
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b[7], b[6], b[5], b[4], b[3], b[2], b[1], b[0]);
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var y = _mul8h(a[15] + a[7], a[14] + a[6], a[13] + a[5], a[12]
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+ a[4],
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a[11] + a[3], a[10] + a[2], a[9] + a[1], a[8]
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+ a[0],
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b[15] + b[7], b[14] + b[6], b[13] + b[5], b[12]
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+ b[4],
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b[11] + b[3], b[10] + b[2], b[9] + b[1], b[8]
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+ b[0]);
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var r = [];
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var v;
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r[0] = (v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80)
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* 38) & 0xffff;
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r[1] = (v = 0x7fff80 + (v >>> 16) + z[1]
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+ (y[9] - x[9] - z[9] + x[1]) * 38) & 0xffff;
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r[2] = (v = 0x7fff80 + (v >>> 16) + z[2]
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+ (y[10] - x[10] - z[10] + x[2]) * 38) & 0xffff;
|
||
|
|
r[3] = (v = 0x7fff80 + (v >>> 16) + z[3]
|
||
|
|
+ (y[11] - x[11] - z[11] + x[3]) * 38) & 0xffff;
|
||
|
|
r[4] = (v = 0x7fff80 + (v >>> 16) + z[4]
|
||
|
|
+ (y[12] - x[12] - z[12] + x[4]) * 38) & 0xffff;
|
||
|
|
r[5] = (v = 0x7fff80 + (v >>> 16) + z[5]
|
||
|
|
+ (y[13] - x[13] - z[13] + x[5]) * 38) & 0xffff;
|
||
|
|
r[6] = (v = 0x7fff80 + (v >>> 16) + z[6]
|
||
|
|
+ (y[14] - x[14] - z[14] + x[6]) * 38) & 0xffff;
|
||
|
|
r[7] = (v = 0x7fff80 + (v >>> 16) + z[7]
|
||
|
|
+ (y[15] - x[15] - z[15] + x[7]) * 38) & 0xffff;
|
||
|
|
r[8] = (v = 0x7fff80 + (v >>> 16) + z[8] + y[0] - x[0] - z[0]
|
||
|
|
+ x[8] * 38) & 0xffff;
|
||
|
|
r[9] = (v = 0x7fff80 + (v >>> 16) + z[9] + y[1] - x[1] - z[1]
|
||
|
|
+ x[9] * 38) & 0xffff;
|
||
|
|
r[10] = (v = 0x7fff80 + (v >>> 16) + z[10] + y[2] - x[2] - z[2]
|
||
|
|
+ x[10] * 38) & 0xffff;
|
||
|
|
r[11] = (v = 0x7fff80 + (v >>> 16) + z[11] + y[3] - x[3] - z[3]
|
||
|
|
+ x[11] * 38) & 0xffff;
|
||
|
|
r[12] = (v = 0x7fff80 + (v >>> 16) + z[12] + y[4] - x[4] - z[4]
|
||
|
|
+ x[12] * 38) & 0xffff;
|
||
|
|
r[13] = (v = 0x7fff80 + (v >>> 16) + z[13] + y[5] - x[5] - z[5]
|
||
|
|
+ x[13] * 38) & 0xffff;
|
||
|
|
r[14] = (v = 0x7fff80 + (v >>> 16) + z[14] + y[6] - x[6] - z[6]
|
||
|
|
+ x[14] * 38) & 0xffff;
|
||
|
|
r[15] = 0x7fff80 + (v >>> 16) + z[15] + y[7] - x[7] - z[7]
|
||
|
|
+ x[15] * 38;
|
||
|
|
_reduce(r);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _reduce(arr) {
|
||
|
|
var aCopy = arr.slice(0);
|
||
|
|
var choice = [arr, aCopy];
|
||
|
|
var v = arr[15];
|
||
|
|
// Use the dummy copy instead of just returning to be more constant time.
|
||
|
|
var a = choice[(v < 0x8000) & 1];
|
||
|
|
a[15] = v & 0x7fff;
|
||
|
|
// >32-bits of precision are required here so '/ 0x8000' can not be
|
||
|
|
// replaced by the arithmetic equivalent '>>> 15'
|
||
|
|
v = (0 | (v / 0x8000)) * 19;
|
||
|
|
a[0] = (v += a[0]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[1] = (v += a[1]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[2] = (v += a[2]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[3] = (v += a[3]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[4] = (v += a[4]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[5] = (v += a[5]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[6] = (v += a[6]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[7] = (v += a[7]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[8] = (v += a[8]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[9] = (v += a[9]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[10] = (v += a[10]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[11] = (v += a[11]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[12] = (v += a[12]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[13] = (v += a[13]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[14] = (v += a[14]) & 0xffff;
|
||
|
|
v = v >>> 16;
|
||
|
|
a[15] += v;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _addmodp(a, b) {
|
||
|
|
var r = [];
|
||
|
|
var v;
|
||
|
|
r[0] = (v = ((0 | (a[15] >>> 15)) + (0 | (b[15] >>> 15))) * 19
|
||
|
|
+ a[0] + b[0]) & 0xffff;
|
||
|
|
r[1] = (v = (v >>> 16) + a[1] + b[1]) & 0xffff;
|
||
|
|
r[2] = (v = (v >>> 16) + a[2] + b[2]) & 0xffff;
|
||
|
|
r[3] = (v = (v >>> 16) + a[3] + b[3]) & 0xffff;
|
||
|
|
r[4] = (v = (v >>> 16) + a[4] + b[4]) & 0xffff;
|
||
|
|
r[5] = (v = (v >>> 16) + a[5] + b[5]) & 0xffff;
|
||
|
|
r[6] = (v = (v >>> 16) + a[6] + b[6]) & 0xffff;
|
||
|
|
r[7] = (v = (v >>> 16) + a[7] + b[7]) & 0xffff;
|
||
|
|
r[8] = (v = (v >>> 16) + a[8] + b[8]) & 0xffff;
|
||
|
|
r[9] = (v = (v >>> 16) + a[9] + b[9]) & 0xffff;
|
||
|
|
r[10] = (v = (v >>> 16) + a[10] + b[10]) & 0xffff;
|
||
|
|
r[11] = (v = (v >>> 16) + a[11] + b[11]) & 0xffff;
|
||
|
|
r[12] = (v = (v >>> 16) + a[12] + b[12]) & 0xffff;
|
||
|
|
r[13] = (v = (v >>> 16) + a[13] + b[13]) & 0xffff;
|
||
|
|
r[14] = (v = (v >>> 16) + a[14] + b[14]) & 0xffff;
|
||
|
|
r[15] = (v >>> 16) + (a[15] & 0x7fff) + (b[15] & 0x7fff);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _submodp(a, b) {
|
||
|
|
var r = [];
|
||
|
|
var v;
|
||
|
|
r[0] = (v = 0x80000
|
||
|
|
+ ((0 | (a[15] >>> 15)) - (0 | (b[15] >>> 15)) - 1)
|
||
|
|
* 19 + a[0] - b[0]) & 0xffff;
|
||
|
|
r[1] = (v = (v >>> 16) + 0x7fff8 + a[1] - b[1]) & 0xffff;
|
||
|
|
r[2] = (v = (v >>> 16) + 0x7fff8 + a[2] - b[2]) & 0xffff;
|
||
|
|
r[3] = (v = (v >>> 16) + 0x7fff8 + a[3] - b[3]) & 0xffff;
|
||
|
|
r[4] = (v = (v >>> 16) + 0x7fff8 + a[4] - b[4]) & 0xffff;
|
||
|
|
r[5] = (v = (v >>> 16) + 0x7fff8 + a[5] - b[5]) & 0xffff;
|
||
|
|
r[6] = (v = (v >>> 16) + 0x7fff8 + a[6] - b[6]) & 0xffff;
|
||
|
|
r[7] = (v = (v >>> 16) + 0x7fff8 + a[7] - b[7]) & 0xffff;
|
||
|
|
r[8] = (v = (v >>> 16) + 0x7fff8 + a[8] - b[8]) & 0xffff;
|
||
|
|
r[9] = (v = (v >>> 16) + 0x7fff8 + a[9] - b[9]) & 0xffff;
|
||
|
|
r[10] = (v = (v >>> 16) + 0x7fff8 + a[10] - b[10]) & 0xffff;
|
||
|
|
r[11] = (v = (v >>> 16) + 0x7fff8 + a[11] - b[11]) & 0xffff;
|
||
|
|
r[12] = (v = (v >>> 16) + 0x7fff8 + a[12] - b[12]) & 0xffff;
|
||
|
|
r[13] = (v = (v >>> 16) + 0x7fff8 + a[13] - b[13]) & 0xffff;
|
||
|
|
r[14] = (v = (v >>> 16) + 0x7fff8 + a[14] - b[14]) & 0xffff;
|
||
|
|
r[15] = (v >>> 16) + 0x7ff8 + (a[15] & 0x7fff)
|
||
|
|
- (b[15] & 0x7fff);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _invmodp(a) {
|
||
|
|
var c = a;
|
||
|
|
var i = 250;
|
||
|
|
while (--i) {
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _mulmodp(a, c);
|
||
|
|
}
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _mulmodp(a, c);
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _mulmodp(a, c);
|
||
|
|
a = _sqrmodp(a);
|
||
|
|
a = _mulmodp(a, c);
|
||
|
|
return a;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _mulasmall(a) {
|
||
|
|
// 'division by 0x10000' can not be replaced by '>> 16' because
|
||
|
|
// more than 32 bits of precision are needed
|
||
|
|
var m = 121665;
|
||
|
|
var r = [];
|
||
|
|
var v;
|
||
|
|
r[0] = (v = a[0] * m) & 0xffff;
|
||
|
|
r[1] = (v = (0 | (v / 0x10000)) + a[1] * m) & 0xffff;
|
||
|
|
r[2] = (v = (0 | (v / 0x10000)) + a[2] * m) & 0xffff;
|
||
|
|
r[3] = (v = (0 | (v / 0x10000)) + a[3] * m) & 0xffff;
|
||
|
|
r[4] = (v = (0 | (v / 0x10000)) + a[4] * m) & 0xffff;
|
||
|
|
r[5] = (v = (0 | (v / 0x10000)) + a[5] * m) & 0xffff;
|
||
|
|
r[6] = (v = (0 | (v / 0x10000)) + a[6] * m) & 0xffff;
|
||
|
|
r[7] = (v = (0 | (v / 0x10000)) + a[7] * m) & 0xffff;
|
||
|
|
r[8] = (v = (0 | (v / 0x10000)) + a[8] * m) & 0xffff;
|
||
|
|
r[9] = (v = (0 | (v / 0x10000)) + a[9] * m) & 0xffff;
|
||
|
|
r[10] = (v = (0 | (v / 0x10000)) + a[10] * m) & 0xffff;
|
||
|
|
r[11] = (v = (0 | (v / 0x10000)) + a[11] * m) & 0xffff;
|
||
|
|
r[12] = (v = (0 | (v / 0x10000)) + a[12] * m) & 0xffff;
|
||
|
|
r[13] = (v = (0 | (v / 0x10000)) + a[13] * m) & 0xffff;
|
||
|
|
r[14] = (v = (0 | (v / 0x10000)) + a[14] * m) & 0xffff;
|
||
|
|
r[15] = (0 | (v / 0x10000)) + a[15] * m;
|
||
|
|
_reduce(r);
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
function _dbl(x, z) {
|
||
|
|
var x_2, z_2, m, n, o;
|
||
|
|
m = _sqrmodp(_addmodp(x, z));
|
||
|
|
n = _sqrmodp(_submodp(x, z));
|
||
|
|
o = _submodp(m, n);
|
||
|
|
x_2 = _mulmodp(n, m);
|
||
|
|
z_2 = _mulmodp(_addmodp(_mulasmall(o), m), o);
|
||
|
|
return [x_2, z_2];
|
||
|
|
}
|
||
|
|
|
||
|
|
function _sum(x, z, x_p, z_p, x_1) {
|
||
|
|
var x_3, z_3, p, q;
|
||
|
|
p = _mulmodp(_submodp(x, z), _addmodp(x_p, z_p));
|
||
|
|
q = _mulmodp(_addmodp(x, z), _submodp(x_p, z_p));
|
||
|
|
x_3 = _sqrmodp(_addmodp(p, q));
|
||
|
|
z_3 = _mulmodp(_sqrmodp(_submodp(p, q)), x_1);
|
||
|
|
return [x_3, z_3];
|
||
|
|
}
|
||
|
|
|
||
|
|
function _generateKey(curve25519) {
|
||
|
|
var buffer = crypto.randomBytes(32);
|
||
|
|
|
||
|
|
// For Curve25519 DH keys, we need to apply some bit mask on generated
|
||
|
|
// keys:
|
||
|
|
// * clear bit 0, 1, 2 of first byte
|
||
|
|
// * clear bit 7 of last byte
|
||
|
|
// * set bit 6 of last byte
|
||
|
|
if (curve25519 === true) {
|
||
|
|
buffer[0] &= 0xf8;
|
||
|
|
buffer[31] = (buffer[31] & 0x7f) | 0x40;
|
||
|
|
}
|
||
|
|
var result = [];
|
||
|
|
for (var i = 0; i < buffer.length; i++) {
|
||
|
|
result.push(String.fromCharCode(buffer[i]));
|
||
|
|
}
|
||
|
|
return result.join('');
|
||
|
|
}
|
||
|
|
|
||
|
|
// Expose some functions to the outside through this name space.
|
||
|
|
// Note: This is not part of the public API.
|
||
|
|
ns.getbit = _getbit;
|
||
|
|
ns.setbit = _setbit;
|
||
|
|
ns.addmodp = _addmodp;
|
||
|
|
ns.invmodp = _invmodp;
|
||
|
|
ns.mulmodp = _mulmodp;
|
||
|
|
ns.reduce = _reduce;
|
||
|
|
ns.dbl = _dbl;
|
||
|
|
ns.sum = _sum;
|
||
|
|
ns.ZERO = _ZERO;
|
||
|
|
ns.ONE = _ONE;
|
||
|
|
ns.BASE = _BASE;
|
||
|
|
ns.bigintadd = _bigintadd;
|
||
|
|
ns.bigintsub = _bigintsub;
|
||
|
|
ns.bigintcmp = _bigintcmp;
|
||
|
|
ns.mulmodp = _mulmodp;
|
||
|
|
ns.sqrmodp = _sqrmodp;
|
||
|
|
ns.generateKey = _generateKey;
|
||
|
|
|
||
|
|
|
||
|
|
module.exports = ns;
|