"use strict";
/**
 * @fileOverview
 * Core operations on curve 25519 required for the higher level modules.
 */

/*
 * Copyright (c) 2007, 2013, 2014 Michele Bini
 * Copyright (c) 2014 Mega Limited
 * under the MIT License.
 *
 * Authors: Guy K. Kloss, Michele Bini
 *
 * You should have received a copy of the license along with this program.
 */

var crypto = require('crypto');

    /**
     * @exports jodid25519/core
     * Core operations on curve 25519 required for the higher level modules.
     *
     * @description
     * Core operations on curve 25519 required for the higher level modules.
     *
     * <p>
     * This core code is extracted from Michele Bini's curve255.js implementation,
     * which is used as a base for Curve25519 ECDH and Ed25519 EdDSA operations.
     * </p>
     */
    var ns = {};

    function _setbit(n, c, v) {
        var i = c >> 4;
        var a = n[i];
        a = a + (1 << (c & 0xf)) * v;
        n[i] = a;
    }

    function _getbit(n, c) {
        return (n[c >> 4] >> (c & 0xf)) & 1;
    }

    function _ZERO() {
        return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    }

    function _ONE() {
        return [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    }

    // Basepoint.
    function _BASE() {
        return [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    }

    // return -1, 0, +1 when a is less than, equal, or greater than b
    function _bigintcmp(a, b) {
        // The following code is a bit tricky to avoid code branching
        var c, abs_r, mask;
        var r = 0;
        for (c = 15; c >= 0; c--) {
            var x = a[c];
            var y = b[c];
            r = r + (x - y) * (1 - r * r);
            // http://graphics.stanford.edu/~seander/bithacks.html#IntegerAbs
            // correct for [-294967295, 294967295]
            mask = r >> 31;
            abs_r = (r + mask) ^ mask;
            // http://stackoverflow.com/questions/596467/how-do-i-convert-a-number-to-an-integer-in-javascript
            // this rounds towards zero
            r = ~~((r << 1) / (abs_r + 1));
        }
        return r;
    }

    function _bigintadd(a, b) {
        var r = [];
        var v;
        r[0] = (v = 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] + b[15];
        return r;
    }

    function _bigintsub(a, b) {
        var r = [];
        var v;
        r[0] = (v = 0x80000 + 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) - 8 + a[15] - b[15];
        return r;
    }

    function _sqr8h(a7, a6, a5, a4, a3, a2, a1, a0) {
        // 'division by 0x10000' can not be replaced by '>> 16' because
        // more than 32 bits of precision are needed similarly
        // 'multiplication by 2' cannot be replaced by '<< 1'
        var r = [];
        var v;
        r[0] = (v = a0 * a0) & 0xffff;
        r[1] = (v = (0 | (v / 0x10000)) + 2 * a0 * a1) & 0xffff;
        r[2] = (v = (0 | (v / 0x10000)) + 2 * a0 * a2 + a1 * a1) & 0xffff;
        r[3] = (v = (0 | (v / 0x10000)) + 2 * a0 * a3 + 2 * a1 * a2) & 0xffff;
        r[4] = (v = (0 | (v / 0x10000)) + 2 * a0 * a4 + 2 * a1 * a3 + a2
                    * a2) & 0xffff;
        r[5] = (v = (0 | (v / 0x10000)) + 2 * a0 * a5 + 2 * a1 * a4 + 2
                    * a2 * a3) & 0xffff;
        r[6] = (v = (0 | (v / 0x10000)) + 2 * a0 * a6 + 2 * a1 * a5 + 2
                    * a2 * a4 + a3 * a3) & 0xffff;
        r[7] = (v = (0 | (v / 0x10000)) + 2 * a0 * a7 + 2 * a1 * a6 + 2
                    * a2 * a5 + 2 * a3 * a4) & 0xffff;
        r[8] = (v = (0 | (v / 0x10000)) + 2 * a1 * a7 + 2 * a2 * a6 + 2
                    * a3 * a5 + a4 * a4) & 0xffff;
        r[9] = (v = (0 | (v / 0x10000)) + 2 * a2 * a7 + 2 * a3 * a6 + 2
                    * a4 * a5) & 0xffff;
        r[10] = (v = (0 | (v / 0x10000)) + 2 * a3 * a7 + 2 * a4 * a6
                     + a5 * a5) & 0xffff;
        r[11] = (v = (0 | (v / 0x10000)) + 2 * a4 * a7 + 2 * a5 * a6) & 0xffff;
        r[12] = (v = (0 | (v / 0x10000)) + 2 * a5 * a7 + a6 * a6) & 0xffff;
        r[13] = (v = (0 | (v / 0x10000)) + 2 * a6 * a7) & 0xffff;
        r[14] = (v = (0 | (v / 0x10000)) + a7 * a7) & 0xffff;
        r[15] = 0 | (v / 0x10000);
        return r;
    }

    function _sqrmodp(a) {
        var x = _sqr8h(a[15], a[14], a[13], a[12], a[11], a[10], a[9],
                       a[8]);
        var z = _sqr8h(a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0]);
        var y = _sqr8h(a[15] + a[7], a[14] + a[6], a[13] + a[5], a[12]
                                                                 + a[4],
                       a[11] + a[3], a[10] + a[2], a[9] + a[1], a[8]
                                                                + a[0]);
        var r = [];
        var v;
        r[0] = (v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80)
                    * 38) & 0xffff;
        r[1] = (v = 0x7fff80 + (v >>> 16) + z[1]
                    + (y[9] - x[9] - z[9] + x[1]) * 38) & 0xffff;
        r[2] = (v = 0x7fff80 + (v >>> 16) + z[2]
                    + (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 _mul8h(a7, a6, a5, a4, a3, a2, a1, a0, b7, b6, b5, b4, b3,
                    b2, b1, b0) {
        // 'division by 0x10000' can not be replaced by '>> 16' because
        // more than 32 bits of precision are needed
        var r = [];
        var v;
        r[0] = (v = a0 * b0) & 0xffff;
        r[1] = (v = (0 | (v / 0x10000)) + a0 * b1 + a1 * b0) & 0xffff;
        r[2] = (v = (0 | (v / 0x10000)) + a0 * b2 + a1 * b1 + a2 * b0) & 0xffff;
        r[3] = (v = (0 | (v / 0x10000)) + a0 * b3 + a1 * b2 + a2 * b1
                    + a3 * b0) & 0xffff;
        r[4] = (v = (0 | (v / 0x10000)) + a0 * b4 + a1 * b3 + a2 * b2
                    + a3 * b1 + a4 * b0) & 0xffff;
        r[5] = (v = (0 | (v / 0x10000)) + a0 * b5 + a1 * b4 + a2 * b3
                    + a3 * b2 + a4 * b1 + a5 * b0) & 0xffff;
        r[6] = (v = (0 | (v / 0x10000)) + a0 * b6 + a1 * b5 + a2 * b4
                    + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0) & 0xffff;
        r[7] = (v = (0 | (v / 0x10000)) + a0 * b7 + a1 * b6 + a2 * b5
                    + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0) & 0xffff;
        r[8] = (v = (0 | (v / 0x10000)) + a1 * b7 + a2 * b6 + a3 * b5
                    + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1) & 0xffff;
        r[9] = (v = (0 | (v / 0x10000)) + a2 * b7 + a3 * b6 + a4 * b5
                    + a5 * b4 + a6 * b3 + a7 * b2) & 0xffff;
        r[10] = (v = (0 | (v / 0x10000)) + a3 * b7 + a4 * b6 + a5 * b5
                     + a6 * b4 + a7 * b3) & 0xffff;
        r[11] = (v = (0 | (v / 0x10000)) + a4 * b7 + a5 * b6 + a6 * b5
                     + a7 * b4) & 0xffff;
        r[12] = (v = (0 | (v / 0x10000)) + a5 * b7 + a6 * b6 + a7 * b5) & 0xffff;
        r[13] = (v = (0 | (v / 0x10000)) + a6 * b7 + a7 * b6) & 0xffff;
        r[14] = (v = (0 | (v / 0x10000)) + a7 * b7) & 0xffff;
        r[15] = (0 | (v / 0x10000));
        return r;
    }

    function _mulmodp(a, b) {
        // Karatsuba multiplication scheme: x*y = (b^2+b)*x1*y1 -
        // b*(x1-x0)*(y1-y0) + (b+1)*x0*y0
        var x = _mul8h(a[15], a[14], a[13], a[12], a[11], a[10], a[9],
                       a[8], b[15], b[14], b[13], b[12], b[11], b[10],
                       b[9], b[8]);
        var z = _mul8h(a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0],
                       b[7], b[6], b[5], b[4], b[3], b[2], b[1], b[0]);
        var y = _mul8h(a[15] + a[7], a[14] + a[6], a[13] + a[5], a[12]
                                                                 + a[4],
                       a[11] + a[3], a[10] + a[2], a[9] + a[1], a[8]
                                                                + a[0],
                       b[15] + b[7], b[14] + b[6], b[13] + b[5], b[12]
                                                                 + b[4],
                       b[11] + b[3], b[10] + b[2], b[9] + b[1], b[8]
                                                                + b[0]);
        var r = [];
        var v;
        r[0] = (v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80)
                    * 38) & 0xffff;
        r[1] = (v = 0x7fff80 + (v >>> 16) + z[1]
                    + (y[9] - x[9] - z[9] + x[1]) * 38) & 0xffff;
        r[2] = (v = 0x7fff80 + (v >>> 16) + z[2]
                    + (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;