x25519.ts

// Copyright (C) 2016 Dmitry Chestnykh
// MIT License. See LICENSE file for details.

import { randomBytes } from "../random";
import { assert } from "../../utils/assert";
import { wipe } from "../../utils/wipe";

// TODO(dchest): some functions ara copies of ../sign/ed25519.
// Find a way to combine them without opening up to public.

// Ported from TweetNaCl.js, which is ported from TweetNaCl
// by Dmitry Chestnykh and Devi Mandiri.
// Public domain.
// https://tweetnacl.js.org

// TweetNaCl contributors:
// Daniel J. Bernstein, Bernard van Gastel, Wesley Janssen,
// Tanja Lange, Peter Schwabe, Sjaak Smetsers.
// Public domain.
// https://tweetnacl.cr.yp.to/

type GF = Float64Array;

// Returns new zero-filled 16-element GF (Float64Array).
// If passed an array of numbers, prefills the returned
// array with them.
//
// We use Float64Array, because we need 48-bit numbers
// for this implementation.
function gf(init?: number[]): GF {
    const r = new Float64Array(16);
    if (init) {
        for (let i = 0; i < init.length; i++) {
            r[i] = init[i];
        }
    }
    return r;
};

// Base point.
const _9 = new Uint8Array(32); _9[0] = 9;

const _121665 = gf([0xdb41, 1]);

function car25519(o: GF) {
    let c = 1;
    for (let i = 0; i < 16; i++) {
        let v = o[i] + c + 65535;
        c = Math.floor(v / 65536);
        o[i] = v - c * 65536;
    }
    o[0] += c - 1 + 37 * (c - 1);
}

function sel25519(p: GF, q: GF, b: number) {
    const c = ~(b - 1);
    for (let i = 0; i < 16; i++) {
        const t = c & (p[i] ^ q[i]);
        p[i] ^= t;
        q[i] ^= t;
    }
}

function pack25519(o: Uint8Array, n: GF) {
    const m = gf();
    const t = gf();
    for (let i = 0; i < 16; i++) {
        t[i] = n[i];
    }
    car25519(t);
    car25519(t);
    car25519(t);
    for (let j = 0; j < 2; j++) {
        m[0] = t[0] - 0xffed;
        for (let i = 1; i < 15; i++) {
            m[i] = t[i] - 0xffff - ((m[i - 1] >> 16) & 1);
            m[i - 1] &= 0xffff;
        }
        m[15] = t[15] - 0x7fff - ((m[14] >> 16) & 1);
        const b = (m[15] >> 16) & 1;
        m[14] &= 0xffff;
        sel25519(t, m, 1 - b);
    }
    for (let i = 0; i < 16; i++) {
        o[2 * i] = t[i] & 0xff;
        o[2 * i + 1] = t[i] >> 8;
    }
}

function unpack25519(o: GF, n: Uint8Array) {
    for (let i = 0; i < 16; i++) {
        o[i] = n[2 * i] + (n[2 * i + 1] << 8);
    }
    o[15] &= 0x7fff;
}

function add(o: GF, a: GF, b: GF) {
    for (let i = 0; i < 16; i++) {
        o[i] = a[i] + b[i];
    }
}

function sub(o: GF, a: GF, b: GF) {
    for (let i = 0; i < 16; i++) {
        o[i] = a[i] - b[i];
    }
}

function mul(o: GF, a: GF, b: GF) {
    let v: number, c: number,
        t0 = 0, t1 = 0, t2 = 0, t3 = 0, t4 = 0, t5 = 0, t6 = 0, t7 = 0,
        t8 = 0, t9 = 0, t10 = 0, t11 = 0, t12 = 0, t13 = 0, t14 = 0, t15 = 0,
        t16 = 0, t17 = 0, t18 = 0, t19 = 0, t20 = 0, t21 = 0, t22 = 0, t23 = 0,
        t24 = 0, t25 = 0, t26 = 0, t27 = 0, t28 = 0, t29 = 0, t30 = 0,
        b0 = b[0],
        b1 = b[1],
        b2 = b[2],
        b3 = b[3],
        b4 = b[4],
        b5 = b[5],
        b6 = b[6],
        b7 = b[7],
        b8 = b[8],
        b9 = b[9],
        b10 = b[10],
        b11 = b[11],
        b12 = b[12],
        b13 = b[13],
        b14 = b[14],
        b15 = b[15];

    v = a[0];
    t0 += v * b0;
    t1 += v * b1;
    t2 += v * b2;
    t3 += v * b3;
    t4 += v * b4;
    t5 += v * b5;
    t6 += v * b6;
    t7 += v * b7;
    t8 += v * b8;
    t9 += v * b9;
    t10 += v * b10;
    t11 += v * b11;
    t12 += v * b12;
    t13 += v * b13;
    t14 += v * b14;
    t15 += v * b15;
    v = a[1];
    t1 += v * b0;
    t2 += v * b1;
    t3 += v * b2;
    t4 += v * b3;
    t5 += v * b4;
    t6 += v * b5;
    t7 += v * b6;
    t8 += v * b7;
    t9 += v * b8;
    t10 += v * b9;
    t11 += v * b10;
    t12 += v * b11;
    t13 += v * b12;
    t14 += v * b13;
    t15 += v * b14;
    t16 += v * b15;
    v = a[2];
    t2 += v * b0;
    t3 += v * b1;
    t4 += v * b2;
    t5 += v * b3;
    t6 += v * b4;
    t7 += v * b5;
    t8 += v * b6;
    t9 += v * b7;
    t10 += v * b8;
    t11 += v * b9;
    t12 += v * b10;
    t13 += v * b11;
    t14 += v * b12;
    t15 += v * b13;
    t16 += v * b14;
    t17 += v * b15;
    v = a[3];
    t3 += v * b0;
    t4 += v * b1;
    t5 += v * b2;
    t6 += v * b3;
    t7 += v * b4;
    t8 += v * b5;
    t9 += v * b6;
    t10 += v * b7;
    t11 += v * b8;
    t12 += v * b9;
    t13 += v * b10;
    t14 += v * b11;
    t15 += v * b12;
    t16 += v * b13;
    t17 += v * b14;
    t18 += v * b15;
    v = a[4];
    t4 += v * b0;
    t5 += v * b1;
    t6 += v * b2;
    t7 += v * b3;
    t8 += v * b4;
    t9 += v * b5;
    t10 += v * b6;
    t11 += v * b7;
    t12 += v * b8;
    t13 += v * b9;
    t14 += v * b10;
    t15 += v * b11;
    t16 += v * b12;
    t17 += v * b13;
    t18 += v * b14;
    t19 += v * b15;
    v = a[5];
    t5 += v * b0;
    t6 += v * b1;
    t7 += v * b2;
    t8 += v * b3;
    t9 += v * b4;
    t10 += v * b5;
    t11 += v * b6;
    t12 += v * b7;
    t13 += v * b8;
    t14 += v * b9;
    t15 += v * b10;
    t16 += v * b11;
    t17 += v * b12;
    t18 += v * b13;
    t19 += v * b14;
    t20 += v * b15;
    v = a[6];
    t6 += v * b0;
    t7 += v * b1;
    t8 += v * b2;
    t9 += v * b3;
    t10 += v * b4;
    t11 += v * b5;
    t12 += v * b6;
    t13 += v * b7;
    t14 += v * b8;
    t15 += v * b9;
    t16 += v * b10;
    t17 += v * b11;
    t18 += v * b12;
    t19 += v * b13;
    t20 += v * b14;
    t21 += v * b15;
    v = a[7];
    t7 += v * b0;
    t8 += v * b1;
    t9 += v * b2;
    t10 += v * b3;
    t11 += v * b4;
    t12 += v * b5;
    t13 += v * b6;
    t14 += v * b7;
    t15 += v * b8;
    t16 += v * b9;
    t17 += v * b10;
    t18 += v * b11;
    t19 += v * b12;
    t20 += v * b13;
    t21 += v * b14;
    t22 += v * b15;
    v = a[8];
    t8 += v * b0;
    t9 += v * b1;
    t10 += v * b2;
    t11 += v * b3;
    t12 += v * b4;
    t13 += v * b5;
    t14 += v * b6;
    t15 += v * b7;
    t16 += v * b8;
    t17 += v * b9;
    t18 += v * b10;
    t19 += v * b11;
    t20 += v * b12;
    t21 += v * b13;
    t22 += v * b14;
    t23 += v * b15;
    v = a[9];
    t9 += v * b0;
    t10 += v * b1;
    t11 += v * b2;
    t12 += v * b3;
    t13 += v * b4;
    t14 += v * b5;
    t15 += v * b6;
    t16 += v * b7;
    t17 += v * b8;
    t18 += v * b9;
    t19 += v * b10;
    t20 += v * b11;
    t21 += v * b12;
    t22 += v * b13;
    t23 += v * b14;
    t24 += v * b15;
    v = a[10];
    t10 += v * b0;
    t11 += v * b1;
    t12 += v * b2;
    t13 += v * b3;
    t14 += v * b4;
    t15 += v * b5;
    t16 += v * b6;
    t17 += v * b7;
    t18 += v * b8;
    t19 += v * b9;
    t20 += v * b10;
    t21 += v * b11;
    t22 += v * b12;
    t23 += v * b13;
    t24 += v * b14;
    t25 += v * b15;
    v = a[11];
    t11 += v * b0;
    t12 += v * b1;
    t13 += v * b2;
    t14 += v * b3;
    t15 += v * b4;
    t16 += v * b5;
    t17 += v * b6;
    t18 += v * b7;
    t19 += v * b8;
    t20 += v * b9;
    t21 += v * b10;
    t22 += v * b11;
    t23 += v * b12;
    t24 += v * b13;
    t25 += v * b14;
    t26 += v * b15;
    v = a[12];
    t12 += v * b0;
    t13 += v * b1;
    t14 += v * b2;
    t15 += v * b3;
    t16 += v * b4;
    t17 += v * b5;
    t18 += v * b6;
    t19 += v * b7;
    t20 += v * b8;
    t21 += v * b9;
    t22 += v * b10;
    t23 += v * b11;
    t24 += v * b12;
    t25 += v * b13;
    t26 += v * b14;
    t27 += v * b15;
    v = a[13];
    t13 += v * b0;
    t14 += v * b1;
    t15 += v * b2;
    t16 += v * b3;
    t17 += v * b4;
    t18 += v * b5;
    t19 += v * b6;
    t20 += v * b7;
    t21 += v * b8;
    t22 += v * b9;
    t23 += v * b10;
    t24 += v * b11;
    t25 += v * b12;
    t26 += v * b13;
    t27 += v * b14;
    t28 += v * b15;
    v = a[14];
    t14 += v * b0;
    t15 += v * b1;
    t16 += v * b2;
    t17 += v * b3;
    t18 += v * b4;
    t19 += v * b5;
    t20 += v * b6;
    t21 += v * b7;
    t22 += v * b8;
    t23 += v * b9;
    t24 += v * b10;
    t25 += v * b11;
    t26 += v * b12;
    t27 += v * b13;
    t28 += v * b14;
    t29 += v * b15;
    v = a[15];
    t15 += v * b0;
    t16 += v * b1;
    t17 += v * b2;
    t18 += v * b3;
    t19 += v * b4;
    t20 += v * b5;
    t21 += v * b6;
    t22 += v * b7;
    t23 += v * b8;
    t24 += v * b9;
    t25 += v * b10;
    t26 += v * b11;
    t27 += v * b12;
    t28 += v * b13;
    t29 += v * b14;
    t30 += v * b15;

    t0 += 38 * t16;
    t1 += 38 * t17;
    t2 += 38 * t18;
    t3 += 38 * t19;
    t4 += 38 * t20;
    t5 += 38 * t21;
    t6 += 38 * t22;
    t7 += 38 * t23;
    t8 += 38 * t24;
    t9 += 38 * t25;
    t10 += 38 * t26;
    t11 += 38 * t27;
    t12 += 38 * t28;
    t13 += 38 * t29;
    t14 += 38 * t30;
    // t15 left as is

    // first car
    c = 1;
    v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536;
    v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536;
    v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536;
    v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536;
    v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536;
    v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536;
    v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536;
    v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536;
    v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536;
    v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536;
    v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536;
    v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536;
    v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536;
    v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536;
    v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536;
    v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536;
    t0 += c - 1 + 37 * (c - 1);

    // second car
    c = 1;
    v = t0 + c + 65535; c = Math.floor(v / 65536); t0 = v - c * 65536;
    v = t1 + c + 65535; c = Math.floor(v / 65536); t1 = v - c * 65536;
    v = t2 + c + 65535; c = Math.floor(v / 65536); t2 = v - c * 65536;
    v = t3 + c + 65535; c = Math.floor(v / 65536); t3 = v - c * 65536;
    v = t4 + c + 65535; c = Math.floor(v / 65536); t4 = v - c * 65536;
    v = t5 + c + 65535; c = Math.floor(v / 65536); t5 = v - c * 65536;
    v = t6 + c + 65535; c = Math.floor(v / 65536); t6 = v - c * 65536;
    v = t7 + c + 65535; c = Math.floor(v / 65536); t7 = v - c * 65536;
    v = t8 + c + 65535; c = Math.floor(v / 65536); t8 = v - c * 65536;
    v = t9 + c + 65535; c = Math.floor(v / 65536); t9 = v - c * 65536;
    v = t10 + c + 65535; c = Math.floor(v / 65536); t10 = v - c * 65536;
    v = t11 + c + 65535; c = Math.floor(v / 65536); t11 = v - c * 65536;
    v = t12 + c + 65535; c = Math.floor(v / 65536); t12 = v - c * 65536;
    v = t13 + c + 65535; c = Math.floor(v / 65536); t13 = v - c * 65536;
    v = t14 + c + 65535; c = Math.floor(v / 65536); t14 = v - c * 65536;
    v = t15 + c + 65535; c = Math.floor(v / 65536); t15 = v - c * 65536;
    t0 += c - 1 + 37 * (c - 1);

    o[0] = t0;
    o[1] = t1;
    o[2] = t2;
    o[3] = t3;
    o[4] = t4;
    o[5] = t5;
    o[6] = t6;
    o[7] = t7;
    o[8] = t8;
    o[9] = t9;
    o[10] = t10;
    o[11] = t11;
    o[12] = t12;
    o[13] = t13;
    o[14] = t14;
    o[15] = t15;
}

function square(o: GF, a: GF) {
    mul(o, a, a);
}

function inv25519(o: GF, i: GF) {
    const c = gf();
    let a: number;
    for (a = 0; a < 16; a++) {
        c[a] = i[a];
    }
    for (a = 253; a >= 0; a--) {
        square(c, c);
        if (a !== 2 && a !== 4) {
            mul(c, c, i);
        }
    }
    for (a = 0; a < 16; a++) {
        o[a] = c[a];
    }
}

export function scalarMult(n: Uint8Array, p: Uint8Array): Uint8Array {
    const z = new Uint8Array(32);
    const x = new Float64Array(80);
    const a = gf(), b = gf(), c = gf(),
        d = gf(), e = gf(), f = gf();

    for (let i = 0; i < 31; i++) {
        z[i] = n[i];
    }
    z[31] = (n[31] & 127) | 64;
    z[0] &= 248;

    unpack25519(x, p);

    for (let i = 0; i < 16; i++) {
        b[i] = x[i];
        d[i] = a[i] = c[i] = 0; //TODO(dchest): not needed?
    }

    a[0] = d[0] = 1;

    for (let i = 254; i >= 0; --i) {
        const r = (z[i >>> 3] >>> (i & 7)) & 1;
        sel25519(a, b, r);
        sel25519(c, d, r);
        add(e, a, c);
        sub(a, a, c);
        add(c, b, d);
        sub(b, b, d);
        square(d, e);
        square(f, a);
        mul(a, c, a);
        mul(c, b, e);
        add(e, a, c);
        sub(a, a, c);
        square(b, a);
        sub(c, d, f);
        mul(a, c, _121665);
        add(a, a, d);
        mul(c, c, a);
        mul(a, d, f);
        mul(d, b, x);
        square(b, e);
        sel25519(a, b, r);
        sel25519(c, d, r);
    }
    for (let i = 0; i < 16; i++) {
        x[i + 16] = a[i];
        x[i + 32] = c[i];
        x[i + 48] = b[i];
        x[i + 64] = d[i];
    }
    const x32 = x.subarray(32);
    const x16 = x.subarray(16);
    inv25519(x32, x32);
    mul(x16, x16, x32);
    const q = new Uint8Array(32);
    pack25519(q, x16);
    return q;
}

export function scalarMultBase(n: Uint8Array): Uint8Array {
    return scalarMult(n, _9);
}

export interface KeyPair {
    publicKey: Uint8Array;
    secretKey: Uint8Array;
}

export function generateKeyPairFromSeed(seed: Uint8Array): KeyPair {
    assert(seed.length === 32);
    const secretKey = new Uint8Array(seed);
    const publicKey = scalarMultBase(secretKey);
    return {
        publicKey,
        secretKey
    };
}

export function generateKeyPair(): KeyPair {
    const seed = randomBytes(32);
    const result = generateKeyPairFromSeed(seed);
    wipe(seed);
    return result;
}