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

/**
 * Package ed25519 implements Ed25519 public-key signature algorithm.
 */

import { randomBytes, RandomSource } from "@stablelib/random";
import { hash, SHA512 } from "@stablelib/sha512";
import { wipe } from "@stablelib/wipe";

export const SIGNATURE_LENGTH = 64;
export const PUBLIC_KEY_LENGTH = 32;
export const SECRET_KEY_LENGTH = 64;
export const SEED_LENGTH = 32;

// TODO(dchest): some functions are copies of ../kex/x25519.
// Find a way to combine them without opening up to public.

// Ported from TweetNaCl.js, which was 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 gf0 = gf();

const gf1 = gf([1]);

const D = gf([
    0x78a3, 0x1359, 0x4dca, 0x75eb, 0xd8ab, 0x4141, 0x0a4d, 0x0070,
    0xe898, 0x7779, 0x4079, 0x8cc7, 0xfe73, 0x2b6f, 0x6cee, 0x5203
]);

const D2 = gf([
    0xf159, 0x26b2, 0x9b94, 0xebd6, 0xb156, 0x8283, 0x149a, 0x00e0,
    0xd130, 0xeef3, 0x80f2, 0x198e, 0xfce7, 0x56df, 0xd9dc, 0x2406
]);

const X = gf([
    0xd51a, 0x8f25, 0x2d60, 0xc956, 0xa7b2, 0x9525, 0xc760, 0x692c,
    0xdc5c, 0xfdd6, 0xe231, 0xc0a4, 0x53fe, 0xcd6e, 0x36d3, 0x2169
]);

const Y = gf([
    0x6658, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666,
    0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666, 0x6666
]);

const I = gf([
    0xa0b0, 0x4a0e, 0x1b27, 0xc4ee, 0xe478, 0xad2f, 0x1806, 0x2f43,
    0xd7a7, 0x3dfb, 0x0099, 0x2b4d, 0xdf0b, 0x4fc1, 0x2480, 0x2b83
]);

function set25519(r: GF, a: GF) {
    for (let i = 0; i < 16; i++) {
        r[i] = a[i] | 0;
    }
}

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 verify32(x: Uint8Array, y: Uint8Array) {
    let d = 0;
    for (let i = 0; i < 32; i++) {
        d |= x[i] ^ y[i];
    }
    return (1 & ((d - 1) >>> 8)) - 1;
}


function neq25519(a: GF, b: GF) {
    const c = new Uint8Array(32);
    const d = new Uint8Array(32);
    pack25519(c, a);
    pack25519(d, b);
    return verify32(c, d);
}

function par25519(a: GF) {
    const d = new Uint8Array(32);
    pack25519(d, a);
    return d[0] & 1;
}

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];
    }
}

function pow2523(o: GF, i: GF) {
    const c = gf();
    let a: number;
    for (a = 0; a < 16; a++) {
        c[a] = i[a];
    }
    for (a = 250; a >= 0; a--) {
        square(c, c);
        if (a !== 1) {
            mul(c, c, i);
        }
    }
    for (a = 0; a < 16; a++) {
        o[a] = c[a];
    }
}


function edadd(p: GF[], q: GF[]) {
    const a = gf(), b = gf(), c = gf(),
        d = gf(), e = gf(), f = gf(),
        g = gf(), h = gf(), t = gf();

    sub(a, p[1], p[0]);
    sub(t, q[1], q[0]);
    mul(a, a, t);
    add(b, p[0], p[1]);
    add(t, q[0], q[1]);
    mul(b, b, t);
    mul(c, p[3], q[3]);
    mul(c, c, D2);
    mul(d, p[2], q[2]);
    add(d, d, d);
    sub(e, b, a);
    sub(f, d, c);
    add(g, d, c);
    add(h, b, a);

    mul(p[0], e, f);
    mul(p[1], h, g);
    mul(p[2], g, f);
    mul(p[3], e, h);
}

function cswap(p: GF[], q: GF[], b: number) {
    for (let i = 0; i < 4; i++) {
        sel25519(p[i], q[i], b);
    }
}

function pack(r: Uint8Array, p: GF[]) {
    const tx = gf(), ty = gf(), zi = gf();
    inv25519(zi, p[2]);
    mul(tx, p[0], zi);
    mul(ty, p[1], zi);
    pack25519(r, ty);
    r[31] ^= par25519(tx) << 7;
}

function scalarmult(p: GF[], q: GF[], s: Uint8Array) {
    set25519(p[0], gf0);
    set25519(p[1], gf1);
    set25519(p[2], gf1);
    set25519(p[3], gf0);
    for (let i = 255; i >= 0; --i) {
        const b = (s[(i / 8) | 0] >> (i & 7)) & 1;
        cswap(p, q, b);
        edadd(q, p);
        edadd(p, p);
        cswap(p, q, b);
    }
}

function scalarbase(p: GF[], s: Uint8Array) {
    const q = [gf(), gf(), gf(), gf()];
    set25519(q[0], X);
    set25519(q[1], Y);
    set25519(q[2], gf1);
    mul(q[3], X, Y);
    scalarmult(p, q, s);
}

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

// Generates key pair from secret 32-byte seed.
export function generateKeyPairFromSeed(seed: Uint8Array): KeyPair {
    if (seed.length !== SEED_LENGTH) {
        throw new Error(`ed25519: seed must be ${SEED_LENGTH} bytes`);
    }

    const d = hash(seed);
    d[0] &= 248;
    d[31] &= 127;
    d[31] |= 64;

    const publicKey = new Uint8Array(32);
    const p = [gf(), gf(), gf(), gf()];
    scalarbase(p, d);
    pack(publicKey, p);

    const secretKey = new Uint8Array(64);
    secretKey.set(seed);
    secretKey.set(publicKey, 32);

    return {
        publicKey,
        secretKey
    };
}

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

export function extractPublicKeyFromSecretKey(secretKey: Uint8Array): Uint8Array {
    if (secretKey.length !== SECRET_KEY_LENGTH) {
        throw new Error(`ed25519: secret key must be ${SECRET_KEY_LENGTH} bytes`);
    }
    return new Uint8Array(secretKey.subarray(32));
}

const L = new Float64Array([
    0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, 0xa2,
    0xde, 0xf9, 0xde, 0x14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0x10
]);

function modL(r: Uint8Array, x: Float64Array) {
    let carry: number;
    let i: number;
    let j: number;
    let k: number;
    for (i = 63; i >= 32; --i) {
        carry = 0;
        for (j = i - 32, k = i - 12; j < k; ++j) {
            x[j] += carry - 16 * x[i] * L[j - (i - 32)];
            carry = Math.floor((x[j] + 128) / 256);
            x[j] -= carry * 256;
        }
        x[j] += carry;
        x[i] = 0;
    }
    carry = 0;
    for (j = 0; j < 32; j++) {
        x[j] += carry - (x[31] >> 4) * L[j];
        carry = x[j] >> 8;
        x[j] &= 255;
    }
    for (j = 0; j < 32; j++) {
        x[j] -= carry * L[j];
    }
    for (i = 0; i < 32; i++) {
        x[i + 1] += x[i] >> 8;
        r[i] = x[i] & 255;
    }
}

function reduce(r: Uint8Array) {
    const x = new Float64Array(64);
    for (let i = 0; i < 64; i++) {
        x[i] = r[i];
    }
    for (let i = 0; i < 64; i++) {
        r[i] = 0;
    }
    modL(r, x);
}

// Returns 64-byte signature of the message under the 64-byte secret key.
export function sign(secretKey: Uint8Array, message: Uint8Array): Uint8Array {
    const x = new Float64Array(64);
    const p = [gf(), gf(), gf(), gf()];

    const d = hash(secretKey.subarray(0, 32));
    d[0] &= 248;
    d[31] &= 127;
    d[31] |= 64;

    const signature = new Uint8Array(64);
    signature.set(d.subarray(32), 32);

    const hs = new SHA512();
    hs.update(signature.subarray(32));
    hs.update(message);
    const r = hs.digest();
    hs.clean();
    reduce(r);
    scalarbase(p, r);
    pack(signature, p);

    hs.reset();
    hs.update(signature.subarray(0, 32));
    hs.update(secretKey.subarray(32));
    hs.update(message);
    const h = hs.digest();
    reduce(h);

    for (let i = 0; i < 32; i++) {
        x[i] = r[i];
    }
    for (let i = 0; i < 32; i++) {
        for (let j = 0; j < 32; j++) {
            x[i + j] += h[i] * d[j];
        }
    }
    modL(signature.subarray(32), x);

    return signature;
}

function unpackneg(r: GF[], p: Uint8Array) {
    const t = gf(), chk = gf(), num = gf(),
        den = gf(), den2 = gf(), den4 = gf(),
        den6 = gf();

    set25519(r[2], gf1);
    unpack25519(r[1], p);
    square(num, r[1]);
    mul(den, num, D);
    sub(num, num, r[2]);
    add(den, r[2], den);

    square(den2, den);
    square(den4, den2);
    mul(den6, den4, den2);
    mul(t, den6, num);
    mul(t, t, den);

    pow2523(t, t);
    mul(t, t, num);
    mul(t, t, den);
    mul(t, t, den);
    mul(r[0], t, den);

    square(chk, r[0]);
    mul(chk, chk, den);
    if (neq25519(chk, num)) {
        mul(r[0], r[0], I);
    }

    square(chk, r[0]);
    mul(chk, chk, den);
    if (neq25519(chk, num)) {
        return -1;
    }

    if (par25519(r[0]) === (p[31] >> 7)) {
        sub(r[0], gf0, r[0]);
    }

    mul(r[3], r[0], r[1]);
    return 0;
}

export function verify(publicKey: Uint8Array, message: Uint8Array, signature: Uint8Array): boolean {
    const t = new Uint8Array(32);
    const p = [gf(), gf(), gf(), gf()];
    const q = [gf(), gf(), gf(), gf()];

    if (signature.length !== SIGNATURE_LENGTH) {
        throw new Error(`ed25519: signature must be ${SIGNATURE_LENGTH} bytes`);
    }

    if (unpackneg(q, publicKey)) {
        return false;
    }

    const hs = new SHA512();
    hs.update(signature.subarray(0, 32));
    hs.update(publicKey);
    hs.update(message);
    const h = hs.digest();
    reduce(h);
    scalarmult(p, q, h);

    scalarbase(q, signature.subarray(32));
    edadd(p, q);
    pack(t, p);

    if (verify32(signature, t)) {
        return false;
    }
    return true;
}

/**
 * Convert Ed25519 public key to X25519 public key.
 *
 * Throws if given an invalid public key.
 */
export function convertPublicKeyToX25519(publicKey: Uint8Array): Uint8Array {
    let q = [gf(), gf(), gf(), gf()];

    if (unpackneg(q, publicKey)) {
        throw new Error("Ed25519: invalid public key");
    }

    // Formula: montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p
    let a = gf();
    let b = gf();
    let y = q[1];
    add(a, gf1, y);
    sub(b, gf1, y);
    inv25519(b, b);
    mul(a, a, b);

    let z = new Uint8Array(32);
    pack25519(z, a);
    return z;
}

/**
 *  Convert Ed25519 secret (private) key to X25519 secret key.
 */
export function convertSecretKeyToX25519(secretKey: Uint8Array): Uint8Array {
    const d = hash(secretKey.subarray(0, 32));
    d[0] &= 248;
    d[31] &= 127;
    d[31] |= 64;
    const o = new Uint8Array(d.subarray(0, 32));
    wipe(d);
    return o;
}