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x25519.ts
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x25519.ts
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// Copyright (C) 2016 Dmitry Chestnykh
// MIT License. See LICENSE file for details.
/**
* Package x25519 implements X25519 key agreement.
*/
import { randomBytes, RandomSource } from "@stablelib/random";
import { wipe } from "@stablelib/wipe";
export const PUBLIC_KEY_LENGTH = 32;
export const SECRET_KEY_LENGTH = 32;
export const SHARED_KEY_LENGTH = 32;
// TODO(dchest): some functions are 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, inp: GF) {
const c = gf();
for (let i = 0; i < 16; i++) {
c[i] = inp[i];
}
for (let i = 253; i >= 0; i--) {
square(c, c);
if (i !== 2 && i !== 4) {
mul(c, c, inp);
}
}
for (let i = 0; i < 16; i++) {
o[i] = c[i];
}
}
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];
}
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 {
if (seed.length !== SECRET_KEY_LENGTH) {
throw new Error(`x25519: seed must be ${SECRET_KEY_LENGTH} bytes`);
}
const secretKey = new Uint8Array(seed);
const publicKey = scalarMultBase(secretKey);
return {
publicKey,
secretKey
};
}
export function generateKeyPair(prng?: RandomSource): KeyPair {
const seed = randomBytes(32, prng);
const result = generateKeyPairFromSeed(seed);
wipe(seed);
return result;
}
/**
* Returns a shared key between our secret key and a peer's public key.
*
* Throws an error if the given keys are of wrong length.
*
* If rejectZero is true throws if the calculated shared key is all-zero.
* From RFC 7748:
*
* > Protocol designers using Diffie-Hellman over the curves defined in
* > this document must not assume "contributory behavior". Specially,
* > contributory behavior means that both parties' private keys
* > contribute to the resulting shared key. Since curve25519 and
* > curve448 have cofactors of 8 and 4 (respectively), an input point of
* > small order will eliminate any contribution from the other party's
* > private key. This situation can be detected by checking for the all-
* > zero output, which implementations MAY do, as specified in Section 6.
* > However, a large number of existing implementations do not do this.
*
* IMPORTANT: the returned key is a raw result of scalar multiplication.
* To use it as a key material, hash it with a cryptographic hash function.
*/
export function sharedKey(mySecretKey: Uint8Array, theirPublicKey: Uint8Array, rejectZero = false): Uint8Array {
if (mySecretKey.length !== PUBLIC_KEY_LENGTH) {
throw new Error("X25519: incorrect secret key length");
}
if (theirPublicKey.length !== PUBLIC_KEY_LENGTH) {
throw new Error("X25519: incorrect public key length");
}
const result = scalarMult(mySecretKey, theirPublicKey);
if (rejectZero) {
let zeros = 0;
for (let i = 0; i < result.length; i++) {
zeros |= result[i];
}
if (zeros === 0) {
throw new Error("X25519: invalid shared key");
}
}
return result;
}