@signumjs/crypto
Version:
Cryptographic functions for building Signum Network apps.
632 lines • 26.4 kB
JavaScript
"use strict";
/** @ignore */
/** @internal */
Object.defineProperty(exports, "__esModule", { value: true });
exports.Curve25519 = void 0;
/* tslint:disable */
/*
* Ported to TypeScript 2.4.2 (https://github.com/Microsoft/TypeScript/issues/18158) 09/02/17.
* Ported to JavaScript from Java 07/01/14.
* Ported from C to Java by Dmitry Skiba [sahn0], 23/02/08.
* Original: http://cds.xs4all.nl:8081/ecdh/
*/
/*
* Generic 64-bit integer implementation of Curve25519 ECDH
* Written by Matthijs van Duin, 200608242056
* Public domain.
*
* Based on work by Daniel J Bernstein, http://cr.yp.to/ecdh.html
*/
class Curve25519 {
//region Constants
static KEY_SIZE = 32;
/* array length */
static UNPACKED_SIZE = 16;
/* group order (a prime near 2^252+2^124) */
static ORDER = [
237, 211, 245, 92,
26, 99, 18, 88,
214, 156, 247, 162,
222, 249, 222, 20,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 16
];
/* smallest multiple of the order that's >= 2^255 */
static ORDER_TIMES_8 = [
104, 159, 174, 231,
210, 24, 147, 192,
178, 230, 188, 23,
245, 206, 247, 166,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 128
];
/* constants 2Gy and 1/(2Gy) */
static BASE_2Y = [
22587, 610, 29883, 44076,
15515, 9479, 25859, 56197,
23910, 4462, 17831, 16322,
62102, 36542, 52412, 16035
];
static BASE_R2Y = [
5744, 16384, 61977, 54121,
8776, 18501, 26522, 34893,
23833, 5823, 55924, 58749,
24147, 14085, 13606, 6080
];
static C1 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
static C9 = [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
static C486671 = [0x6D0F, 0x0007, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
static C39420360 = [0x81C8, 0x0259, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
static P25 = 33554431; /* (1 << 25) - 1 */
static P26 = 67108863; /* (1 << 26) - 1 */
//#endregion
//region Key Agreement
/* Private key clamping
* k [out] your private key for key agreement
* k [in] 32 random bytes
*/
static clamp(k) {
k[31] &= 0x7F;
k[31] |= 0x40;
k[0] &= 0xF8;
}
//endregion
//region radix 2^8 math
static cpy32(d, s) {
for (let i = 0; i < 32; i++)
d[i] = s[i];
}
/* p[m..n+m-1] = q[m..n+m-1] + z * x */
/* n is the size of x */
/* n+m is the size of p and q */
static mula_small(p, q, m, x, n, z) {
m = m | 0;
n = n | 0;
z = z | 0;
let v = 0;
for (let i = 0; i < n; ++i) {
v += (q[i + m] & 0xFF) + z * (x[i] & 0xFF);
p[i + m] = (v & 0xFF);
v >>= 8;
}
return v;
}
/* p += x * y * z where z is a small integer
* x is size 32, y is size t, p is size 32+t
* y is allowed to overlap with p+32 if you don't care about the upper half */
static mula32(p, x, y, t, z) {
t = t | 0;
z = z | 0;
let n = 31;
let w = 0;
let i = 0;
for (; i < t; i++) {
let zy = z * (y[i] & 0xFF);
w += Curve25519.mula_small(p, p, i, x, n, zy) + (p[i + n] & 0xFF) + zy * (x[n] & 0xFF);
p[i + n] = w & 0xFF;
w >>= 8;
}
p[i + n] = (w + (p[i + n] & 0xFF)) & 0xFF;
return w >> 8;
}
/* divide r (size n) by d (size t), returning quotient q and remainder r
* quotient is size n-t+1, remainder is size t
* requires t > 0 && d[t-1] !== 0
* requires that r[-1] and d[-1] are valid memory locations
* q may overlap with r+t */
static divmod(q, r, n, d, t) {
n = n | 0;
t = t | 0;
let rn = 0;
let dt = (d[t - 1] & 0xFF) << 8;
if (t > 1)
dt |= (d[t - 2] & 0xFF);
while (n-- >= t) {
let z = (rn << 16) | ((r[n] & 0xFF) << 8);
if (n > 0)
z |= (r[n - 1] & 0xFF);
let i = n - t + 1;
z /= dt;
rn += Curve25519.mula_small(r, r, i, d, t, -z);
q[i] = (z + rn) & 0xFF;
/* rn is 0 or -1 (underflow) */
Curve25519.mula_small(r, r, i, d, t, -rn);
rn = r[n] & 0xFF;
r[n] = 0;
}
r[t - 1] = rn & 0xFF;
}
static numsize(x, n) {
while (n-- !== 0 && x[n] === 0) { }
return n + 1;
}
/* Returns x if a contains the gcd, y if b.
* Also, the returned buffer contains the inverse of a mod b,
* as 32-byte signed.
* x and y must have 64 bytes space for temporary use.
* requires that a[-1] and b[-1] are valid memory locations */
static egcd32(x, y, a, b) {
let an, bn = 32, qn, i;
for (i = 0; i < 32; i++)
x[i] = y[i] = 0;
x[0] = 1;
an = Curve25519.numsize(a, 32);
if (an === 0)
return y; /* division by zero */
let temp = new Array(32);
while (true) {
qn = bn - an + 1;
Curve25519.divmod(temp, b, bn, a, an);
bn = Curve25519.numsize(b, bn);
if (bn === 0)
return x;
Curve25519.mula32(y, x, temp, qn, -1);
qn = an - bn + 1;
Curve25519.divmod(temp, a, an, b, bn);
an = Curve25519.numsize(a, an);
if (an === 0)
return y;
Curve25519.mula32(x, y, temp, qn, -1);
}
}
//endregion
//region radix 2^25.5 GF(2^255-19) math
//region pack / unpack
/* Convert to internal format from little-endian byte format */
static unpack(x, m) {
for (let i = 0; i < Curve25519.KEY_SIZE; i += 2)
x[i / 2] = m[i] & 0xFF | ((m[i + 1] & 0xFF) << 8);
}
/* Check if reduced-form input >= 2^255-19 */
static is_overflow(x) {
return (((x[0] > Curve25519.P26 - 19)) &&
((x[1] & x[3] & x[5] & x[7] & x[9]) === Curve25519.P25) &&
((x[2] & x[4] & x[6] & x[8]) === Curve25519.P26)) || (x[9] > Curve25519.P25);
}
/* Convert from internal format to little-endian byte format. The
* number must be in a reduced form which is output by the following ops:
* unpack, mul, sqr
* set -- if input in range 0 .. P25
* If you're unsure if the number is reduced, first multiply it by 1. */
static pack(x, m) {
for (let i = 0; i < Curve25519.UNPACKED_SIZE; ++i) {
m[2 * i] = x[i] & 0x00FF;
m[2 * i + 1] = (x[i] & 0xFF00) >> 8;
}
}
//endregion
static createUnpackedArray() {
return new Uint16Array(Curve25519.UNPACKED_SIZE);
}
/* Copy a number */
static cpy(d, s) {
for (let i = 0; i < Curve25519.UNPACKED_SIZE; ++i)
d[i] = s[i];
}
/* Set a number to value, which must be in range -185861411 .. 185861411 */
static set(d, s) {
d[0] = s;
for (let i = 1; i < Curve25519.UNPACKED_SIZE; ++i)
d[i] = 0;
}
/* Calculates a reciprocal. The output is in reduced form, the inputs need not
* be. Simply calculates y = x^(p-2) so it's not too fast. */
/* When sqrtassist is true, it instead calculates y = x^((p-5)/8) */
static recip(y, x, sqrtassist) {
let t0 = Curve25519.createUnpackedArray();
let t1 = Curve25519.createUnpackedArray();
let t2 = Curve25519.createUnpackedArray();
let t3 = Curve25519.createUnpackedArray();
let t4 = Curve25519.createUnpackedArray();
/* the chain for x^(2^255-21) is straight from djb's implementation */
let i;
Curve25519.sqr(t1, x); /* 2 === 2 * 1 */
Curve25519.sqr(t2, t1); /* 4 === 2 * 2 */
Curve25519.sqr(t0, t2); /* 8 === 2 * 4 */
Curve25519.mul(t2, t0, x); /* 9 === 8 + 1 */
Curve25519.mul(t0, t2, t1); /* 11 === 9 + 2 */
Curve25519.sqr(t1, t0); /* 22 === 2 * 11 */
Curve25519.mul(t3, t1, t2); /* 31 === 22 + 9 === 2^5 - 2^0 */
Curve25519.sqr(t1, t3); /* 2^6 - 2^1 */
Curve25519.sqr(t2, t1); /* 2^7 - 2^2 */
Curve25519.sqr(t1, t2); /* 2^8 - 2^3 */
Curve25519.sqr(t2, t1); /* 2^9 - 2^4 */
Curve25519.sqr(t1, t2); /* 2^10 - 2^5 */
Curve25519.mul(t2, t1, t3); /* 2^10 - 2^0 */
Curve25519.sqr(t1, t2); /* 2^11 - 2^1 */
Curve25519.sqr(t3, t1); /* 2^12 - 2^2 */
for (i = 1; i < 5; i++) {
Curve25519.sqr(t1, t3);
Curve25519.sqr(t3, t1);
} /* t3 */ /* 2^20 - 2^10 */
Curve25519.mul(t1, t3, t2); /* 2^20 - 2^0 */
Curve25519.sqr(t3, t1); /* 2^21 - 2^1 */
Curve25519.sqr(t4, t3); /* 2^22 - 2^2 */
for (i = 1; i < 10; i++) {
Curve25519.sqr(t3, t4);
Curve25519.sqr(t4, t3);
} /* t4 */ /* 2^40 - 2^20 */
Curve25519.mul(t3, t4, t1); /* 2^40 - 2^0 */
for (i = 0; i < 5; i++) {
Curve25519.sqr(t1, t3);
Curve25519.sqr(t3, t1);
} /* t3 */ /* 2^50 - 2^10 */
Curve25519.mul(t1, t3, t2); /* 2^50 - 2^0 */
Curve25519.sqr(t2, t1); /* 2^51 - 2^1 */
Curve25519.sqr(t3, t2); /* 2^52 - 2^2 */
for (i = 1; i < 25; i++) {
Curve25519.sqr(t2, t3);
Curve25519.sqr(t3, t2);
} /* t3 */ /* 2^100 - 2^50 */
Curve25519.mul(t2, t3, t1); /* 2^100 - 2^0 */
Curve25519.sqr(t3, t2); /* 2^101 - 2^1 */
Curve25519.sqr(t4, t3); /* 2^102 - 2^2 */
for (i = 1; i < 50; i++) {
Curve25519.sqr(t3, t4);
Curve25519.sqr(t4, t3);
} /* t4 */ /* 2^200 - 2^100 */
Curve25519.mul(t3, t4, t2); /* 2^200 - 2^0 */
for (i = 0; i < 25; i++) {
Curve25519.sqr(t4, t3);
Curve25519.sqr(t3, t4);
} /* t3 */ /* 2^250 - 2^50 */
Curve25519.mul(t2, t3, t1); /* 2^250 - 2^0 */
Curve25519.sqr(t1, t2); /* 2^251 - 2^1 */
Curve25519.sqr(t2, t1); /* 2^252 - 2^2 */
if (sqrtassist !== 0) {
Curve25519.mul(y, x, t2); /* 2^252 - 3 */
}
else {
Curve25519.sqr(t1, t2); /* 2^253 - 2^3 */
Curve25519.sqr(t2, t1); /* 2^254 - 2^4 */
Curve25519.sqr(t1, t2); /* 2^255 - 2^5 */
Curve25519.mul(y, t1, t0); /* 2^255 - 21 */
}
}
/* checks if x is "negative", requires reduced input */
static is_negative(x) {
let isOverflowOrNegative = Curve25519.is_overflow(x) || x[9] < 0;
let leastSignificantBit = x[0] & 1;
return ((isOverflowOrNegative ? 1 : 0) ^ leastSignificantBit) & 0xFFFFFFFF;
}
/* a square root */
static sqrt(x, u) {
let v = Curve25519.createUnpackedArray();
let t1 = Curve25519.createUnpackedArray();
let t2 = Curve25519.createUnpackedArray();
Curve25519.add(t1, u, u); /* t1 = 2u */
Curve25519.recip(v, t1, 1); /* v = (2u)^((p-5)/8) */
Curve25519.sqr(x, v); /* x = v^2 */
Curve25519.mul(t2, t1, x); /* t2 = 2uv^2 */
Curve25519.sub(t2, t2, Curve25519.C1); /* t2 = 2uv^2-1 */
Curve25519.mul(t1, v, t2); /* t1 = v(2uv^2-1) */
Curve25519.mul(x, u, t1); /* x = uv(2uv^2-1) */
}
//endregion
//region JavaScript Fast Math
static c255lsqr8h(a7, a6, a5, a4, a3, a2, a1, a0) {
let r = [];
let v;
v = a0 * a0;
r[0] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a1;
r[1] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a2 + a1 * a1;
r[2] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a3 + 2 * a1 * a2;
r[3] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a4 + 2 * a1 * a3 + a2 * a2;
r[4] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a5 + 2 * a1 * a4 + 2 * a2 * a3;
r[5] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a6 + 2 * a1 * a5 + 2 * a2 * a4 + a3 * a3;
r[6] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a0 * a7 + 2 * a1 * a6 + 2 * a2 * a5 + 2 * a3 * a4;
r[7] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a1 * a7 + 2 * a2 * a6 + 2 * a3 * a5 + a4 * a4;
r[8] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a2 * a7 + 2 * a3 * a6 + 2 * a4 * a5;
r[9] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a3 * a7 + 2 * a4 * a6 + a5 * a5;
r[10] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a4 * a7 + 2 * a5 * a6;
r[11] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a5 * a7 + a6 * a6;
r[12] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + 2 * a6 * a7;
r[13] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a7 * a7;
r[14] = v & 0xFFFF;
r[15] = ((v / 0x10000) | 0);
return r;
}
/* Square a number. Optimization of mul25519(x2, x, x) c255lsqrmodp*/
static sqr(r, a) {
let x = Curve25519.c255lsqr8h(a[15], a[14], a[13], a[12], a[11], a[10], a[9], a[8]);
let z = Curve25519.c255lsqr8h(a[7], a[6], a[5], a[4], a[3], a[2], a[1], a[0]);
let y = Curve25519.c255lsqr8h(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]);
let v;
v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80) * 38;
r[0] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[1] + (y[9] - x[9] - z[9] + x[1]) * 38;
r[1] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[2] + (y[10] - x[10] - z[10] + x[2]) * 38;
r[2] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[3] + (y[11] - x[11] - z[11] + x[3]) * 38;
r[3] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[4] + (y[12] - x[12] - z[12] + x[4]) * 38;
r[4] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[5] + (y[13] - x[13] - z[13] + x[5]) * 38;
r[5] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[6] + (y[14] - x[14] - z[14] + x[6]) * 38;
r[6] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[7] + (y[15] - x[15] - z[15] + x[7]) * 38;
r[7] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[8] + y[0] - x[0] - z[0] + x[8] * 38;
r[8] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[9] + y[1] - x[1] - z[1] + x[9] * 38;
r[9] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[10] + y[2] - x[2] - z[2] + x[10] * 38;
r[10] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[11] + y[3] - x[3] - z[3] + x[11] * 38;
r[11] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[12] + y[4] - x[4] - z[4] + x[12] * 38;
r[12] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[13] + y[5] - x[5] - z[5] + x[13] * 38;
r[13] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[14] + y[6] - x[6] - z[6] + x[14] * 38;
r[14] = v & 0xFFFF;
let r15 = 0x7fff80 + ((v / 0x10000) | 0) + z[15] + y[7] - x[7] - z[7] + x[15] * 38;
Curve25519.c255lreduce(r, r15);
}
static c255lmul8h(a7, a6, a5, a4, a3, a2, a1, a0, b7, b6, b5, b4, b3, b2, b1, b0) {
let r = [];
let v;
v = a0 * b0;
r[0] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b1 + a1 * b0;
r[1] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b2 + a1 * b1 + a2 * b0;
r[2] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
r[3] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
r[4] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
r[5] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
r[6] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
r[7] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1;
r[8] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2;
r[9] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3;
r[10] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4;
r[11] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a5 * b7 + a6 * b6 + a7 * b5;
r[12] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a6 * b7 + a7 * b6;
r[13] = v & 0xFFFF;
v = ((v / 0x10000) | 0) + a7 * b7;
r[14] = v & 0xFFFF;
r[15] = ((v / 0x10000) | 0);
return r;
}
/* Multiply two numbers. The output is in reduced form, the inputs need not be. c255lmulmodp*/
static mul(r, a, b) {
// Karatsuba multiplication scheme: x*y = (b^2+b)*x1*y1 - b*(x1-x0)*(y1-y0) + (b+1)*x0*y0
let x = Curve25519.c255lmul8h(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]);
let z = Curve25519.c255lmul8h(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]);
let y = Curve25519.c255lmul8h(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]);
let v;
v = 0x800000 + z[0] + (y[8] - x[8] - z[8] + x[0] - 0x80) * 38;
r[0] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[1] + (y[9] - x[9] - z[9] + x[1]) * 38;
r[1] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[2] + (y[10] - x[10] - z[10] + x[2]) * 38;
r[2] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[3] + (y[11] - x[11] - z[11] + x[3]) * 38;
r[3] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[4] + (y[12] - x[12] - z[12] + x[4]) * 38;
r[4] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[5] + (y[13] - x[13] - z[13] + x[5]) * 38;
r[5] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[6] + (y[14] - x[14] - z[14] + x[6]) * 38;
r[6] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[7] + (y[15] - x[15] - z[15] + x[7]) * 38;
r[7] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[8] + y[0] - x[0] - z[0] + x[8] * 38;
r[8] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[9] + y[1] - x[1] - z[1] + x[9] * 38;
r[9] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[10] + y[2] - x[2] - z[2] + x[10] * 38;
r[10] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[11] + y[3] - x[3] - z[3] + x[11] * 38;
r[11] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[12] + y[4] - x[4] - z[4] + x[12] * 38;
r[12] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[13] + y[5] - x[5] - z[5] + x[13] * 38;
r[13] = v & 0xFFFF;
v = 0x7fff80 + ((v / 0x10000) | 0) + z[14] + y[6] - x[6] - z[6] + x[14] * 38;
r[14] = v & 0xFFFF;
let r15 = 0x7fff80 + ((v / 0x10000) | 0) + z[15] + y[7] - x[7] - z[7] + x[15] * 38;
Curve25519.c255lreduce(r, r15);
}
static c255lreduce(a, a15) {
let v = a15;
a[15] = v & 0x7FFF;
v = ((v / 0x8000) | 0) * 19;
for (let i = 0; i <= 14; ++i) {
v += a[i];
a[i] = v & 0xFFFF;
v = ((v / 0x10000) | 0);
}
a[15] += v;
}
/* Add/subtract two numbers. The inputs must be in reduced form, and the
* output isn't, so to do another addition or subtraction on the output,
* first multiply it by one to reduce it. c255laddmodp*/
static add(r, a, b) {
let v;
v = (((a[15] / 0x8000) | 0) + ((b[15] / 0x8000) | 0)) * 19 + a[0] + b[0];
r[0] = v & 0xFFFF;
for (let i = 1; i <= 14; ++i) {
v = ((v / 0x10000) | 0) + a[i] + b[i];
r[i] = v & 0xFFFF;
}
r[15] = ((v / 0x10000) | 0) + (a[15] & 0x7FFF) + (b[15] & 0x7FFF);
}
/* Add/subtract two numbers. The inputs must be in reduced form, and the
* output isn't, so to do another addition or subtraction on the output,
* first multiply it by one to reduce it. c255lsubmodp*/
static sub(r, a, b) {
let v;
v = 0x80000 + (((a[15] / 0x8000) | 0) - ((b[15] / 0x8000) | 0) - 1) * 19 + a[0] - b[0];
r[0] = v & 0xFFFF;
for (let i = 1; i <= 14; ++i) {
v = ((v / 0x10000) | 0) + 0x7fff8 + a[i] - b[i];
r[i] = v & 0xFFFF;
}
r[15] = ((v / 0x10000) | 0) + 0x7ff8 + (a[15] & 0x7FFF) - (b[15] & 0x7FFF);
}
/* Multiply a number by a small integer in range -185861411 .. 185861411.
* The output is in reduced form, the input x need not be. x and xy may point
* to the same buffer. c255lmulasmall*/
static mul_small(r, a, m) {
let v;
v = a[0] * m;
r[0] = v & 0xFFFF;
for (let i = 1; i <= 14; ++i) {
v = ((v / 0x10000) | 0) + a[i] * m;
r[i] = v & 0xFFFF;
}
let r15 = ((v / 0x10000) | 0) + a[15] * m;
Curve25519.c255lreduce(r, r15);
}
//endregion
/********************* Elliptic curve *********************/
/* y^2 = x^3 + 486662 x^2 + x over GF(2^255-19) */
/* t1 = ax + az
* t2 = ax - az */
static mont_prep(t1, t2, ax, az) {
Curve25519.add(t1, ax, az);
Curve25519.sub(t2, ax, az);
}
/* A = P + Q where
* X(A) = ax/az
* X(P) = (t1+t2)/(t1-t2)
* X(Q) = (t3+t4)/(t3-t4)
* X(P-Q) = dx
* clobbers t1 and t2, preserves t3 and t4 */
static mont_add(t1, t2, t3, t4, ax, az, dx) {
Curve25519.mul(ax, t2, t3);
Curve25519.mul(az, t1, t4);
Curve25519.add(t1, ax, az);
Curve25519.sub(t2, ax, az);
Curve25519.sqr(ax, t1);
Curve25519.sqr(t1, t2);
Curve25519.mul(az, t1, dx);
}
/* B = 2 * Q where
* X(B) = bx/bz
* X(Q) = (t3+t4)/(t3-t4)
* clobbers t1 and t2, preserves t3 and t4 */
static mont_dbl(t1, t2, t3, t4, bx, bz) {
Curve25519.sqr(t1, t3);
Curve25519.sqr(t2, t4);
Curve25519.mul(bx, t1, t2);
Curve25519.sub(t2, t1, t2);
Curve25519.mul_small(bz, t2, 121665);
Curve25519.add(t1, t1, bz);
Curve25519.mul(bz, t1, t2);
}
/* Y^2 = X^3 + 486662 X^2 + X
* t is a temporary */
static x_to_y2(t, y2, x) {
Curve25519.sqr(t, x);
Curve25519.mul_small(y2, x, 486662);
Curve25519.add(t, t, y2);
Curve25519.add(t, t, Curve25519.C1);
Curve25519.mul(y2, t, x);
}
/* P = kG and s = sign(P)/k */
static core(Px, s, k, Gx) {
let dx = Curve25519.createUnpackedArray();
let t1 = Curve25519.createUnpackedArray();
let t2 = Curve25519.createUnpackedArray();
let t3 = Curve25519.createUnpackedArray();
let t4 = Curve25519.createUnpackedArray();
let x = [Curve25519.createUnpackedArray(), Curve25519.createUnpackedArray()];
let z = [Curve25519.createUnpackedArray(), Curve25519.createUnpackedArray()];
let i, j;
/* unpack the base */
if (Gx !== null)
Curve25519.unpack(dx, Gx);
else
Curve25519.set(dx, 9);
/* 0G = point-at-infinity */
Curve25519.set(x[0], 1);
Curve25519.set(z[0], 0);
/* 1G = G */
Curve25519.cpy(x[1], dx);
Curve25519.set(z[1], 1);
for (i = 32; i-- !== 0;) {
for (j = 8; j-- !== 0;) {
/* swap arguments depending on bit */
let bit1 = (k[i] & 0xFF) >> j & 1;
let bit0 = ~(k[i] & 0xFF) >> j & 1;
let ax = x[bit0];
let az = z[bit0];
let bx = x[bit1];
let bz = z[bit1];
/* a' = a + b */
/* b' = 2 b */
Curve25519.mont_prep(t1, t2, ax, az);
Curve25519.mont_prep(t3, t4, bx, bz);
Curve25519.mont_add(t1, t2, t3, t4, ax, az, dx);
Curve25519.mont_dbl(t1, t2, t3, t4, bx, bz);
}
}
Curve25519.recip(t1, z[0], 0);
Curve25519.mul(dx, x[0], t1);
Curve25519.pack(dx, Px);
/* calculate s such that s abs(P) = G .. assumes G is std base point */
if (s !== null) {
Curve25519.x_to_y2(t2, t1, dx); /* t1 = Py^2 */
Curve25519.recip(t3, z[1], 0); /* where Q=P+G ... */
Curve25519.mul(t2, x[1], t3); /* t2 = Qx */
Curve25519.add(t2, t2, dx); /* t2 = Qx + Px */
Curve25519.add(t2, t2, Curve25519.C486671); /* t2 = Qx + Px + Gx + 486662 */
Curve25519.sub(dx, dx, Curve25519.C9); /* dx = Px - Gx */
Curve25519.sqr(t3, dx); /* t3 = (Px - Gx)^2 */
Curve25519.mul(dx, t2, t3); /* dx = t2 (Px - Gx)^2 */
Curve25519.sub(dx, dx, t1); /* dx = t2 (Px - Gx)^2 - Py^2 */
Curve25519.sub(dx, dx, Curve25519.C39420360); /* dx = t2 (Px - Gx)^2 - Py^2 - Gy^2 */
Curve25519.mul(t1, dx, Curve25519.BASE_R2Y); /* t1 = -Py */
if (Curve25519.is_negative(t1) !== 0) /* sign is 1, so just copy */
Curve25519.cpy32(s, k);
else /* sign is -1, so negate */
Curve25519.mula_small(s, Curve25519.ORDER_TIMES_8, 0, k, 32, -1);
/* reduce s mod q
* (is this needed? do it just in case, it's fast anyway) */
//divmod((dstptr) t1, s, 32, order25519, 32);
/* take reciprocal of s mod q */
let temp1 = new Array(32);
let temp2 = new Array(64);
let temp3 = new Array(64);
Curve25519.cpy32(temp1, Curve25519.ORDER);
Curve25519.cpy32(s, Curve25519.egcd32(temp2, temp3, s, temp1));
if ((s[31] & 0x80) !== 0)
Curve25519.mula_small(s, s, 0, Curve25519.ORDER, 32, 1);
}
}
}
exports.Curve25519 = Curve25519;
//# sourceMappingURL=curve25519.js.map