path: root/src/crypto/curve25519-u128.h

/* SPDX-License-Identifier: GPL-2.0
 *
 * Copyright (C) 2008 Google Inc. All Rights Reserved.
 * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
 *
 * Original author: Adam Langley <agl@imperialviolet.org>
 */

typedef u64 limb;
typedef limb felem[5];
typedef __uint128_t u128;

/* Sum two numbers: output += in */
static __always_inline void fsum(limb *output, const limb *in)
{
	output[0] += in[0];
	output[1] += in[1];
	output[2] += in[2];
	output[3] += in[3];
	output[4] += in[4];
}

/* Find the difference of two numbers: output = in - output
 * (note the order of the arguments!)
 *
 * Assumes that out[i] < 2**52
 * On return, out[i] < 2**55
 */
static __always_inline void fdifference_backwards(felem out, const felem in)
{
	/* 152 is 19 << 3 */
	static const limb two54m152 = (((limb)1) << 54) - 152;
	static const limb two54m8 = (((limb)1) << 54) - 8;

	out[0] = in[0] + two54m152 - out[0];
	out[1] = in[1] + two54m8 - out[1];
	out[2] = in[2] + two54m8 - out[2];
	out[3] = in[3] + two54m8 - out[3];
	out[4] = in[4] + two54m8 - out[4];
}

/* Multiply a number by a scalar: output = in * scalar */
static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
{
	u128 a;

	a = ((u128) in[0]) * scalar;
	output[0] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[1]) * scalar + ((limb) (a >> 51));
	output[1] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[2]) * scalar + ((limb) (a >> 51));
	output[2] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[3]) * scalar + ((limb) (a >> 51));
	output[3] = ((limb)a) & 0x7ffffffffffffUL;

	a = ((u128) in[4]) * scalar + ((limb) (a >> 51));
	output[4] = ((limb)a) & 0x7ffffffffffffUL;

	output[0] += (a >> 51) * 19;
}

/* Multiply two numbers: output = in2 * in
 *
 * output must be distinct to both inputs. The inputs are reduced coefficient
 * form, the output is not.
 *
 * Assumes that in[i] < 2**55 and likewise for in2.
 * On return, output[i] < 2**52
 */
static __always_inline void fmul(felem output, const felem in2, const felem in)
{
	u128 t[5];
	limb r0, r1, r2, r3, r4, s0, s1, s2, s3, s4, c;

	r0 = in[0];
	r1 = in[1];
	r2 = in[2];
	r3 = in[3];
	r4 = in[4];

	s0 = in2[0];
	s1 = in2[1];
	s2 = in2[2];
	s3 = in2[3];
	s4 = in2[4];

	t[0]  =  ((u128) r0) * s0;
	t[1]  =  ((u128) r0) * s1 + ((u128) r1) * s0;
	t[2]  =  ((u128) r0) * s2 + ((u128) r2) * s0 + ((u128) r1) * s1;
	t[3]  =  ((u128) r0) * s3 + ((u128) r3) * s0 + ((u128) r1) * s2 + ((u128) r2) * s1;
	t[4]  =  ((u128) r0) * s4 + ((u128) r4) * s0 + ((u128) r3) * s1 + ((u128) r1) * s3 + ((u128) r2) * s2;

	r4 *= 19;
	r1 *= 19;
	r2 *= 19;
	r3 *= 19;

	t[0] += ((u128) r4) * s1 + ((u128) r1) * s4 + ((u128) r2) * s3 + ((u128) r3) * s2;
	t[1] += ((u128) r4) * s2 + ((u128) r2) * s4 + ((u128) r3) * s3;
	t[2] += ((u128) r4) * s3 + ((u128) r3) * s4;
	t[3] += ((u128) r4) * s4;

			r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
	t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
	t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
	t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
	t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
	r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
	r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
	r2 +=   c;

	output[0] = r0;
	output[1] = r1;
	output[2] = r2;
	output[3] = r3;
	output[4] = r4;
}

static __always_inline void fsquare_times(felem output, const felem in, limb count)
{
	u128 t[5];
	limb r0, r1, r2, r3, r4, c;
	limb d0, d1, d2, d4, d419;

	r0 = in[0];
	r1 = in[1];
	r2 = in[2];
	r3 = in[3];
	r4 = in[4];

	do {
		d0 = r0 * 2;
		d1 = r1 * 2;
		d2 = r2 * 2 * 19;
		d419 = r4 * 19;
		d4 = d419 * 2;

		t[0] = ((u128) r0) * r0 + ((u128) d4) * r1 + (((u128) d2) * (r3     ));
		t[1] = ((u128) d0) * r1 + ((u128) d4) * r2 + (((u128) r3) * (r3 * 19));
		t[2] = ((u128) d0) * r2 + ((u128) r1) * r1 + (((u128) d4) * (r3     ));
		t[3] = ((u128) d0) * r3 + ((u128) d1) * r2 + (((u128) r4) * (d419   ));
		t[4] = ((u128) d0) * r4 + ((u128) d1) * r3 + (((u128) r2) * (r2     ));

				r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
		t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
		t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
		t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
		t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
		r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
		r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
		r2 +=   c;
	} while (--count);

	output[0] = r0;
	output[1] = r1;
	output[2] = r2;
	output[3] = r3;
	output[4] = r4;
}

/* Load a little-endian 64-bit number  */
static inline limb load_limb(const u8 *in)
{
	return le64_to_cpu(*(__le64 *)in);
}

static inline void store_limb(u8 *out, limb in)
{
	*(__le64 *)out = cpu_to_le64(in);
}

/* Take a little-endian, 32-byte number and expand it into polynomial form */
static inline void fexpand(limb *output, const u8 *in)
{
	output[0] = load_limb(in) & 0x7ffffffffffffUL;
	output[1] = (load_limb(in + 6) >> 3) & 0x7ffffffffffffUL;
	output[2] = (load_limb(in + 12) >> 6) & 0x7ffffffffffffUL;
	output[3] = (load_limb(in + 19) >> 1) & 0x7ffffffffffffUL;
	output[4] = (load_limb(in + 24) >> 12) & 0x7ffffffffffffUL;
}

/* Take a fully reduced polynomial form number and contract it into a
 * little-endian, 32-byte array
 */
static void fcontract(u8 *output, const felem input)
{
	u128 t[5];

	t[0] = input[0];
	t[1] = input[1];
	t[2] = input[2];
	t[3] = input[3];
	t[4] = input[4];

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	/* now t is between 0 and 2^255-1, properly carried. */
	/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */

	t[0] += 19;

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;

	/* now between 19 and 2^255-1 in both cases, and offset by 19. */

	t[0] += 0x8000000000000UL - 19;
	t[1] += 0x8000000000000UL - 1;
	t[2] += 0x8000000000000UL - 1;
	t[3] += 0x8000000000000UL - 1;
	t[4] += 0x8000000000000UL - 1;

	/* now between 2^255 and 2^256-20, and offset by 2^255. */

	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
	t[4] &= 0x7ffffffffffffUL;

	store_limb(output,    t[0] | (t[1] << 51));
	store_limb(output+8,  (t[1] >> 13) | (t[2] << 38));
	store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
	store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
}

/* Input: Q, Q', Q-Q'
 * Output: 2Q, Q+Q'
 *
 *   x2 z3: long form
 *   x3 z3: long form
 *   x z: short form, destroyed
 *   xprime zprime: short form, destroyed
 *   qmqp: short form, preserved
 */
static void fmonty(limb *x2, limb *z2, /* output 2Q */
			 limb *x3, limb *z3, /* output Q + Q' */
			 limb *x, limb *z,   /* input Q */
			 limb *xprime, limb *zprime, /* input Q' */

			 const limb *qmqp /* input Q - Q' */)
{
	limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];

	memcpy(origx, x, 5 * sizeof(limb));
	fsum(x, z);
	fdifference_backwards(z, origx);  // does x - z

	memcpy(origxprime, xprime, sizeof(limb) * 5);
	fsum(xprime, zprime);
	fdifference_backwards(zprime, origxprime);
	fmul(xxprime, xprime, z);
	fmul(zzprime, x, zprime);
	memcpy(origxprime, xxprime, sizeof(limb) * 5);
	fsum(xxprime, zzprime);
	fdifference_backwards(zzprime, origxprime);
	fsquare_times(x3, xxprime, 1);
	fsquare_times(zzzprime, zzprime, 1);
	fmul(z3, zzzprime, qmqp);

	fsquare_times(xx, x, 1);
	fsquare_times(zz, z, 1);
	fmul(x2, xx, zz);
	fdifference_backwards(zz, xx);  // does zz = xx - zz
	fscalar_product(zzz, zz, 121665);
	fsum(zzz, xx);
	fmul(z2, zz, zzz);
}

/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
 * long. Perform the swap iff @swap is non-zero.
 *
 * This function performs the swap without leaking any side-channel
 * information.
 */
static void swap_conditional(limb a[5], limb b[5], limb iswap)
{
	unsigned int i;
	const limb swap = -iswap;

	for (i = 0; i < 5; ++i) {
		const limb x = swap & (a[i] ^ b[i]);

		a[i] ^= x;
		b[i] ^= x;
	}
}

/* Calculates nQ where Q is the x-coordinate of a point on the curve
 *
 *   resultx/resultz: the x coordinate of the resulting curve point (short form)
 *   n: a little endian, 32-byte number
 *   q: a point of the curve (short form)
 */
static void cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q)
{
	limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
	limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
	limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
	limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;

	unsigned int i, j;

	memcpy(nqpqx, q, sizeof(limb) * 5);

	for (i = 0; i < 32; ++i) {
		u8 byte = n[31 - i];

		for (j = 0; j < 8; ++j) {
			const limb bit = byte >> 7;

			swap_conditional(nqx, nqpqx, bit);
			swap_conditional(nqz, nqpqz, bit);
			fmonty(nqx2, nqz2,
						 nqpqx2, nqpqz2,
						 nqx, nqz,
						 nqpqx, nqpqz,
						 q);
			swap_conditional(nqx2, nqpqx2, bit);
			swap_conditional(nqz2, nqpqz2, bit);

			t = nqx;
			nqx = nqx2;
			nqx2 = t;
			t = nqz;
			nqz = nqz2;
			nqz2 = t;
			t = nqpqx;
			nqpqx = nqpqx2;
			nqpqx2 = t;
			t = nqpqz;
			nqpqz = nqpqz2;
			nqpqz2 = t;

			byte <<= 1;
		}
	}

	memcpy(resultx, nqx, sizeof(limb) * 5);
	memcpy(resultz, nqz, sizeof(limb) * 5);
}

static void crecip(felem out, const felem z)
{
	felem a, t0, b, c;

	/* 2 */ fsquare_times(a, z, 1); // a = 2
	/* 8 */ fsquare_times(t0, a, 2);
	/* 9 */ fmul(b, t0, z); // b = 9
	/* 11 */ fmul(a, b, a); // a = 11
	/* 22 */ fsquare_times(t0, a, 1);
	/* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
	/* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
	/* 2^10 - 2^0 */ fmul(b, t0, b);
	/* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
	/* 2^20 - 2^0 */ fmul(c, t0, b);
	/* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
	/* 2^40 - 2^0 */ fmul(t0, t0, c);
	/* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
	/* 2^50 - 2^0 */ fmul(b, t0, b);
	/* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
	/* 2^100 - 2^0 */ fmul(c, t0, b);
	/* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
	/* 2^200 - 2^0 */ fmul(t0, t0, c);
	/* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
	/* 2^250 - 2^0 */ fmul(t0, t0, b);
	/* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
	/* 2^255 - 21 */ fmul(out, t0, a);
}

static bool curve25519_donna(u8 mypublic[CURVE25519_POINT_SIZE], const u8 secret[CURVE25519_POINT_SIZE], const u8 basepoint[CURVE25519_POINT_SIZE])
{
	limb bp[5], x[5], z[5], zmone[5];
	u8 e[32];

	memcpy(e, secret, 32);
	normalize_secret(e);

	fexpand(bp, basepoint);
	cmult(x, z, e, bp);
	crecip(zmone, z);
	fmul(z, x, zmone);
	fcontract(mypublic, z);

	memzero_explicit(e, sizeof(e));
	memzero_explicit(bp, sizeof(bp));
	memzero_explicit(x, sizeof(x));
	memzero_explicit(z, sizeof(z));
	memzero_explicit(zmone, sizeof(zmone));

	return true;
}