path: root/src/ec25519_gf.c

/*
  Copyright (c) 2012-2015, Matthias Schiffer <mschiffer@universe-factory.net>
  Partly based on public domain code by Matthew Dempsky and D. J. Bernstein.
  All rights reserved.

  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:

    1. Redistributions of source code must retain the above copyright notice,
       this list of conditions and the following disclaimer.
    2. Redistributions in binary form must reproduce the above copyright notice,
       this list of conditions and the following disclaimer in the documentation
       and/or other materials provided with the distribution.

  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
  DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
  FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
  OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

/** \file
 * Simple finite field operations on the prime field \f$ F_q \f$ for
 * \f$ q = 2^{252} + 27742317777372353535851937790883648493 \f$, which
 * is the order of the base point used for ec25519
 *
 * Doxygen comments for public APIs can be found in the public header file.
 */

#include <libuecc/ecc.h>


/** Checks if the highest bit of an uint32_teger is set */
#define IS_NEGATIVE(n) ((int)((((unsigned)n) >> (8*sizeof(n)-1))&1))

/** Performs an arithmetic right shift */
#define ASR(n,s) (((n) >> s)|(IS_NEGATIVE(n)*((unsigned)-1) << (8*sizeof(n)-s)))


const ecc_int256_t ecc_25519_gf_order = {{
	0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
	0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
}};

/** An internal alias for \ref ecc_25519_gf_order */
static const uint8_t *q = ecc_25519_gf_order.p;

/**
 * Copies the content of r into out if b == 0, the contents of s if b == 1
 */
static void select(uint8_t out[32], const uint8_t r[32], const uint8_t s[32], uint32_t b) {
	unsigned int j;
	uint8_t t;
	uint8_t bminus1;

	bminus1 = b - 1;
	for (j = 0;j < 32;++j) {
		t = bminus1 & (r[j] ^ s[j]);
		out[j] = s[j] ^ t;
	}
}

int ecc_25519_gf_is_zero(const ecc_int256_t *in) {
	int i;
	ecc_int256_t r;
	uint32_t bits = 0;

	ecc_25519_gf_reduce(&r, in);

	for (i = 0; i < 32; i++)
		bits |= r.p[i];

	return (((bits-1)>>8) & 1);
}

void ecc_25519_gf_add(ecc_int256_t *out, const ecc_int256_t *in1, const ecc_int256_t *in2) {
	unsigned int j;
	uint32_t u;
	int nq = 1 - (in1->p[31]>>4) - (in2->p[31]>>4);

	u = 0;
	for (j = 0; j < 32; ++j) {
		u += in1->p[j] + in2->p[j] + nq*q[j];

		out->p[j] = u;
		u = ASR(u, 8);
	}
}

void ecc_25519_gf_sub(ecc_int256_t *out, const ecc_int256_t *in1, const ecc_int256_t *in2) {
	unsigned int j;
	uint32_t u;
	int nq = 8 - (in1->p[31]>>4) + (in2->p[31]>>4);

	u = 0;
	for (j = 0; j < 32; ++j) {
		u += in1->p[j] - in2->p[j] + nq*q[j];

		out->p[j] = u;
		u = ASR(u, 8);
	}
}

/** Reduces an integer to a unique representation in the range \f$ [0,q-1] \f$ */
static void reduce(uint8_t a[32]) {
	unsigned int j;
	uint32_t nq = a[31] >> 4;
	uint32_t u1, u2;
	uint8_t out1[32], out2[32];

	u1 = u2 = 0;
	for (j = 0; j < 31; ++j) {
		u1 += a[j] - nq*q[j];
		u2 += a[j] - (nq-1)*q[j];

		out1[j] = u1; out2[j] = u2;
		u1 = ASR(u1, 8);
		u2 = ASR(u2, 8);
	}
	u1 += a[31] - nq*q[31];
	u2 += a[31] - (nq-1)*q[31];
	out1[31] = u1; out2[31] = u2;

	select(a, out1, out2, IS_NEGATIVE(u1));
}

void ecc_25519_gf_reduce(ecc_int256_t *out, const ecc_int256_t *in) {
	int i;

	for (i = 0; i < 32; i++)
		out->p[i] = in->p[i];

	reduce(out->p);
}

/** Montgomery modular multiplication algorithm */
static void montgomery(uint8_t out[32], const uint8_t a[32], const uint8_t b[32]) {
	unsigned int i, j;
	uint32_t nq;
	uint32_t u;

	for (i = 0; i < 32; i++)
		out[i] = 0;

	for (i = 0; i < 32; i++) {
		u = out[0] + a[i]*b[0];
		nq = (u*27) & 255;
		u += nq*q[0];

		for (j = 1; j < 32; ++j) {
			u += (out[j] + a[i]*b[j] + nq*q[j]) << 8;
			u >>= 8;
			out[j-1] = u;
		}

		out[31] = u >> 8;
	}
}

void ecc_25519_gf_mult(ecc_int256_t *out, const ecc_int256_t *in1, const ecc_int256_t *in2) {
	/* 2^512 mod q */
	static const uint8_t C[32] = {
		0x01, 0x0f, 0x9c, 0x44, 0xe3, 0x11, 0x06, 0xa4,
		0x47, 0x93, 0x85, 0x68, 0xa7, 0x1b, 0x0e, 0xd0,
		0x65, 0xbe, 0xf5, 0x17, 0xd2, 0x73, 0xec, 0xce,
		0x3d, 0x9a, 0x30, 0x7c, 0x1b, 0x41, 0x99, 0x03
	};

	uint8_t B[32];
	uint8_t R[32];
	unsigned int i;

	for (i = 0; i < 32; i++)
		B[i] = in2->p[i];

	reduce(B);

	montgomery(R, in1->p, B);
	montgomery(out->p, R, C);
}

void ecc_25519_gf_recip(ecc_int256_t *out, const ecc_int256_t *in) {
	static const uint8_t C[32] = {
		0x01
	};

	uint8_t A[32], B[32];
	uint8_t R1[32], R2[32];
	int use_r2 = 0;
	unsigned int i, j;

	for (i = 0; i < 32; i++) {
		R1[i] = (i == 0);
		A[i] = in->p[i];
	}

	reduce(A);

	for (i = 0; i < 32; i++) {
		uint8_t c;

		if (i == 0)
			c = 0xeb; /* q[0] - 2 */
		else
			c = q[i];

		for (j = 0; j < 8; j+=2) {
			if (c & (1 << j)) {
				if (use_r2)
					montgomery(R1, R2, A);
				else
					montgomery(R2, R1, A);

				use_r2 = !use_r2;
			}

			montgomery(B, A, A);

			if (c & (2 << j)) {
				if (use_r2)
					montgomery(R1, R2, B);
				else
					montgomery(R2, R1, B);

				use_r2 = !use_r2;
			}

			montgomery(A, B, B);
		}
	}

	montgomery(out->p, R2, C);
}

void ecc_25519_gf_sanitize_secret(ecc_int256_t *out, const ecc_int256_t *in) {
	int i;

	for (i = 0; i < 32; i++)
		out->p[i] = in->p[i];

	out->p[0] &= 0xf8;
	out->p[31] &= 0x7f;
	out->p[31] |= 0x40;
}