src/lib/libcrypto/ec/ec_mult.c

/* $OpenBSD: ec_mult.c,v 1.31 2023/06/24 17:49:44 jsing Exp $ */
/*
 * Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
 */
/* ====================================================================
 * Copyright (c) 1998-2007 The OpenSSL Project.  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.
 *
 * 3. All advertising materials mentioning features or use of this
 *    software must display the following acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */
/* ====================================================================
 * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
 * Portions of this software developed by SUN MICROSYSTEMS, INC.,
 * and contributed to the OpenSSL project.
 */

#include <string.h>

#include <openssl/err.h>

#include "ec_local.h"

/*
 * This file implements the wNAF-based interleaving multi-exponentation method
 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#multiexp>);
 * for multiplication with precomputation, we use wNAF splitting
 * (<URL:http://www.informatik.tu-darmstadt.de/TI/Mitarbeiter/moeller.html#fastexp>).
 */

/* Determine the modified width-(w+1) Non-Adjacent Form (wNAF) of 'scalar'.
 * This is an array  r[]  of values that are either zero or odd with an
 * absolute value less than  2^w  satisfying
 *     scalar = \sum_j r[j]*2^j
 * where at most one of any  w+1  consecutive digits is non-zero
 * with the exception that the most significant digit may be only
 * w-1 zeros away from that next non-zero digit.
 */
static signed char *
compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
{
	int window_val;
	int ok = 0;
	signed char *r = NULL;
	int sign = 1;
	int bit, next_bit, mask;
	size_t len = 0, j;

	if (BN_is_zero(scalar)) {
		r = malloc(1);
		if (!r) {
			ECerror(ERR_R_MALLOC_FAILURE);
			goto err;
		}
		r[0] = 0;
		*ret_len = 1;
		return r;
	}
	if (w <= 0 || w > 7) {
		/* 'signed char' can represent integers with
		 * absolute values less than 2^7 */
		ECerror(ERR_R_INTERNAL_ERROR);
		goto err;
	}
	bit = 1 << w;		/* at most 128 */
	next_bit = bit << 1;	/* at most 256 */
	mask = next_bit - 1;	/* at most 255 */

	if (BN_is_negative(scalar)) {
		sign = -1;
	}
	if (scalar->d == NULL || scalar->top == 0) {
		ECerror(ERR_R_INTERNAL_ERROR);
		goto err;
	}
	len = BN_num_bits(scalar);
	r = malloc(len + 1);	/* modified wNAF may be one digit longer than
				 * binary representation (*ret_len will be
				 * set to the actual length, i.e. at most
				 * BN_num_bits(scalar) + 1) */
	if (r == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}
	window_val = scalar->d[0] & mask;
	j = 0;
	while ((window_val != 0) || (j + w + 1 < len)) {
		/* if j+w+1 >= len, window_val will not increase */
		int digit = 0;

		/* 0 <= window_val <= 2^(w+1) */
		if (window_val & 1) {
			/* 0 < window_val < 2^(w+1) */
			if (window_val & bit) {
				digit = window_val - next_bit;	/* -2^w < digit < 0 */

#if 1				/* modified wNAF */
				if (j + w + 1 >= len) {
					/*
					 * special case for generating
					 * modified wNAFs: no new bits will
					 * be added into window_val, so using
					 * a positive digit here will
					 * decrease the total length of the
					 * representation
					 */

					digit = window_val & (mask >> 1);	/* 0 < digit < 2^w */
				}
#endif
			} else {
				digit = window_val;	/* 0 < digit < 2^w */
			}

			if (digit <= -bit || digit >= bit || !(digit & 1)) {
				ECerror(ERR_R_INTERNAL_ERROR);
				goto err;
			}
			window_val -= digit;

			/*
			 * now window_val is 0 or 2^(w+1) in standard wNAF
			 * generation; for modified window NAFs, it may also
			 * be 2^w
			 */
			if (window_val != 0 && window_val != next_bit && window_val != bit) {
				ECerror(ERR_R_INTERNAL_ERROR);
				goto err;
			}
		}
		r[j++] = sign * digit;

		window_val >>= 1;
		window_val += bit * BN_is_bit_set(scalar, j + w);

		if (window_val > next_bit) {
			ECerror(ERR_R_INTERNAL_ERROR);
			goto err;
		}
	}

	if (j > len + 1) {
		ECerror(ERR_R_INTERNAL_ERROR);
		goto err;
	}
	len = j;
	ok = 1;

 err:
	if (!ok) {
		free(r);
		r = NULL;
	}
	if (ok)
		*ret_len = len;
	return r;
}


/* TODO: table should be optimised for the wNAF-based implementation,
 *       sometimes smaller windows will give better performance
 *       (thus the boundaries should be increased)
 */
#define EC_window_bits_for_scalar_size(b) \
		((size_t) \
		 ((b) >= 2000 ? 6 : \
		  (b) >=  800 ? 5 : \
		  (b) >=  300 ? 4 : \
		  (b) >=   70 ? 3 : \
		  (b) >=   20 ? 2 : \
		  1))

/* Compute
 *      \sum scalars[i]*points[i],
 * also including
 *      scalar*generator
 * in the addition if scalar != NULL
 */
int
ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
    size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
{
	const EC_POINT *generator = NULL;
	EC_POINT *tmp = NULL;
	size_t totalnum;
	size_t numblocks = 0;	/* for wNAF splitting */
	size_t i, j;
	int k;
	int r_is_inverted = 0;
	int r_is_at_infinity = 1;
	size_t *wsize = NULL;	/* individual window sizes */
	signed char **wNAF = NULL;	/* individual wNAFs */
	signed char *tmp_wNAF = NULL;
	size_t *wNAF_len = NULL;
	size_t max_len = 0;
	size_t num_val;
	EC_POINT **val = NULL;	/* precomputation */
	EC_POINT **v;
	EC_POINT ***val_sub = NULL;	/* pointers to sub-arrays of 'val' or
					 * 'pre_comp->points' */
	int num_scalar = 0;	/* flag: will be set to 1 if 'scalar' must be
				 * treated like other scalars, i.e.
				 * precomputation is not available */
	int ret = 0;

	if (group->meth != r->meth) {
		ECerror(EC_R_INCOMPATIBLE_OBJECTS);
		return 0;
	}
	if ((scalar == NULL) && (num == 0)) {
		return EC_POINT_set_to_infinity(group, r);
	}
	for (i = 0; i < num; i++) {
		if (group->meth != points[i]->meth) {
			ECerror(EC_R_INCOMPATIBLE_OBJECTS);
			return 0;
		}
	}

	if (scalar != NULL) {
		generator = EC_GROUP_get0_generator(group);
		if (generator == NULL) {
			ECerror(EC_R_UNDEFINED_GENERATOR);
			goto err;
		}

		numblocks = 1;
		num_scalar = 1;	/* treat 'scalar' like 'num'-th
				 * element of 'scalars' */
	}
	totalnum = num + numblocks;

	/* includes space for pivot */
	wNAF = reallocarray(NULL, (totalnum + 1), sizeof wNAF[0]);
	if (wNAF == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}

	wNAF[0] = NULL;		/* preliminary pivot */

	wsize = reallocarray(NULL, totalnum, sizeof wsize[0]);
	wNAF_len = reallocarray(NULL, totalnum, sizeof wNAF_len[0]);
	val_sub = reallocarray(NULL, totalnum, sizeof val_sub[0]);

	if (wsize == NULL || wNAF_len == NULL || val_sub == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}

	/* num_val will be the total number of temporarily precomputed points */
	num_val = 0;

	for (i = 0; i < num + num_scalar; i++) {
		size_t bits;

		bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
		wsize[i] = EC_window_bits_for_scalar_size(bits);
		num_val += (size_t) 1 << (wsize[i] - 1);
		wNAF[i + 1] = NULL;	/* make sure we always have a pivot */
		wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]);
		if (wNAF[i] == NULL)
			goto err;
		if (wNAF_len[i] > max_len)
			max_len = wNAF_len[i];
	}

	if (numblocks) {
		/* we go here iff scalar != NULL */

		if (num_scalar != 1) {
			ECerror(ERR_R_INTERNAL_ERROR);
			goto err;
		}
	}
	/*
	 * All points we precompute now go into a single array 'val'.
	 * 'val_sub[i]' is a pointer to the subarray for the i-th point, or
	 * to a subarray of 'pre_comp->points' if we already have
	 * precomputation.
	 */
	val = reallocarray(NULL, (num_val + 1), sizeof val[0]);
	if (val == NULL) {
		ECerror(ERR_R_MALLOC_FAILURE);
		goto err;
	}
	val[num_val] = NULL;	/* pivot element */

	/* allocate points for precomputation */
	v = val;
	for (i = 0; i < num + num_scalar; i++) {
		val_sub[i] = v;
		for (j = 0; j < ((size_t) 1 << (wsize[i] - 1)); j++) {
			*v = EC_POINT_new(group);
			if (*v == NULL)
				goto err;
			v++;
		}
	}
	if (!(v == val + num_val)) {
		ECerror(ERR_R_INTERNAL_ERROR);
		goto err;
	}
	if (!(tmp = EC_POINT_new(group)))
		goto err;

	/*
	 * prepare precomputed values: val_sub[i][0] :=     points[i]
	 * val_sub[i][1] := 3 * points[i] val_sub[i][2] := 5 * points[i] ...
	 */
	for (i = 0; i < num + num_scalar; i++) {
		if (i < num) {
			if (!EC_POINT_copy(val_sub[i][0], points[i]))
				goto err;
		} else {
			if (!EC_POINT_copy(val_sub[i][0], generator))
				goto err;
		}

		if (wsize[i] > 1) {
			if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx))
				goto err;
			for (j = 1; j < ((size_t) 1 << (wsize[i] - 1)); j++) {
				if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx))
					goto err;
			}
		}
	}

	if (!EC_POINTs_make_affine(group, num_val, val, ctx))
		goto err;

	r_is_at_infinity = 1;

	for (k = max_len - 1; k >= 0; k--) {
		if (!r_is_at_infinity) {
			if (!EC_POINT_dbl(group, r, r, ctx))
				goto err;
		}
		for (i = 0; i < totalnum; i++) {
			if (wNAF_len[i] > (size_t) k) {
				int digit = wNAF[i][k];
				int is_neg;

				if (digit) {
					is_neg = digit < 0;

					if (is_neg)
						digit = -digit;

					if (is_neg != r_is_inverted) {
						if (!r_is_at_infinity) {
							if (!EC_POINT_invert(group, r, ctx))
								goto err;
						}
						r_is_inverted = !r_is_inverted;
					}
					/* digit > 0 */

					if (r_is_at_infinity) {
						if (!EC_POINT_copy(r, val_sub[i][digit >> 1]))
							goto err;
						r_is_at_infinity = 0;
					} else {
						if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx))
							goto err;
					}
				}
			}
		}
	}

	if (r_is_at_infinity) {
		if (!EC_POINT_set_to_infinity(group, r))
			goto err;
	} else {
		if (r_is_inverted)
			if (!EC_POINT_invert(group, r, ctx))
				goto err;
	}

	ret = 1;

 err:
	EC_POINT_free(tmp);
	free(wsize);
	free(wNAF_len);
	free(tmp_wNAF);
	if (wNAF != NULL) {
		signed char **w;

		for (w = wNAF; *w != NULL; w++)
			free(*w);

		free(wNAF);
	}
	if (val != NULL) {
		for (v = val; *v != NULL; v++)
			EC_POINT_free(*v);
		free(val);
	}
	free(val_sub);
	return ret;
}