diff options
author | Bodo Möller <bodo@openssl.org> | 2011-10-18 19:43:54 +0000 |
---|---|---|
committer | Bodo Möller <bodo@openssl.org> | 2011-10-18 19:43:54 +0000 |
commit | 9c37519b55f790647e4c25a4665b1bac54455f9a (patch) | |
tree | ae24367ca0913bfa62ed2156e80283ca12cd6338 | |
parent | 7e9cfcd0dc72eeb4edc9b4846ffa92ff4739aa9b (diff) |
Improve optional 64-bit NIST-P224 implementation, and add NIST-P256 and
NIST-P521. (Now -DEC_NISTP_64_GCC_128 enables all three of these;
-DEC_NISTP224_64_GCC_128 no longer works.)
Submitted by: Google Inc.
-rw-r--r-- | CHANGES | 30 | ||||
-rw-r--r-- | crypto/ec/Makefile | 9 | ||||
-rw-r--r-- | crypto/ec/ec.h | 20 | ||||
-rw-r--r-- | crypto/ec/ec_curve.c | 13 | ||||
-rw-r--r-- | crypto/ec/ec_err.c | 10 | ||||
-rw-r--r-- | crypto/ec/ec_lcl.h | 48 | ||||
-rw-r--r-- | crypto/ec/ecp_nistp224.c | 1254 | ||||
-rw-r--r-- | crypto/ec/ecp_nistp256.c | 2158 | ||||
-rw-r--r-- | crypto/ec/ecp_nistp521.c | 2017 | ||||
-rw-r--r-- | crypto/ec/ecp_nistputil.c | 196 | ||||
-rw-r--r-- | crypto/ec/ectest.c | 177 |
11 files changed, 5305 insertions, 627 deletions
@@ -4,6 +4,24 @@ Changes between 1.0.0f and 1.0.1 [xx XXX xxxx] + *) Add optional 64-bit optimized implementations of elliptic curves NIST-P224, + NIST-P256, NIST-P521, with constant-time single point multiplication on + typical inputs. Compiler support for the nonstandard type __uint128_t is + required to use this. Code made available under Apache License version 2.0. + + To include this in your build of OpenSSL, use -DEC_NISTP_64_GCC_128 on + the Configure (or config) command line, and run "make depend" (or "make + update"). This enables the following EC_METHODs: + + EC_GFp_nistp224_method() + EC_GFp_nistp256_method() + EC_GFp_nistp521_method() + + EC_GROUP_new_by_curve_name() will automatically use these (while + EC_GROUP_new_curve_GFp() currently prefers the more flexible + implementations). + [Emilia Käsper, Adam Langley, Bodo Moeller (Google)] + *) Use type ossl_ssize_t instad of ssize_t which isn't available on all platforms. Move ssize_t definition from e_os.h to the public header file e_os2.h as it now appears in public header file cms.h @@ -190,18 +208,6 @@ *) Add functions to copy EVP_PKEY_METHOD and retrieve flags and id. [Steve Henson] - *) Add EC_GFp_nistp224_method(), a 64-bit optimized implementation for - elliptic curve NIST-P224 with constant-time single point multiplication on - typical inputs. EC_GROUP_new_by_curve_name() will automatically use this - (while EC_GROUP_new_curve_GFp() currently won't and prefers the more - flexible implementations). - - The implementation requires support for the nonstandard type __uint128_t, - and so is disabled by default. To include this in your build of OpenSSL, - use -DEC_NISTP224_64_GCC_128 on the Configure (or config) command line, - and run "make depend" (or "make update"). - [Emilia Käsper <emilia.kasper@esat.kuleuven.be> (Google)] - *) Permit abbreviated handshakes when renegotiating using the function SSL_renegotiate_abbreviated(). [Robin Seggelmann <seggelmann@fh-muenster.de>] diff --git a/crypto/ec/Makefile b/crypto/ec/Makefile index 7d0b5df8fe..f85fc845ca 100644 --- a/crypto/ec/Makefile +++ b/crypto/ec/Makefile @@ -20,12 +20,14 @@ LIB=$(TOP)/libcrypto.a LIBSRC= ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c\ ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c\ ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c \ - ecp_nistp224.c ecp_oct.c ec2_oct.c ec_oct.c + ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c \ + ecp_oct.c ec2_oct.c ec_oct.c LIBOBJ= ec_lib.o ecp_smpl.o ecp_mont.o ecp_nist.o ec_cvt.o ec_mult.o\ ec_err.o ec_curve.o ec_check.o ec_print.o ec_asn1.o ec_key.o\ ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o \ - ecp_nistp224.o ecp_oct.o ec2_oct.o ec_oct.o + ecp_nistp224.o ecp_nistp256.o ecp_nistp521.o ecp_nistputil.o \ + ecp_oct.o ec2_oct.o ec_oct.o SRC= $(LIBSRC) @@ -240,6 +242,9 @@ ecp_nist.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ecp_nist.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ecp_nist.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_nist.c ecp_nistp224.o: ../../include/openssl/opensslconf.h ecp_nistp224.c +ecp_nistp256.o: ../../include/openssl/opensslconf.h ecp_nistp256.c +ecp_nistp521.o: ../../include/openssl/opensslconf.h ecp_nistp521.c +ecp_nistputil.o: ../../include/openssl/opensslconf.h ecp_nistputil.c ecp_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ecp_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ecp_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h index c4fedeec25..57ea19ba4e 100644 --- a/crypto/ec/ec.h +++ b/crypto/ec/ec.h @@ -151,11 +151,21 @@ const EC_METHOD *EC_GFp_mont_method(void); */ const EC_METHOD *EC_GFp_nist_method(void); -#ifndef OPENSSL_NO_EC_NISTP224_64_GCC_128 +#ifdef EC_NISTP_64_GCC_128 /** Returns 64-bit optimized methods for nistp224 * \return EC_METHOD object */ const EC_METHOD *EC_GFp_nistp224_method(void); + +/** Returns 64-bit optimized methods for nistp256 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp256_method(void); + +/** Returns 64-bit optimized methods for nistp521 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp521_method(void); #endif #ifndef OPENSSL_NO_EC2M @@ -1003,6 +1013,12 @@ void ERR_load_EC_strings(void); #define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225 #define EC_F_EC_GFP_NISTP224_POINTS_MUL 228 #define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226 +#define EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE 230 +#define EC_F_EC_GFP_NISTP256_POINTS_MUL 231 +#define EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES 232 +#define EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE 233 +#define EC_F_EC_GFP_NISTP521_POINTS_MUL 234 +#define EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES 235 #define EC_F_EC_GFP_NIST_FIELD_MUL 200 #define EC_F_EC_GFP_NIST_FIELD_SQR 201 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202 @@ -1077,6 +1093,8 @@ void ERR_load_EC_strings(void); #define EC_F_I2D_ECPRIVATEKEY 192 #define EC_F_I2O_ECPUBLICKEY 151 #define EC_F_NISTP224_PRE_COMP_NEW 227 +#define EC_F_NISTP256_PRE_COMP_NEW 236 +#define EC_F_NISTP521_PRE_COMP_NEW 237 #define EC_F_O2I_ECPUBLICKEY 152 #define EC_F_OLD_EC_PRIV_DECODE 222 #define EC_F_PKEY_EC_CTRL 197 diff --git a/crypto/ec/ec_curve.c b/crypto/ec/ec_curve.c index 85cd3b6b3d..200af3fa3b 100644 --- a/crypto/ec/ec_curve.c +++ b/crypto/ec/ec_curve.c @@ -1841,16 +1841,19 @@ static const ec_list_element curve_list[] = { /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, -#ifdef EC_NISTP224_64_GCC_128 - { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field,\n" - "\t\t64-bit optimized implementation." }, +#ifdef EC_NISTP_64_GCC_128 + { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" }, #else { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, #endif { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, +#ifdef EC_NISTP_64_GCC_128 + { NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" }, +#else { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, +#endif /* X9.62 curves */ { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, @@ -1858,7 +1861,11 @@ static const ec_list_element curve_list[] = { { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, +#ifdef EC_NISTP_64_GCC_128 + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" }, +#else { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, +#endif #ifndef OPENSSL_NO_EC2M /* characteristic two field curves */ /* NIST/SECG curves */ diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c index 15d539cbf4..0d19398731 100644 --- a/crypto/ec/ec_err.c +++ b/crypto/ec/ec_err.c @@ -1,6 +1,6 @@ /* crypto/ec/ec_err.c */ /* ==================================================================== - * Copyright (c) 1999-2010 The OpenSSL Project. All rights reserved. + * Copyright (c) 1999-2011 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 @@ -116,6 +116,12 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE), "ec_GFp_nistp224_group_set_curve"}, {ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL), "ec_GFp_nistp224_points_mul"}, {ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp224_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE), "ec_GFp_nistp256_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINTS_MUL), "ec_GFp_nistp256_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp256_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE), "ec_GFp_nistp521_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINTS_MUL), "ec_GFp_nistp521_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp521_point_get_affine_coordinates"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"}, {ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE), "ec_GFp_nist_group_set_curve"}, @@ -190,6 +196,8 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_I2D_ECPRIVATEKEY), "i2d_ECPrivateKey"}, {ERR_FUNC(EC_F_I2O_ECPUBLICKEY), "i2o_ECPublicKey"}, {ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "NISTP224_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP256_PRE_COMP_NEW), "NISTP256_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP521_PRE_COMP_NEW), "NISTP521_PRE_COMP_NEW"}, {ERR_FUNC(EC_F_O2I_ECPUBLICKEY), "o2i_ECPublicKey"}, {ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE), "OLD_EC_PRIV_DECODE"}, {ERR_FUNC(EC_F_PKEY_EC_CTRL), "PKEY_EC_CTRL"}, diff --git a/crypto/ec/ec_lcl.h b/crypto/ec/ec_lcl.h index afa1efa4bc..72c0638a18 100644 --- a/crypto/ec/ec_lcl.h +++ b/crypto/ec/ec_lcl.h @@ -398,15 +398,49 @@ int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GF2m_have_precompute_mult(const EC_GROUP *group); -#ifdef EC_NISTP224_64_GCC_128 +#ifdef EC_NISTP_64_GCC_128 +/* method functions in ec2_mult.c */ +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + /* method functions in ecp_nistp224.c */ int ec_GFp_nistp224_group_init(EC_GROUP *group); -int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *n, BN_CTX *); -int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); -int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, - size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp256.c */ +int ec_GFp_nistp256_group_init(EC_GROUP *group); +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp521.c */ +int ec_GFp_nistp521_group_init(EC_GROUP *group); +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); + +/* utility functions in ecp_nistputil.c */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)); +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in); #endif diff --git a/crypto/ec/ecp_nistp224.c b/crypto/ec/ecp_nistp224.c index 90c3589bdf..8b2c6d39c8 100644 --- a/crypto/ec/ecp_nistp224.c +++ b/crypto/ec/ecp_nistp224.c @@ -2,58 +2,20 @@ /* * Written by Emilia Kasper (Google) for the OpenSSL project. */ -/* ==================================================================== - * Copyright (c) 2000-2010 The OpenSSL Project. All rights reserved. +/* Copyright 2011 Google Inc. * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: + * Licensed under the Apache License, Version 2.0 (the "License"); * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at * - * 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 - * licensing@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). + * http://www.apache.org/licenses/LICENSE-2.0 * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. */ /* @@ -62,8 +24,7 @@ * Inspired by Daniel J. Bernstein's public domain nistp224 implementation * and Adam Langley's public domain 64-bit C implementation of curve25519 */ -#include <openssl/opensslconf.h> -#ifndef OPENSSL_NO_EC_NISTP224_64_GCC_128 +#ifdef EC_NISTP_64_GCC_128 #include <stdint.h> #include <string.h> #include <openssl/err.h> @@ -77,28 +38,39 @@ #endif typedef uint8_t u8; +typedef uint64_t u64; +typedef int64_t s64; /******************************************************************************/ /* INTERNAL REPRESENTATION OF FIELD ELEMENTS * * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 - * where each slice a_i is a 64-bit word, i.e., a field element is an fslice - * array a with 4 elements, where a[i] = a_i. - * Outputs from multiplications are represented as unreduced polynomials + * using 64-bit coefficients called 'limbs', + * and sometimes (for multiplication results) as * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 - * where each b_i is a 128-bit word. We ensure that inputs to each field + * using 128-bit coefficients called 'widelimbs'. + * A 4-limb representation is an 'felem'; + * a 7-widelimb representation is a 'widefelem'. + * Even within felems, bits of adjacent limbs overlap, and we don't always + * reduce the representations: we ensure that inputs to each felem * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, * and fit into a 128-bit word without overflow. The coefficients are then - * again partially reduced to a_i < 2^57. We only reduce to the unique minimal - * representation at the end of the computation. - * + * again partially reduced to obtain an felem satisfying a_i < 2^57. + * We only reduce to the unique minimal representation at the end of the + * computation. */ -typedef uint64_t fslice; +typedef uint64_t limb; +typedef uint128_t widelimb; + +typedef limb felem[4]; +typedef widelimb widefelem[7]; /* Field element represented as a byte arrary. - * 28*8 = 224 bits is also the group order size for the elliptic curve. */ + * 28*8 = 224 bits is also the group order size for the elliptic curve, + * and we also use this type for scalars for point multiplication. + */ typedef u8 felem_bytearray[28]; static const felem_bytearray nistp224_curve_params[5] = { @@ -120,72 +92,143 @@ static const felem_bytearray nistp224_curve_params[5] = { }; /* Precomputed multiples of the standard generator - * b_0*G + b_1*2^56*G + b_2*2^112*G + b_3*2^168*G for - * (b_3, b_2, b_1, b_0) in [0,15], i.e., gmul[0] = point_at_infinity, - * gmul[1] = G, gmul[2] = 2^56*G, gmul[3] = 2^56*G + G, etc. - * Points are given in Jacobian projective coordinates: words 0-3 represent the - * X-coordinate (slice a_0 is word 0, etc.), words 4-7 represent the - * Y-coordinate and words 8-11 represent the Z-coordinate. */ -static const fslice gmul[16][3][4] = { - {{0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, - {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, - {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, - {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, - {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, - {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, - {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, - {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, - {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, - {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, - {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, - {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, - {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, - {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, - {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, - {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, - {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, - {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}} -}; + * Points are given in coordinates (X, Y, Z) where Z normally is 1 + * (0 for the point at infinity). + * For each field element, slice a_0 is word 0, etc. + * + * The table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^56G + * 3 | 0 0 1 1 | (2^56 + 1)G + * 4 | 0 1 0 0 | 2^112G + * 5 | 0 1 0 1 | (2^112 + 1)G + * 6 | 0 1 1 0 | (2^112 + 2^56)G + * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G + * 8 | 1 0 0 0 | 2^168G + * 9 | 1 0 0 1 | (2^168 + 1)G + * 10 | 1 0 1 0 | (2^168 + 2^56)G + * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G + * 12 | 1 1 0 0 | (2^168 + 2^112)G + * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G + * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G + * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G + * followed by a copy of this with each element multiplied by 2^28. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + */ +static const felem gmul[2][16][3] = +{{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}}}; /* Precomputation for the group generator. */ typedef struct { - fslice g_pre_comp[16][3][4]; + felem g_pre_comp[2][16][3]; int references; } NISTP224_PRE_COMP; const EC_METHOD *EC_GFp_nistp224_method(void) { static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_nistp224_group_init, ec_GFp_simple_group_finish, @@ -204,9 +247,9 @@ const EC_METHOD *EC_GFp_nistp224_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_nistp224_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -229,7 +272,7 @@ const EC_METHOD *EC_GFp_nistp224_method(void) } /* Helper functions to convert field elements to/from internal representation */ -static void bin28_to_felem(fslice out[4], const u8 in[28]) +static void bin28_to_felem(felem out, const u8 in[28]) { out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; @@ -237,7 +280,7 @@ static void bin28_to_felem(fslice out[4], const u8 in[28]) out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; } -static void felem_to_bin28(u8 out[28], const fslice in[4]) +static void felem_to_bin28(u8 out[28], const felem in) { unsigned i; for (i = 0; i < 7; ++i) @@ -258,9 +301,9 @@ static void flip_endian(u8 *out, const u8 *in, unsigned len) } /* From OpenSSL BIGNUM to internal representation */ -static int BN_to_felem(fslice out[4], const BIGNUM *bn) +static int BN_to_felem(felem out, const BIGNUM *bn) { - felem_bytearray b_in; + felem_bytearray b_in; felem_bytearray b_out; unsigned num_bytes; @@ -284,7 +327,7 @@ static int BN_to_felem(fslice out[4], const BIGNUM *bn) } /* From internal representation to OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4]) +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) { felem_bytearray b_in, b_out; felem_to_bin28(b_in, in); @@ -302,8 +345,24 @@ static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4]) * */ +static void felem_one(felem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + /* Sum two field elements: out += in */ -static void felem_sum64(fslice out[4], const fslice in[4]) +static void felem_sum(felem out, const felem in) { out[0] += in[0]; out[1] += in[1]; @@ -311,14 +370,30 @@ static void felem_sum64(fslice out[4], const fslice in[4]) out[3] += in[3]; } +/* Get negative value: out = -in */ +/* Assumes in[i] < 2^57 */ +static void felem_neg(felem out, const felem in) + { + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; + } + /* Subtract field elements: out -= in */ /* Assumes in[i] < 2^57 */ -static void felem_diff64(fslice out[4], const fslice in[4]) +static void felem_diff(felem out, const felem in) { - static const uint64_t two58p2 = (((uint64_t) 1) << 58) + (((uint64_t) 1) << 2); - static const uint64_t two58m2 = (((uint64_t) 1) << 58) - (((uint64_t) 1) << 2); - static const uint64_t two58m42m2 = (((uint64_t) 1) << 58) - - (((uint64_t) 1) << 42) - (((uint64_t) 1) << 2); + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); /* Add 0 mod 2^224-2^96+1 to ensure out > in */ out[0] += two58p2; @@ -332,15 +407,15 @@ static void felem_diff64(fslice out[4], const fslice in[4]) out[3] -= in[3]; } -/* Subtract in unreduced 128-bit mode: out128 -= in128 */ +/* Subtract in unreduced 128-bit mode: out -= in */ /* Assumes in[i] < 2^119 */ -static void felem_diff128(uint128_t out[7], const uint128_t in[4]) +static void widefelem_diff(widefelem out, const widefelem in) { - static const uint128_t two120 = ((uint128_t) 1) << 120; - static const uint128_t two120m64 = (((uint128_t) 1) << 120) - - (((uint128_t) 1) << 64); - static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) - - (((uint128_t) 1) << 104) - (((uint |