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openssl-ec-56-bit-Limb-Solinas-Strategy-for-sec...
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File openssl-ec-56-bit-Limb-Solinas-Strategy-for-secp384r1.patch of Package openssl-3
From 01d901e470d9e035a3bd78e77b9438a4cc0da785 Mon Sep 17 00:00:00 2001 From: Rohan McLure <rohanmclure@linux.ibm.com> Date: Wed, 12 Jul 2023 12:25:22 +1000 Subject: [PATCH] ec: 56-bit Limb Solinas' Strategy for secp384r1 Adopt a 56-bit redundant-limb Solinas' reduction approach for efficient modular multiplication in P384. This has the affect of accelerating digital signing by 446% and verification by 106%. The implementation strategy and names of methods are the same as that provided in ecp_nistp224 and ecp_nistp521. As in Commit 1036749883cc ("ec: Add run time code selection for p521 field operations"), allow for run time selection of implementation for felem_{square,mul}, where an assembly implementation is proclaimed to be present when ECP_NISTP384_ASM is present. Signed-off-by: Rohan McLure <rohanmclure@linux.ibm.com> Reviewed-by: Paul Dale <pauli@openssl.org> Reviewed-by: Shane Lontis <shane.lontis@oracle.com> Reviewed-by: Dmitry Belyavskiy <beldmit@gmail.com> Reviewed-by: Todd Short <todd.short@me.com> (Merged from https://github.com/openssl/openssl/pull/21471) --- crypto/ec/build.info | 2 crypto/ec/ec_curve.c | 4 crypto/ec/ec_lib.c | 8 crypto/ec/ec_local.h | 27 crypto/ec/ecp_nistp384.c | 1988 +++++++++++++++++++++++++++++++++++++++++++++++ 5 files changed, 2027 insertions(+), 2 deletions(-) create mode 100644 crypto/ec/ecp_nistp384.c --- a/crypto/ec/build.info +++ b/crypto/ec/build.info @@ -59,7 +59,7 @@ $COMMON=ec_lib.c ecp_smpl.c ecp_mont.c e curve448/arch_32/f_impl32.c IF[{- !$disabled{'ec_nistp_64_gcc_128'} -}] - $COMMON=$COMMON ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c + $COMMON=$COMMON ecp_nistp224.c ecp_nistp256.c ecp_nistp384.c ecp_nistp521.c ecp_nistputil.c ENDIF SOURCE[../../libcrypto]=$COMMON ec_ameth.c ec_pmeth.c ecx_meth.c \ --- a/crypto/ec/ec_curve.c +++ b/crypto/ec/ec_curve.c @@ -2838,6 +2838,8 @@ static const ec_list_element curve_list[ {NID_secp384r1, &_EC_NIST_PRIME_384.h, # if defined(S390X_EC_ASM) EC_GFp_s390x_nistp384_method, +# elif !defined(OPENSSL_NO_EC_NISTP_64_GCC_128) + ossl_ec_GFp_nistp384_method, # else 0, # endif @@ -2931,6 +2933,8 @@ static const ec_list_element curve_list[ {NID_secp384r1, &_EC_NIST_PRIME_384.h, # if defined(S390X_EC_ASM) EC_GFp_s390x_nistp384_method, +# elif !defined(OPENSSL_NO_EC_NISTP_64_GCC_128) + ossl_ec_GFp_nistp384_method, # else 0, # endif --- a/crypto/ec/ec_lib.c +++ b/crypto/ec/ec_lib.c @@ -102,12 +102,16 @@ void EC_pre_comp_free(EC_GROUP *group) case PCT_nistp256: EC_nistp256_pre_comp_free(group->pre_comp.nistp256); break; + case PCT_nistp384: + ossl_ec_nistp384_pre_comp_free(group->pre_comp.nistp384); + break; case PCT_nistp521: EC_nistp521_pre_comp_free(group->pre_comp.nistp521); break; #else case PCT_nistp224: case PCT_nistp256: + case PCT_nistp384: case PCT_nistp521: break; #endif @@ -191,12 +195,16 @@ int EC_GROUP_copy(EC_GROUP *dest, const case PCT_nistp256: dest->pre_comp.nistp256 = EC_nistp256_pre_comp_dup(src->pre_comp.nistp256); break; + case PCT_nistp384: + dest->pre_comp.nistp384 = ossl_ec_nistp384_pre_comp_dup(src->pre_comp.nistp384); + break; case PCT_nistp521: dest->pre_comp.nistp521 = EC_nistp521_pre_comp_dup(src->pre_comp.nistp521); break; #else case PCT_nistp224: case PCT_nistp256: + case PCT_nistp384: case PCT_nistp521: break; #endif --- a/crypto/ec/ec_local.h +++ b/crypto/ec/ec_local.h @@ -203,6 +203,7 @@ struct ec_method_st { */ typedef struct nistp224_pre_comp_st NISTP224_PRE_COMP; typedef struct nistp256_pre_comp_st NISTP256_PRE_COMP; +typedef struct nistp384_pre_comp_st NISTP384_PRE_COMP; typedef struct nistp521_pre_comp_st NISTP521_PRE_COMP; typedef struct nistz256_pre_comp_st NISTZ256_PRE_COMP; typedef struct ec_pre_comp_st EC_PRE_COMP; @@ -264,12 +265,13 @@ struct ec_group_st { */ enum { PCT_none, - PCT_nistp224, PCT_nistp256, PCT_nistp521, PCT_nistz256, + PCT_nistp224, PCT_nistp256, PCT_nistp384, PCT_nistp521, PCT_nistz256, PCT_ec } pre_comp_type; union { NISTP224_PRE_COMP *nistp224; NISTP256_PRE_COMP *nistp256; + NISTP384_PRE_COMP *nistp384; NISTP521_PRE_COMP *nistp521; NISTZ256_PRE_COMP *nistz256; EC_PRE_COMP *ec; @@ -333,6 +335,7 @@ static ossl_inline int ec_point_is_compa NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *); NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); +NISTP384_PRE_COMP *ossl_ec_nistp384_pre_comp_dup(NISTP384_PRE_COMP *); NISTP521_PRE_COMP *EC_nistp521_pre_comp_dup(NISTP521_PRE_COMP *); NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *); NISTP256_PRE_COMP *EC_nistp256_pre_comp_dup(NISTP256_PRE_COMP *); @@ -341,6 +344,7 @@ EC_PRE_COMP *EC_ec_pre_comp_dup(EC_PRE_C void EC_pre_comp_free(EC_GROUP *group); void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *); void EC_nistp256_pre_comp_free(NISTP256_PRE_COMP *); +void ossl_ec_nistp384_pre_comp_free(NISTP384_PRE_COMP *); void EC_nistp521_pre_comp_free(NISTP521_PRE_COMP *); void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *); void EC_ec_pre_comp_free(EC_PRE_COMP *); @@ -552,6 +556,27 @@ int ossl_ec_GFp_nistp256_points_mul(cons int ossl_ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ossl_ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); +/* method functions in ecp_nistp384.c */ +int ossl_ec_GFp_nistp384_group_init(EC_GROUP *group); +int ossl_ec_GFp_nistp384_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *n, + BN_CTX *); +int ossl_ec_GFp_nistp384_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx); +int ossl_ec_GFp_nistp384_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], const BIGNUM *scalars[], + BN_CTX *); +int ossl_ec_GFp_nistp384_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 ossl_ec_GFp_nistp384_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ossl_ec_GFp_nistp384_have_precompute_mult(const EC_GROUP *group); +const EC_METHOD *ossl_ec_GFp_nistp384_method(void); + /* method functions in ecp_nistp521.c */ int ossl_ec_GFp_nistp521_group_init(EC_GROUP *group); int ossl_ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, --- /dev/null +++ b/crypto/ec/ecp_nistp384.c @@ -0,0 +1,1988 @@ +/* + * Copyright 2023 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the Apache License 2.0 (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2023 IBM Corp. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * 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. + */ + +/* + * Designed for 56-bit limbs by Rohan McLure <rohan.mclure@linux.ibm.com>. + * The layout is based on that of ecp_nistp{224,521}.c, allowing even for asm + * acceleration of felem_{square,mul} as supported in these files. + */ + +#include <openssl/e_os2.h> + +#include <string.h> +#include <openssl/err.h> +#include "ec_local.h" + +#include "internal/numbers.h" + +#ifndef INT128_MAX +# error "Your compiler doesn't appear to support 128-bit integer types" +#endif + +typedef uint8_t u8; +typedef uint64_t u64; + +/* + * The underlying field. P384 operates over GF(2^384-2^128-2^96+2^32-1). We + * can serialize an element of this field into 48 bytes. We call this an + * felem_bytearray. + */ + +typedef u8 felem_bytearray[48]; + +/* + * These are the parameters of P384, taken from FIPS 186-3, section D.1.2.4. + * These values are big-endian. + */ +static const felem_bytearray nistp384_curve_params[5] = { + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFF}, + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a = -3 */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xFF, 0xFF, 0xFF, 0xFC}, + {0xB3, 0x31, 0x2F, 0xA7, 0xE2, 0x3E, 0xE7, 0xE4, 0x98, 0x8E, 0x05, 0x6B, /* b */ + 0xE3, 0xF8, 0x2D, 0x19, 0x18, 0x1D, 0x9C, 0x6E, 0xFE, 0x81, 0x41, 0x12, + 0x03, 0x14, 0x08, 0x8F, 0x50, 0x13, 0x87, 0x5A, 0xC6, 0x56, 0x39, 0x8D, + 0x8A, 0x2E, 0xD1, 0x9D, 0x2A, 0x85, 0xC8, 0xED, 0xD3, 0xEC, 0x2A, 0xEF}, + {0xAA, 0x87, 0xCA, 0x22, 0xBE, 0x8B, 0x05, 0x37, 0x8E, 0xB1, 0xC7, 0x1E, /* x */ + 0xF3, 0x20, 0xAD, 0x74, 0x6E, 0x1D, 0x3B, 0x62, 0x8B, 0xA7, 0x9B, 0x98, + 0x59, 0xF7, 0x41, 0xE0, 0x82, 0x54, 0x2A, 0x38, 0x55, 0x02, 0xF2, 0x5D, + 0xBF, 0x55, 0x29, 0x6C, 0x3A, 0x54, 0x5E, 0x38, 0x72, 0x76, 0x0A, 0xB7}, + {0x36, 0x17, 0xDE, 0x4A, 0x96, 0x26, 0x2C, 0x6F, 0x5D, 0x9E, 0x98, 0xBF, /* y */ + 0x92, 0x92, 0xDC, 0x29, 0xF8, 0xF4, 0x1D, 0xBD, 0x28, 0x9A, 0x14, 0x7C, + 0xE9, 0xDA, 0x31, 0x13, 0xB5, 0xF0, 0xB8, 0xC0, 0x0A, 0x60, 0xB1, 0xCE, + 0x1D, 0x7E, 0x81, 0x9D, 0x7A, 0x43, 0x1D, 0x7C, 0x90, 0xEA, 0x0E, 0x5F}, +}; + +/*- + * The representation of field elements. + * ------------------------------------ + * + * We represent field elements with seven values. These values are either 64 or + * 128 bits and the field element represented is: + * v[0]*2^0 + v[1]*2^56 + v[2]*2^112 + ... + v[6]*2^336 (mod p) + * Each of the seven values is called a 'limb'. Since the limbs are spaced only + * 56 bits apart, but are greater than 56 bits in length, the most significant + * bits of each limb overlap with the least significant bits of the next + * + * This representation is considered to be 'redundant' in the sense that + * intermediate values can each contain more than a 56-bit value in each limb. + * Reduction causes all but the final limb to be reduced to contain a value less + * than 2^56, with the final value represented allowed to be larger than 2^384, + * inasmuch as we can be sure that arithmetic overflow remains impossible. The + * reduced value must of course be congruent to the unreduced value. + * + * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a + * 'widefelem', featuring enough bits to store the result of a multiplication + * and even some further arithmetic without need for immediate reduction. + */ + +#define NLIMBS 7 + +typedef uint64_t limb; +typedef uint128_t widelimb; +typedef limb limb_aX __attribute((__aligned__(1))); +typedef limb felem[NLIMBS]; +typedef widelimb widefelem[2*NLIMBS-1]; + +static const limb bottom56bits = 0xffffffffffffff; + +/* Helper functions (de)serialising reduced field elements in little endian */ +static void bin48_to_felem(felem out, const u8 in[48]) +{ + memset(out, 0, 56); + out[0] = (*((limb *) & in[0])) & bottom56bits; + out[1] = (*((limb_aX *) & in[7])) & bottom56bits; + out[2] = (*((limb_aX *) & in[14])) & bottom56bits; + out[3] = (*((limb_aX *) & in[21])) & bottom56bits; + out[4] = (*((limb_aX *) & in[28])) & bottom56bits; + out[5] = (*((limb_aX *) & in[35])) & bottom56bits; + memmove(&out[6], &in[42], 6); +} + +static void felem_to_bin48(u8 out[48], const felem in) +{ + memset(out, 0, 48); + (*((limb *) & out[0])) |= (in[0] & bottom56bits); + (*((limb_aX *) & out[7])) |= (in[1] & bottom56bits); + (*((limb_aX *) & out[14])) |= (in[2] & bottom56bits); + (*((limb_aX *) & out[21])) |= (in[3] & bottom56bits); + (*((limb_aX *) & out[28])) |= (in[4] & bottom56bits); + (*((limb_aX *) & out[35])) |= (in[5] & bottom56bits); + memmove(&out[42], &in[6], 6); +} + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) +{ + felem_bytearray b_out; + int num_bytes; + + if (BN_is_negative(bn)) { + ERR_raise(ERR_LIB_EC, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2lebinpad(bn, b_out, sizeof(b_out)); + if (num_bytes < 0) { + ERR_raise(ERR_LIB_EC, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + bin48_to_felem(out, b_out); + return 1; +} + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) +{ + felem_bytearray b_out; + + felem_to_bin48(b_out, in); + return BN_lebin2bn(b_out, sizeof(b_out), out); +} + +/*- + * Field operations + * ---------------- + */ + +static void felem_one(felem out) +{ + out[0] = 1; + memset(&out[1], 0, sizeof(limb) * (NLIMBS-1)); +} + +static void felem_assign(felem out, const felem in) +{ + memcpy(out, in, sizeof(felem)); +} + +/* felem_sum64 sets out = out + in. */ +static void felem_sum64(felem out, const felem in) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out[i] += in[i]; +} + +/* felem_scalar sets out = in * scalar */ +static void felem_scalar(felem out, const felem in, limb scalar) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out[i] = in[i] * scalar; +} + +/* felem_scalar64 sets out = out * scalar */ +static void felem_scalar64(felem out, limb scalar) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out[i] *= scalar; +} + +/* felem_scalar128 sets out = out * scalar */ +static void felem_scalar128(widefelem out, limb scalar) +{ + unsigned int i; + + for (i = 0; i < 2*NLIMBS-1; i++) + out[i] *= scalar; +} + +/*- + * felem_neg sets |out| to |-in| + * On entry: + * in[i] < 2^60 - 2^29 + * On exit: + * out[i] < 2^60 + */ +static void felem_neg(felem out, const felem in) +{ + /* + * In order to prevent underflow, we add a multiple of p before subtracting. + * Use telescopic sums to represent 2^12 * p redundantly with each limb + * of the form 2^60 + ... + */ + static const limb two60m52m4 = (((limb) 1) << 60) + - (((limb) 1) << 52) + - (((limb) 1) << 4); + static const limb two60p44m12 = (((limb) 1) << 60) + + (((limb) 1) << 44) + - (((limb) 1) << 12); + static const limb two60m28m4 = (((limb) 1) << 60) + - (((limb) 1) << 28) + - (((limb) 1) << 4); + static const limb two60m4 = (((limb) 1) << 60) + - (((limb) 1) << 4); + + out[0] = two60p44m12 - in[0]; + out[1] = two60m52m4 - in[1]; + out[2] = two60m28m4 - in[2]; + out[3] = two60m4 - in[3]; + out[4] = two60m4 - in[4]; + out[5] = two60m4 - in[5]; + out[6] = two60m4 - in[6]; +} + +/*- + * felem_diff64 subtracts |in| from |out| + * On entry: + * in[i] < 2^60 - 2^52 - 2^4 + * On exit: + * out[i] < out_orig[i] + 2^60 + 2^44 + */ +static void felem_diff64(felem out, const felem in) +{ + /* + * In order to prevent underflow, we add a multiple of p before subtracting. + * Use telescopic sums to represent 2^12 * p redundantly with each limb + * of the form 2^60 + ... + */ + + static const limb two60m52m4 = (((limb) 1) << 60) + - (((limb) 1) << 52) + - (((limb) 1) << 4); + static const limb two60p44m12 = (((limb) 1) << 60) + + (((limb) 1) << 44) + - (((limb) 1) << 12); + static const limb two60m28m4 = (((limb) 1) << 60) + - (((limb) 1) << 28) + - (((limb) 1) << 4); + static const limb two60m4 = (((limb) 1) << 60) + - (((limb) 1) << 4); + + out[0] += two60p44m12 - in[0]; + out[1] += two60m52m4 - in[1]; + out[2] += two60m28m4 - in[2]; + out[3] += two60m4 - in[3]; + out[4] += two60m4 - in[4]; + out[5] += two60m4 - in[5]; + out[6] += two60m4 - in[6]; +} + +/* + * in[i] < 2^63 + * out[i] < out_orig[i] + 2^64 + 2^48 + */ +static void felem_diff_128_64(widefelem out, const felem in) +{ + /* + * In order to prevent underflow, we add a multiple of p before subtracting. + * Use telescopic sums to represent 2^16 * p redundantly with each limb + * of the form 2^64 + ... + */ + + static const widelimb two64m56m8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 56) + - (((widelimb) 1) << 8); + static const widelimb two64m32m8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 32) + - (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) + - (((widelimb) 1) << 8); + static const widelimb two64p48m16 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 48) + - (((widelimb) 1) << 16); + unsigned int i; + + out[0] += two64p48m16; + out[1] += two64m56m8; + out[2] += two64m32m8; + out[3] += two64m8; + out[4] += two64m8; + out[5] += two64m8; + out[6] += two64m8; + + for (i = 0; i < NLIMBS; i++) + out[i] -= in[i]; +} + +/* + * in[i] < 2^127 - 2^119 - 2^71 + * out[i] < out_orig[i] + 2^127 + 2^111 + */ +static void felem_diff128(widefelem out, const widefelem in) +{ + /* + * In order to prevent underflow, we add a multiple of p before subtracting. + * Use telescopic sums to represent 2^415 * p redundantly with each limb + * of the form 2^127 + ... + */ + + static const widelimb two127 = ((widelimb) 1) << 127; + static const widelimb two127m71 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 71); + static const widelimb two127p111m79m71 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 111) + - (((widelimb) 1) << 79) + - (((widelimb) 1) << 71); + static const widelimb two127m119m71 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 119) + - (((widelimb) 1) << 71); + static const widelimb two127m95m71 = (((widelimb) 1) << 127) + - (((widelimb) 1) << 95) + - (((widelimb) 1) << 71); + unsigned int i; + + out[0] += two127; + out[1] += two127m71; + out[2] += two127m71; + out[3] += two127m71; + out[4] += two127m71; + out[5] += two127m71; + out[6] += two127p111m79m71; + out[7] += two127m119m71; + out[8] += two127m95m71; + out[9] += two127m71; + out[10] += two127m71; + out[11] += two127m71; + out[12] += two127m71; + + for (i = 0; i < 2*NLIMBS-1; i++) + out[i] -= in[i]; +} + +static void felem_square_ref(widefelem out, const felem in) +{ + felem inx2; + felem_scalar(inx2, in, 2); + + out[0] = ((uint128_t) in[0]) * in[0]; + + out[1] = ((uint128_t) in[0]) * inx2[1]; + + out[2] = ((uint128_t) in[0]) * inx2[2] + + ((uint128_t) in[1]) * in[1]; + + out[3] = ((uint128_t) in[0]) * inx2[3] + + ((uint128_t) in[1]) * inx2[2]; + + out[4] = ((uint128_t) in[0]) * inx2[4] + + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; + + out[5] = ((uint128_t) in[0]) * inx2[5] + + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; + + out[6] = ((uint128_t) in[0]) * inx2[6] + + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; + + out[7] = ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; + + out[8] = ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; + + out[9] = ((uint128_t) in[3]) * inx2[6] + + ((uint128_t) in[4]) * inx2[5]; + + out[10] = ((uint128_t) in[4]) * inx2[6] + + ((uint128_t) in[5]) * in[5]; + + out[11] = ((uint128_t) in[5]) * inx2[6]; + + out[12] = ((uint128_t) in[6]) * in[6]; +} + +static void felem_mul_ref(widefelem out, const felem in1, const felem in2) +{ + out[0] = ((uint128_t) in1[0]) * in2[0]; + + out[1] = ((uint128_t) in1[0]) * in2[1] + + ((uint128_t) in1[1]) * in2[0]; + + out[2] = ((uint128_t) in1[0]) * in2[2] + + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; + + out[3] = ((uint128_t) in1[0]) * in2[3] + + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; + + out[4] = ((uint128_t) in1[0]) * in2[4] + + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; + + out[5] = ((uint128_t) in1[0]) * in2[5] + + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; + + out[6] = ((uint128_t) in1[0]) * in2[6] + + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; + + out[7] = ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1]; + + out[8] = ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2]; + + out[9] = ((uint128_t) in1[3]) * in2[6] + + ((uint128_t) in1[4]) * in2[5] + + ((uint128_t) in1[5]) * in2[4] + + ((uint128_t) in1[6]) * in2[3]; + + out[10] = ((uint128_t) in1[4]) * in2[6] + + ((uint128_t) in1[5]) * in2[5] + + ((uint128_t) in1[6]) * in2[4]; + + out[11] = ((uint128_t) in1[5]) * in2[6] + + ((uint128_t) in1[6]) * in2[5]; + + out[12] = ((uint128_t) in1[6]) * in2[6]; +} + +/*- + * Reduce thirteen 128-bit coefficients to seven 64-bit coefficients. + * in[i] < 2^128 - 2^125 + * out[i] < 2^56 for i < 6, + * out[6] <= 2^48 + * + * The technique in use here stems from the format of the prime modulus: + * P384 = 2^384 - delta + * + * Thus we can reduce numbers of the form (X + 2^384 * Y) by substituting + * them with (X + delta Y), with delta = 2^128 + 2^96 + (-2^32 + 1). These + * coefficients are still quite large, and so we repeatedly apply this + * technique on high-order bits in order to guarantee the desired bounds on + * the size of our output. + * + * The three phases of elimination are as follows: + * [1]: Y = 2^120 (in[12] | in[11] | in[10] | in[9]) + * [2]: Y = 2^8 (acc[8] | acc[7]) + * [3]: Y = 2^48 (acc[6] >> 48) + * (Where a | b | c | d = (2^56)^3 a + (2^56)^2 b + (2^56) c + d) + */ +static void felem_reduce(felem out, const widefelem in) +{ + /* + * In order to prevent underflow, we add a multiple of p before subtracting. + * Use telescopic sums to represent 2^76 * p redundantly with each limb + * of the form 2^124 + ... + */ + static const widelimb two124m68 = (((widelimb) 1) << 124) + - (((widelimb) 1) << 68); + static const widelimb two124m116m68 = (((widelimb) 1) << 124) + - (((widelimb) 1) << 116) + - (((widelimb) 1) << 68); + static const widelimb two124p108m76 = (((widelimb) 1) << 124) + + (((widelimb) 1) << 108) + - (((widelimb) 1) << 76); + static const widelimb two124m92m68 = (((widelimb) 1) << 124) + - (((widelimb) 1) << 92) + - (((widelimb) 1) << 68); + widelimb temp, acc[9]; + unsigned int i; + + memcpy(acc, in, sizeof(widelimb) * 9); + + acc[0] += two124p108m76; + acc[1] += two124m116m68; + acc[2] += two124m92m68; + acc[3] += two124m68; + acc[4] += two124m68; + acc[5] += two124m68; + acc[6] += two124m68; + + /* [1]: Eliminate in[9], ..., in[12] */ + acc[8] += in[12] >> 32; + acc[7] += (in[12] & 0xffffffff) << 24; + acc[7] += in[12] >> 8; + acc[6] += (in[12] & 0xff) << 48; + acc[6] -= in[12] >> 16; + acc[5] -= ((in[12] & 0xffff) << 40); + acc[6] += in[12] >> 48; + acc[5] += (in[12] & 0xffffffffffff) << 8; + + acc[7] += in[11] >> 32; + acc[6] += (in[11] & 0xffffffff) << 24; + acc[6] += in[11] >> 8; + acc[5] += (in[11] & 0xff) << 48; + acc[5] -= in[11] >> 16; + acc[4] -= ((in[11] & 0xffff) << 40); + acc[5] += in[11] >> 48; + acc[4] += (in[11] & 0xffffffffffff) << 8; + + acc[6] += in[10] >> 32; + acc[5] += (in[10] & 0xffffffff) << 24; + acc[5] += in[10] >> 8; + acc[4] += (in[10] & 0xff) << 48; + acc[4] -= in[10] >> 16; + acc[3] -= ((in[10] & 0xffff) << 40); + acc[4] += in[10] >> 48; + acc[3] += (in[10] & 0xffffffffffff) << 8; + + acc[5] += in[9] >> 32; + acc[4] += (in[9] & 0xffffffff) << 24; + acc[4] += in[9] >> 8; + acc[3] += (in[9] & 0xff) << 48; + acc[3] -= in[9] >> 16; + acc[2] -= ((in[9] & 0xffff) << 40); + acc[3] += in[9] >> 48; + acc[2] += (in[9] & 0xffffffffffff) << 8; + + /* + * [2]: Eliminate acc[7], acc[8], that is the 7 and eighth limbs, as + * well as the contributions made from eliminating higher limbs. + * acc[7] < in[7] + 2^120 + 2^56 < in[7] + 2^121 + * acc[8] < in[8] + 2^96 + */ + acc[4] += acc[8] >> 32; + acc[3] += (acc[8] & 0xffffffff) << 24; + acc[3] += acc[8] >> 8; + acc[2] += (acc[8] & 0xff) << 48; + acc[2] -= acc[8] >> 16; + acc[1] -= ((acc[8] & 0xffff) << 40); + acc[2] += acc[8] >> 48; + acc[1] += (acc[8] & 0xffffffffffff) << 8; + + acc[3] += acc[7] >> 32; + acc[2] += (acc[7] & 0xffffffff) << 24; + acc[2] += acc[7] >> 8; + acc[1] += (acc[7] & 0xff) << 48; + acc[1] -= acc[7] >> 16; + acc[0] -= ((acc[7] & 0xffff) << 40); + acc[1] += acc[7] >> 48; + acc[0] += (acc[7] & 0xffffffffffff) << 8; + + /*- + * acc[k] < in[k] + 2^124 + 2^121 + * < in[k] + 2^125 + * < 2^128, for k <= 6 + */ + + /* + * Carry 4 -> 5 -> 6 + * This has the effect of ensuring that these more significant limbs + * will be small in value after eliminating high bits from acc[6]. + */ + acc[5] += acc[4] >> 56; + acc[4] &= 0x00ffffffffffffff; + + acc[6] += acc[5] >> 56; + acc[5] &= 0x00ffffffffffffff; + + /*- + * acc[6] < in[6] + 2^124 + 2^121 + 2^72 + 2^16 + * < in[6] + 2^125 + * < 2^128 + */ + + /* [3]: Eliminate high bits of acc[6] */ + temp = acc[6] >> 48; + acc[6] &= 0x0000ffffffffffff; + + /* temp < 2^80 */ + + acc[3] += temp >> 40; + acc[2] += (temp & 0xffffffffff) << 16; + acc[2] += temp >> 16; + acc[1] += (temp & 0xffff) << 40; + acc[1] -= temp >> 24; + acc[0] -= (temp & 0xffffff) << 32; + acc[0] += temp; + + /*- + * acc[k] < acc_old[k] + 2^64 + 2^56 + * < in[k] + 2^124 + 2^121 + 2^72 + 2^64 + 2^56 + 2^16 , k < 4 + */ + + /* Carry 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 */ + acc[1] += acc[0] >> 56; /* acc[1] < acc_old[1] + 2^72 */ + acc[0] &= 0x00ffffffffffffff; + + acc[2] += acc[1] >> 56; /* acc[2] < acc_old[2] + 2^72 + 2^16 */ + acc[1] &= 0x00ffffffffffffff; + + acc[3] += acc[2] >> 56; /* acc[3] < acc_old[3] + 2^72 + 2^16 */ + acc[2] &= 0x00ffffffffffffff; + + /*- + * acc[k] < acc_old[k] + 2^72 + 2^16 + * < in[k] + 2^124 + 2^121 + 2^73 + 2^64 + 2^56 + 2^17 + * < in[k] + 2^125 + * < 2^128 , k < 4 + */ + + acc[4] += acc[3] >> 56; /*- + * acc[4] < acc_old[4] + 2^72 + 2^16 + * < 2^72 + 2^56 + 2^16 + */ + acc[3] &= 0x00ffffffffffffff; + + acc[5] += acc[4] >> 56; /*- + * acc[5] < acc_old[5] + 2^16 + 1 + * < 2^56 + 2^16 + 1 + */ + acc[4] &= 0x00ffffffffffffff; + + acc[6] += acc[5] >> 56; /* acc[6] < 2^48 + 1 <= 2^48 */ + acc[5] &= 0x00ffffffffffffff; + + for (i = 0; i < NLIMBS; i++) + out[i] = acc[i]; +} + +#if defined(ECP_NISTP384_ASM) +static void felem_square_wrapper(widefelem out, const felem in); +static void felem_mul_wrapper(widefelem out, const felem in1, const felem in2); + +static void (*felem_square_p)(widefelem out, const felem in) = + felem_square_wrapper; +static void (*felem_mul_p)(widefelem out, const felem in1, const felem in2) = + felem_mul_wrapper; + +void p384_felem_square(widefelem out, const felem in); +void p384_felem_mul(widefelem out, const felem in1, const felem in2); + +# if defined(_ARCH_PPC64) +# include "crypto/ppc_arch.h" +# endif + +static void felem_select(void) +{ + /* Default */ + felem_square_p = felem_square_ref; + felem_mul_p = felem_mul_ref; +} + +static void felem_square_wrapper(widefelem out, const felem in) +{ + felem_select(); + felem_square_p(out, in); +} + +static void felem_mul_wrapper(widefelem out, const felem in1, const felem in2) +{ + felem_select(); + felem_mul_p(out, in1, in2); +} + +# define felem_square felem_square_p +# define felem_mul felem_mul_p +#else +# define felem_square felem_square_ref +# define felem_mul felem_mul_ref +#endif + +static ossl_inline void felem_square_reduce(felem out, const felem in) +{ + widefelem tmp; + + felem_square(tmp, in); + felem_reduce(out, tmp); +} + +static ossl_inline void felem_mul_reduce(felem out, const felem in1, const felem in2) +{ + widefelem tmp; + + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} + +/*- + * felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6; + unsigned int i = 0; + + felem_square_reduce(ftmp, in); /* 2^1 */ + felem_mul_reduce(ftmp, ftmp, in); /* 2^1 + 2^0 */ + felem_assign(ftmp2, ftmp); + + felem_square_reduce(ftmp, ftmp); /* 2^2 + 2^1 */ + felem_mul_reduce(ftmp, ftmp, in); /* 2^2 + 2^1 * 2^0 */ + felem_assign(ftmp3, ftmp); + + for (i = 0; i < 3; i++) + felem_square_reduce(ftmp, ftmp); /* 2^5 + 2^4 + 2^3 */ + felem_mul_reduce(ftmp, ftmp3, ftmp); /* 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 */ + felem_assign(ftmp4, ftmp); + + for (i = 0; i < 6; i++) + felem_square_reduce(ftmp, ftmp); /* 2^11 + ... + 2^6 */ + felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^11 + ... + 2^0 */ + + for (i = 0; i < 3; i++) + felem_square_reduce(ftmp, ftmp); /* 2^14 + ... + 2^3 */ + felem_mul_reduce(ftmp, ftmp3, ftmp); /* 2^14 + ... + 2^0 */ + felem_assign(ftmp5, ftmp); + + for (i = 0; i < 15; i++) + felem_square_reduce(ftmp, ftmp); /* 2^29 + ... + 2^15 */ + felem_mul_reduce(ftmp, ftmp5, ftmp); /* 2^29 + ... + 2^0 */ + felem_assign(ftmp6, ftmp); + + for (i = 0; i < 30; i++) + felem_square_reduce(ftmp, ftmp); /* 2^59 + ... + 2^30 */ + felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^59 + ... + 2^0 */ + felem_assign(ftmp4, ftmp); + + for (i = 0; i < 60; i++) + felem_square_reduce(ftmp, ftmp); /* 2^119 + ... + 2^60 */ + felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^119 + ... + 2^0 */ + felem_assign(ftmp4, ftmp); + + for (i = 0; i < 120; i++) + felem_square_reduce(ftmp, ftmp); /* 2^239 + ... + 2^120 */ + felem_mul_reduce(ftmp, ftmp4, ftmp); /* 2^239 + ... + 2^0 */ + + for (i = 0; i < 15; i++) + felem_square_reduce(ftmp, ftmp); /* 2^254 + ... + 2^15 */ + felem_mul_reduce(ftmp, ftmp5, ftmp); /* 2^254 + ... + 2^0 */ + + for (i = 0; i < 31; i++) + felem_square_reduce(ftmp, ftmp); /* 2^285 + ... + 2^31 */ + felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^285 + ... + 2^31 + 2^29 + ... + 2^0 */ + + for (i = 0; i < 2; i++) + felem_square_reduce(ftmp, ftmp); /* 2^287 + ... + 2^33 + 2^31 + ... + 2^2 */ + felem_mul_reduce(ftmp, ftmp2, ftmp); /* 2^287 + ... + 2^33 + 2^31 + ... + 2^0 */ + + for (i = 0; i < 94; i++) + felem_square_reduce(ftmp, ftmp); /* 2^381 + ... + 2^127 + 2^125 + ... + 2^94 */ + felem_mul_reduce(ftmp, ftmp6, ftmp); /* 2^381 + ... + 2^127 + 2^125 + ... + 2^94 + 2^29 + ... + 2^0 */ + + for (i = 0; i < 2; i++) + felem_square_reduce(ftmp, ftmp); /* 2^383 + ... + 2^129 + 2^127 + ... + 2^96 + 2^31 + ... + 2^2 */ + felem_mul_reduce(ftmp, in, ftmp); /* 2^383 + ... + 2^129 + 2^127 + ... + 2^96 + 2^31 + ... + 2^2 + 2^0 */ + + memcpy(out, ftmp, sizeof(felem)); +} + +/* + * Zero-check: returns a limb with all bits set if |in| == 0 (mod p) + * and 0 otherwise. We know that field elements are reduced to + * 0 < in < 2p, so we only need to check two cases: + * 0 and 2^384 - 2^128 - 2^96 + 2^32 - 1 + * in[k] < 2^56, k < 6 + * in[6] <= 2^48 + */ +static limb felem_is_zero(const felem in) +{ + limb zero, p384; + + zero = in[0] | in[1] | in[2] | in[3] | in[4] | in[5] | in[6]; + zero = ((int64_t) (zero) - 1) >> 63; + p384 = (in[0] ^ 0x000000ffffffff) | (in[1] ^ 0xffff0000000000) + | (in[2] ^ 0xfffffffffeffff) | (in[3] ^ 0xffffffffffffff) + | (in[4] ^ 0xffffffffffffff) | (in[5] ^ 0xffffffffffffff) + | (in[6] ^ 0xffffffffffff); + p384 = ((int64_t) (p384) - 1) >> 63; + + return (zero | p384); +} + +static int felem_is_zero_int(const void *in) +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} + +/*- + * felem_contract converts |in| to its unique, minimal representation. + * Assume we've removed all redundant bits. + * On entry: + * in[k] < 2^56, k < 6 + * in[6] <= 2^48 + */ +static void felem_contract(felem out, const felem in) +{ + static const int64_t two56 = ((limb) 1) << 56; + + /* + * We know for a fact that 0 <= |in| < 2*p, for p = 2^384 - 2^128 - 2^96 + 2^32 - 1 + * Perform two successive, idempotent subtractions to reduce if |in| >= p. + */ + + int64_t tmp[NLIMBS], cond[5], a; + unsigned int i; + + memcpy(tmp, in, sizeof(felem)); + + /* Case 1: a = 1 iff |in| >= 2^384 */ + a = (in[6] >> 48); + tmp[0] += a; + tmp[0] -= a << 32; + tmp[1] += a << 40; + tmp[2] += a << 16; + tmp[6] &= 0x0000ffffffffffff; + + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be + * non-zero, so we only need one step + */ + + a = tmp[0] >> 63; + tmp[0] += a & two56; + tmp[1] -= a & 1; + + /* Carry 1 -> 2 -> 3 -> 4 -> 5 -> 6 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + tmp[4] += tmp[3] >> 56; + tmp[3] &= 0x00ffffffffffffff; + + tmp[5] += tmp[4] >> 56; + tmp[4] &= 0x00ffffffffffffff; + + tmp[6] += tmp[5] >> 56; /* tmp[6] < 2^48 */ + tmp[5] &= 0x00ffffffffffffff; + + /* + * Case 2: a = all ones if p <= |in| < 2^384, 0 otherwise + */ + + /* 0 iff (2^129..2^383) are all one */ + cond[0] = ((tmp[6] | 0xff000000000000) & tmp[5] & tmp[4] & tmp[3] & (tmp[2] | 0x0000000001ffff)) + 1; + /* 0 iff 2^128 bit is one */ + cond[1] = (tmp[2] | ~0x00000000010000) + 1; + /* 0 iff (2^96..2^127) bits are all one */ + cond[2] = ((tmp[2] | 0xffffffffff0000) & (tmp[1] | 0x0000ffffffffff)) + 1; + /* 0 iff (2^32..2^95) bits are all zero */ + cond[3] = (tmp[1] & ~0xffff0000000000) | (tmp[0] & ~((int64_t) 0x000000ffffffff)); + /* 0 iff (2^0..2^31) bits are all one */ + cond[4] = (tmp[0] | 0xffffff00000000) + 1; + + /* + * In effect, invert our conditions, so that 0 values become all 1's, + * any non-zero value in the low-order 56 bits becomes all 0's + */ + for (i = 0; i < 5; i++) + cond[i] = ((cond[i] & 0x00ffffffffffffff) - 1) >> 63; + + /* + * The condition for determining whether in is greater than our + * prime is given by the following condition. + */ + + /* First subtract 2^384 - 2^129 cheaply */ + a = cond[0] & (cond[1] | (cond[2] & (~cond[3] | cond[4]))); + tmp[6] &= ~a; + tmp[5] &= ~a; + tmp[4] &= ~a; + tmp[3] &= ~a; + tmp[2] &= ~a | 0x0000000001ffff; + + /* + * Subtract 2^128 - 2^96 by + * means of disjoint cases. + */ + + /* subtract 2^128 if that bit is present, and add 2^96 */ + a = cond[0] & cond[1]; + tmp[2] &= ~a | 0xfffffffffeffff; + tmp[1] += a & ((int64_t) 1 << 40); + + /* otherwise, clear bits 2^127 .. 2^96 */ + a = cond[0] & ~cond[1] & (cond[2] & (~cond[3] | cond[4])); + tmp[2] &= ~a | 0xffffffffff0000; + tmp[1] &= ~a | 0x0000ffffffffff; + + /* finally, subtract the last 2^32 - 1 */ + a = cond[0] & (cond[1] | (cond[2] & (~cond[3] | cond[4]))); + tmp[0] += a & (-((int64_t) 1 << 32) + 1); + + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be + * non-zero, so we only need one step + */ + a = tmp[0] >> 63; + tmp[0] += a & two56; + tmp[1] -= a & 1; + + /* Carry 1 -> 2 -> 3 -> 4 -> 5 -> 6 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + tmp[4] += tmp[3] >> 56; + tmp[3] &= 0x00ffffffffffffff; + + tmp[5] += tmp[4] >> 56; + tmp[4] &= 0x00ffffffffffffff; + + tmp[6] += tmp[5] >> 56; + tmp[5] &= 0x00ffffffffffffff; + + memcpy(out, tmp, sizeof(felem)); +} + +/*- + * Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates + */ + +/*- + * point_double calculates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). + */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) +{ + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square_reduce(delta, z_in); /* delta[i] < 2^56 */ + + /* gamma = y^2 */ + felem_square_reduce(gamma, y_in); /* gamma[i] < 2^56 */ + + /* beta = x*gamma */ + felem_mul_reduce(beta, x_in, gamma); /* beta[i] < 2^56 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff64(ftmp, delta); /* ftmp[i] < 2^60 + 2^58 + 2^44 */ + felem_sum64(ftmp2, delta); /* ftmp2[i] < 2^59 */ + felem_scalar64(ftmp2, 3); /* ftmp2[i] < 2^61 */ + felem_mul_reduce(alpha, ftmp, ftmp2); /* alpha[i] < 2^56 */ + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); /* tmp[i] < 2^115 */ + felem_assign(ftmp, beta); /* ftmp[i] < 2^56 */ + felem_scalar64(ftmp, 8); /* ftmp[i] < 2^59 */ + felem_diff_128_64(tmp, ftmp); /* tmp[i] < 2^115 + 2^64 + 2^48 */ + felem_reduce(x_out, tmp); /* x_out[i] < 2^56 */ + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum64(delta, gamma); /* delta[i] < 2^57 */ + felem_assign(ftmp, y_in); /* ftmp[i] < 2^56 */ + felem_sum64(ftmp, z_in); /* ftmp[i] < 2^56 */ + felem_square(tmp, ftmp); /* tmp[i] < 2^115 */ + felem_diff_128_64(tmp, delta); /* tmp[i] < 2^115 + 2^64 + 2^48 */ + felem_reduce(z_out, tmp); /* z_out[i] < 2^56 */ + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar64(beta, 4); /* beta[i] < 2^58 */ + felem_diff64(beta, x_out); /* beta[i] < 2^60 + 2^58 + 2^44 */ + felem_mul(tmp, alpha, beta); /* tmp[i] < 2^119 */ + felem_square(tmp2, gamma); /* tmp2[i] < 2^115 */ + felem_scalar128(tmp2, 8); /* tmp2[i] < 2^118 */ + felem_diff128(tmp, tmp2); /* tmp[i] < 2^127 + 2^119 + 2^111 */ + felem_reduce(y_out, tmp); /* tmp[i] < 2^56 */ +} + +/* copy_conditional copies in to out iff mask is all ones. */ +static void copy_conditional(felem out, const felem in, limb mask) +{ + unsigned int i; + + for (i = 0; i < NLIMBS; i++) + out[i] ^= mask & (in[i] ^ out[i]); +} + +/*- + * point_add calculates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal (while not equal to the point at infinity). See comment below + * on constant-time. + */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, + const felem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + limb points_equal; + + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + felem_square_reduce(ftmp, z1); /* ftmp[i] < 2^56 */ + + if (!mixed) { + /* ftmp2 = z2z2 = z2**2 */ + felem_square_reduce(ftmp2, z2); /* ftmp2[i] < 2^56 */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_mul_reduce(ftmp3, x1, ftmp2); /* ftmp3[i] < 2^56 */ + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); /* ftmp5[i] < 2^56 */ + felem_sum64(ftmp5, z2); /* ftmp5[i] < 2^57 */ + + /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */ + felem_square(tmp, ftmp5); /* tmp[i] < 2^117 */ + felem_diff_128_64(tmp, ftmp); /* tmp[i] < 2^117 + 2^64 + 2^48 */ + felem_diff_128_64(tmp, ftmp2); /* tmp[i] < 2^117 + 2^65 + 2^49 */ + felem_reduce(ftmp5, tmp); /* ftmp5[i] < 2^56 */ + + /* ftmp2 = z2 * z2z2 */ + felem_mul_reduce(ftmp2, ftmp2, z2); /* ftmp2[i] < 2^56 */ + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_mul_reduce(ftmp6, y1, ftmp2); /* ftmp6[i] < 2^56 */ + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); /* ftmp3[i] < 2^56 */ + + /* ftmp5 = 2*z1z2 */ + felem_scalar(ftmp5, z1, 2); /* ftmp5[i] < 2^57 */ + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_assign(ftmp6, y1); /* ftmp6[i] < 2^56 */ + } + /* ftmp3[i] < 2^56, ftmp5[i] < 2^57, ftmp6[i] < 2^56 */ + + /* u2 = x2*z1z1 */ + felem_mul(tmp, x2, ftmp); /* tmp[i] < 2^115 */ + + /* h = ftmp4 = u2 - u1 */ + felem_diff_128_64(tmp, ftmp3); /* tmp[i] < 2^115 + 2^64 + 2^48 */ + felem_reduce(ftmp4, tmp); /* ftmp[4] < 2^56 */ + + x_equal = felem_is_zero(ftmp4); + + /* z_out = ftmp5 * h */ + felem_mul_reduce(z_out, ftmp5, ftmp4); /* z_out[i] < 2^56 */ + + /* ftmp = z1 * z1z1 */ + felem_mul_reduce(ftmp, ftmp, z1); /* ftmp[i] < 2^56 */ + + /* s2 = tmp = y2 * z1**3 */ + felem_mul(tmp, y2, ftmp); /* tmp[i] < 2^115 */ + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_128_64(tmp, ftmp6); /* tmp[i] < 2^115 + 2^64 + 2^48 */ + felem_reduce(ftmp5, tmp); /* ftmp5[i] < 2^56 */ + y_equal = felem_is_zero(ftmp5); + felem_scalar64(ftmp5, 2); /* ftmp5[i] < 2^57 */ + + /* + * The formulae are incorrect if the points are equal, in affine coordinates + * (X_1, Y_1) == (X_2, Y_2), so we check for this and do doubling if this + * happens. + * + * We use bitwise operations to avoid potential side-channels introduced by + * the short-circuiting behaviour of boolean operators. + * + * The special case of either point being the point at infinity (z1 and/or + * z2 are zero), is handled separately later on in this function, so we + * avoid jumping to point_double here in those special cases. + * + * Notice the comment below on the implications of this branching for timing + * leaks and why it is considered practically irrelevant. + */ + points_equal = (x_equal & y_equal & (~z1_is_zero) & (~z2_is_zero)); + + if (points_equal) { + /* + * This is obviously not constant-time but it will almost-never happen + * for ECDH / ECDSA. + */ + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); /* ftmp[i] < 2^56 */ + felem_scalar64(ftmp, 2); /* ftmp[i] < 2^57 */ + felem_square_reduce(ftmp, ftmp); /* ftmp[i] < 2^56 */ + + /* J = ftmp2 = h * I */ + felem_mul_reduce(ftmp2, ftmp4, ftmp); /* ftmp2[i] < 2^56 */ + + /* V = ftmp4 = U1 * I */ + felem_mul_reduce(ftmp4, ftmp3, ftmp); /* ftmp4[i] < 2^56 */ + + /* x_out = r**2 - J - 2V */ + felem_square(tmp, ftmp5); /* tmp[i] < 2^117 */ + felem_diff_128_64(tmp, ftmp2); /* tmp[i] < 2^117 + 2^64 + 2^48 */ + felem_assign(ftmp3, ftmp4); /* ftmp3[i] < 2^56 */ + felem_scalar64(ftmp4, 2); /* ftmp4[i] < 2^57 */ + felem_diff_128_64(tmp, ftmp4); /* tmp[i] < 2^117 + 2^65 + 2^49 */ + felem_reduce(x_out, tmp); /* x_out[i] < 2^56 */ + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff64(ftmp3, x_out); /* ftmp3[i] < 2^60 + 2^56 + 2^44 */ + felem_mul(tmp, ftmp5, ftmp3); /* tmp[i] < 2^116 */ + felem_mul(tmp2, ftmp6, ftmp2); /* tmp2[i] < 2^115 */ + felem_scalar128(tmp2, 2); /* tmp2[i] < 2^116 */ + felem_diff128(tmp, tmp2); /* tmp[i] < 2^127 + 2^116 + 2^111 */ + felem_reduce(y_out, tmp); /* y_out[i] < 2^56 */ + + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} + +/*- + * Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 16 elements: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^95G + * 3 | 0 0 1 1 | (2^95 + 1)G + * 4 | 0 1 0 0 | 2^190G + * 5 | 0 1 0 1 | (2^190 + 1)G + * 6 | 0 1 1 0 | (2^190 + 2^95)G + * 7 | 0 1 1 1 | (2^190 + 2^95 + 1)G + * 8 | 1 0 0 0 | 2^285G + * 9 | 1 0 0 1 | (2^285 + 1)G + * 10 | 1 0 1 0 | (2^285 + 2^95)G + * 11 | 1 0 1 1 | (2^285 + 2^95 + 1)G + * 12 | 1 1 0 0 | (2^285 + 2^190)G + * 13 | 1 1 0 1 | (2^285 + 2^190 + 1)G + * 14 | 1 1 1 0 | (2^285 + 2^190 + 2^95)G + * 15 | 1 1 1 1 | (2^285 + 2^190 + 2^95 + 1)G + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. + */ + +/* gmul is the table of precomputed base points */ +static const felem gmul[16][3] = { +{{0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0}}, +{{0x00545e3872760ab7, 0x00f25dbf55296c3a, 0x00e082542a385502, 0x008ba79b9859f741, + 0x0020ad746e1d3b62, 0x0005378eb1c71ef3, 0x0000aa87ca22be8b}, + {0x00431d7c90ea0e5f, 0x00b1ce1d7e819d7a, 0x0013b5f0b8c00a60, 0x00289a147ce9da31, + 0x0092dc29f8f41dbd, 0x002c6f5d9e98bf92, 0x00003617de4a9626}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00024711cc902a90, 0x00acb2e579ab4fe1, 0x00af818a4b4d57b1, 0x00a17c7bec49c3de, + 0x004280482d726a8b, 0x00128dd0f0a90f3b, 0x00004387c1c3fa3c}, + {0x002ce76543cf5c3a, 0x00de6cee5ef58f0a, 0x00403e42fa561ca6, 0x00bc54d6f9cb9731, + 0x007155f925fb4ff1, 0x004a9ce731b7b9bc, 0x00002609076bd7b2}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00e74c9182f0251d, 0x0039bf54bb111974, 0x00b9d2f2eec511d2, 0x0036b1594eb3a6a4, + 0x00ac3bb82d9d564b, 0x00f9313f4615a100, 0x00006716a9a91b10}, + {0x0046698116e2f15c, 0x00f34347067d3d33, 0x008de4ccfdebd002, 0x00e838c6b8e8c97b, + 0x006faf0798def346, 0x007349794a57563c, 0x00002629e7e6ad84}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x0075300e34fd163b, 0x0092e9db4e8d0ad3, 0x00254be9f625f760, 0x00512c518c72ae68, + 0x009bfcf162bede5a, 0x00bf9341566ce311, 0x0000cd6175bd41cf}, + {0x007dfe52af4ac70f, 0x0002159d2d5c4880, 0x00b504d16f0af8d0, 0x0014585e11f5e64c, + 0x0089c6388e030967, 0x00ffb270cbfa5f71, 0x00009a15d92c3947}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x0033fc1278dc4fe5, 0x00d53088c2caa043, 0x0085558827e2db66, 0x00c192bef387b736, + 0x00df6405a2225f2c, 0x0075205aa90fd91a, 0x0000137e3f12349d}, + {0x00ce5b115efcb07e, 0x00abc3308410deeb, 0x005dc6fc1de39904, 0x00907c1c496f36b4, + 0x0008e6ad3926cbe1, 0x00110747b787928c, 0x0000021b9162eb7e}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x008180042cfa26e1, 0x007b826a96254967, 0x0082473694d6b194, 0x007bd6880a45b589, + 0x00c0a5097072d1a3, 0x0019186555e18b4e, 0x000020278190e5ca}, + {0x00b4bef17de61ac0, 0x009535e3c38ed348, 0x002d4aa8e468ceab, 0x00ef40b431036ad3, + 0x00defd52f4542857, 0x0086edbf98234266, 0x00002025b3a7814d}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00b238aa97b886be, 0x00ef3192d6dd3a32, 0x0079f9e01fd62df8, 0x00742e890daba6c5, + 0x008e5289144408ce, 0x0073bbcc8e0171a5, 0x0000c4fd329d3b52}, + {0x00c6f64a15ee23e7, 0x00dcfb7b171cad8b, 0x00039f6cbd805867, 0x00de024e428d4562, + 0x00be6a594d7c64c5, 0x0078467b70dbcd64, 0x0000251f2ed7079b}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x000e5cc25fc4b872, 0x005ebf10d31ef4e1, 0x0061e0ebd11e8256, 0x0076e026096f5a27, + 0x0013e6fc44662e9a, 0x0042b00289d3597e, 0x000024f089170d88}, + {0x001604d7e0effbe6, 0x0048d77cba64ec2c, 0x008166b16da19e36, 0x006b0d1a0f28c088, + 0x000259fcd47754fd, 0x00cc643e4d725f9a, 0x00007b10f3c79c14}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00430155e3b908af, 0x00b801e4fec25226, 0x00b0d4bcfe806d26, 0x009fc4014eb13d37, + 0x0066c94e44ec07e8, 0x00d16adc03874ba2, 0x000030c917a0d2a7}, + {0x00edac9e21eb891c, 0x00ef0fb768102eff, 0x00c088cef272a5f3, 0x00cbf782134e2964, + 0x0001044a7ba9a0e3, 0x00e363f5b194cf3c, 0x00009ce85249e372}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x001dd492dda5a7eb, 0x008fd577be539fd1, 0x002ff4b25a5fc3f1, 0x0074a8a1b64df72f, + 0x002ba3d8c204a76c, 0x009d5cff95c8235a, 0x0000e014b9406e0f}, + {0x008c2e4dbfc98aba, 0x00f30bb89f1a1436, 0x00b46f7aea3e259c, 0x009224454ac02f54, + 0x00906401f5645fa2, 0x003a1d1940eabc77, 0x00007c9351d680e6}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x005a35d872ef967c, 0x0049f1b7884e1987, 0x0059d46d7e31f552, 0x00ceb4869d2d0fb6, + 0x00e8e89eee56802a, 0x0049d806a774aaf2, 0x0000147e2af0ae24}, + {0x005fd1bd852c6e5e, 0x00b674b7b3de6885, 0x003b9ea5eb9b6c08, 0x005c9f03babf3ef7, + 0x00605337fecab3c7, 0x009a3f85b11bbcc8, 0x0000455470f330ec}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x002197ff4d55498d, 0x00383e8916c2d8af, 0x00eb203f34d1c6d2, 0x0080367cbd11b542, + 0x00769b3be864e4f5, 0x0081a8458521c7bb, 0x0000c531b34d3539}, + {0x00e2a3d775fa2e13, 0x00534fc379573844, 0x00ff237d2a8db54a, 0x00d301b2335a8882, + 0x000f75ea96103a80, 0x0018fecb3cdd96fa, 0x0000304bf61e94eb}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00b2afc332a73dbd, 0x0029a0d5bb007bc5, 0x002d628eb210f577, 0x009f59a36dd05f50, + 0x006d339de4eca613, 0x00c75a71addc86bc, 0x000060384c5ea93c}, + {0x00aa9641c32a30b4, 0x00cc73ae8cce565d, 0x00ec911a4df07f61, 0x00aa4b762ea4b264, + 0x0096d395bb393629, 0x004efacfb7632fe0, 0x00006f252f46fa3f}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00567eec597c7af6, 0x0059ba6795204413, 0x00816d4e6f01196f, 0x004ae6b3eb57951d, + 0x00420f5abdda2108, 0x003401d1f57ca9d9, 0x0000cf5837b0b67a}, + {0x00eaa64b8aeeabf9, 0x00246ddf16bcb4de, 0x000e7e3c3aecd751, 0x0008449f04fed72e, + 0x00307b67ccf09183, 0x0017108c3556b7b1, 0x0000229b2483b3bf}, + {1, 0, 0, 0, 0, 0, 0}}, +{{0x00e7c491a7bb78a1, 0x00eafddd1d3049ab, 0x00352c05e2bc7c98, 0x003d6880c165fa5c, + 0x00b6ac61cc11c97d, 0x00beeb54fcf90ce5, 0x0000dc1f0b455edc}, + {0x002db2e7aee34d60, 0x0073b5f415a2d8c0, 0x00dd84e4193e9a0c, 0x00d02d873467c572, + 0x0018baaeda60aee5, 0x0013fb11d697c61e, 0x000083aafcc3a973}, + {1, 0, 0, 0, 0, 0, 0}} +}; + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + * + * pre_comp below is of the size provided in |size|. + */ +static void select_point(const limb idx, unsigned int size, + const felem pre_comp[][3], felem out[3]) +{ + unsigned int i, j; + limb *outlimbs = &out[0][0]; + + memset(out, 0, sizeof(*out) * 3); + + for (i = 0; i < size; i++) { + const limb *inlimbs = &pre_comp[i][0][0]; + limb mask = i ^ idx; + + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) +{ + if (i < 0 || i >= 384) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], + const unsigned int num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], + const felem g_pre_comp[16][3]) +{ + int i, skip; + unsigned int num, gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + limb bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, sizeof(nq)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (last quarter of rounds) and additions of other + * points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 380 : 98); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 98)) { + bits = get_bit(g_scalar, i + 285) << 3; + if (i < 95) { + bits |= get_bit(g_scalar, i + 190) << 2; + bits |= get_bit(g_scalar, i + 95) << 1; + bits |= get_bit(g_scalar, i); + } + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp, tmp); + if (!skip) { + /* The 1 argument below is for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, + tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ossl_ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* + * select the point to add or subtract, in constant time + */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_conditional(tmp[1], tmp[3], (-(limb) sign)); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], mixed, + tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} + +/* Precomputation for the group generator. */ +struct nistp384_pre_comp_st { + felem g_pre_comp[16][3]; + CRYPTO_REF_COUNT refcnt; + CRYPTO_RWLOCK *refcnt_lock; +}; + +const EC_METHOD *ossl_ec_GFp_nistp384_method(void) +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ossl_ec_GFp_nistp384_group_init, + ossl_ec_GFp_simple_group_finish, + ossl_ec_GFp_simple_group_clear_finish, + ossl_ec_GFp_nist_group_copy, + ossl_ec_GFp_nistp384_group_set_curve, + ossl_ec_GFp_simple_group_get_curve, + ossl_ec_GFp_simple_group_get_degree, + ossl_ec_group_simple_order_bits, + ossl_ec_GFp_simple_group_check_discriminant, + ossl_ec_GFp_simple_point_init, + ossl_ec_GFp_simple_point_finish, + ossl_ec_GFp_simple_point_clear_finish, + ossl_ec_GFp_simple_point_copy, + ossl_ec_GFp_simple_point_set_to_infinity, + ossl_ec_GFp_simple_point_set_affine_coordinates, + ossl_ec_GFp_nistp384_point_get_affine_coordinates, + 0, /* point_set_compressed_coordinates */ + 0, /* point2oct */ + 0, /* oct2point */ + ossl_ec_GFp_simple_add, + ossl_ec_GFp_simple_dbl, + ossl_ec_GFp_simple_invert, + ossl_ec_GFp_simple_is_at_infinity, + ossl_ec_GFp_simple_is_on_curve, + ossl_ec_GFp_simple_cmp, + ossl_ec_GFp_simple_make_affine, + ossl_ec_GFp_simple_points_make_affine, + ossl_ec_GFp_nistp384_points_mul, + ossl_ec_GFp_nistp384_precompute_mult, + ossl_ec_GFp_nistp384_have_precompute_mult, + ossl_ec_GFp_nist_field_mul, + ossl_ec_GFp_nist_field_sqr, + 0, /* field_div */ + ossl_ec_GFp_simple_field_inv, + 0, /* field_encode */ + 0, /* field_decode */ + 0, /* field_set_to_one */ + ossl_ec_key_simple_priv2oct, + ossl_ec_key_simple_oct2priv, + 0, /* set private */ + ossl_ec_key_simple_generate_key, + ossl_ec_key_simple_check_key, + ossl_ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ossl_ecdh_simple_compute_key, + ossl_ecdsa_simple_sign_setup, + ossl_ecdsa_simple_sign_sig, + ossl_ecdsa_simple_verify_sig, + 0, /* field_inverse_mod_ord */ + 0, /* blind_coordinates */ + 0, /* ladder_pre */ + 0, /* ladder_step */ + 0 /* ladder_post */ + }; + + return &ret; +} + +/******************************************************************************/ +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP384_PRE_COMP *nistp384_pre_comp_new(void) +{ + NISTP384_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (ret == NULL || (ret->refcnt_lock = CRYPTO_THREAD_lock_new()) == NULL) { + OPENSSL_free(ret); + return NULL; + } + + ret->refcnt = 1; + return ret; +} + +NISTP384_PRE_COMP *ossl_ec_nistp384_pre_comp_dup(NISTP384_PRE_COMP *p) +{ + int i; + + if (p != NULL) + CRYPTO_UP_REF(&p->refcnt, &i, p->refcnt_lock); + return p; +} + +void ossl_ec_nistp384_pre_comp_free(NISTP384_PRE_COMP *p) +{ + int i; + + if (p == NULL) + return; + + CRYPTO_DOWN_REF(&p->refcnt, &i, p->refcnt_lock); + REF_PRINT_COUNT("ossl_ec_nistp384", p); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + CRYPTO_THREAD_lock_free(p->refcnt_lock); + OPENSSL_free(p); +} + +/******************************************************************************/ +/* + * OPENSSL EC_METHOD FUNCTIONS + */ + +int ossl_ec_GFp_nistp384_group_init(EC_GROUP *group) +{ + int ret; + + ret = ossl_ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} + +int ossl_ec_GFp_nistp384_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BIGNUM *curve_p, *curve_a, *curve_b; +#ifndef FIPS_MODULE + BN_CTX *new_ctx = NULL; + + if (ctx == NULL) + ctx = new_ctx = BN_CTX_new(); +#endif + if (ctx == NULL) + return 0; + + BN_CTX_start(ctx); + curve_p = BN_CTX_get(ctx); + curve_a = BN_CTX_get(ctx); + curve_b = BN_CTX_get(ctx); + if (curve_b == NULL) + goto err; + BN_bin2bn(nistp384_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp384_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp384_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ERR_raise(ERR_LIB_EC, EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_384; + ret = ossl_ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); +#ifndef FIPS_MODULE + BN_CTX_free(new_ctx); +#endif + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ +int ossl_ec_GFp_nistp384_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ERR_raise(ERR_LIB_EC, EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || + (!BN_to_felem(z1, point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +/* points below is of size |num|, and tmp_felems is of size |num+1/ */ +static void make_points_affine(size_t num, felem points[][3], + felem tmp_felems[]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ossl_ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *))felem_one, + felem_is_zero_int, + (void (*)(void *, const void *)) + felem_assign, + (void (*)(void *, const void *)) + felem_square_reduce, + (void (*)(void *, const void *, const void*)) + felem_mul_reduce, + (void (*)(void *, const void *)) + felem_inv, + (void (*)(void *, const void *)) + felem_contract); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ +int ossl_ec_GFp_nistp384_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 ret = 0; + int j; + int mixed = 0; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + unsigned int i; + int num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP384_PRE_COMP *pre = NULL; + felem(*g_pre_comp)[3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + z = BN_CTX_get(ctx); + tmp_scalar = BN_CTX_get(ctx); + if (tmp_scalar == NULL) + goto err; + + if (scalar != NULL) { + pre = group->pre_comp.nistp384; + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = &pre->g_pre_comp[0]; + else + /* try to use the standard precomputation */ + g_pre_comp = (felem(*)[3]) gmul; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[1][0]) || + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + if (!ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(group, + generator, + x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points++; + } + + if (num_points > 0) { + if (num_points >= 2) { + /* + * unless we precompute multiples for just one point, converting + * those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); + pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); + if (mixed) + tmp_felems = + OPENSSL_malloc(sizeof(*tmp_felems) * (num_points * 17 + 1)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_felems == NULL))) + goto err; + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + for (i = 0; i < num_points; ++i) { + if (i == num) { + /* + * we didn't have a valid precomputation, so we pick the + * generator + */ + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else { + /* the i^th point */ + p = points[i]; + p_scalar = scalars[i]; + } + if (p_scalar != NULL && p != NULL) { + /* reduce scalar to 0 <= scalar < 2^384 */ + if ((BN_num_bits(p_scalar) > 384) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2lebinpad(tmp_scalar, + secrets[i], sizeof(secrets[i])); + } else { + num_bytes = BN_bn2lebinpad(p_scalar, + secrets[i], sizeof(secrets[i])); + } + if (num_bytes < 0) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + /* precompute multiples */ + if ((!BN_to_felem(x_out, p->X)) || + (!BN_to_felem(y_out, p->Y)) || + (!BN_to_felem(z_out, p->Z))) + goto err; + memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); + memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); + memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], 0, + pre_comp[i][j - 1][0], pre_comp[i][j - 1][1], pre_comp[i][j - 1][2]); + } else { + point_double(pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j / 2][0], pre_comp[i][j / 2][1], pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if (scalar != NULL && have_pre_comp) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^384 */ + if ((BN_num_bits(scalar) > 384) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2lebinpad(tmp_scalar, g_secret, sizeof(g_secret)); + } else { + num_bytes = BN_bn2lebinpad(scalar, g_secret, sizeof(g_secret)); + } + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3])pre_comp, + (const felem(*)[3])g_pre_comp); + } else { + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); + } + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) { + ERR_raise(ERR_LIB_EC, ERR_R_BN_LIB); + goto err; + } + ret = ossl_ec_GFp_simple_set_Jprojective_coordinates_GFp(group, r, x, y, z, + ctx); + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + OPENSSL_free(secrets); + OPENSSL_free(pre_comp); + OPENSSL_free(tmp_felems); + return ret; +} + +int ossl_ec_GFp_nistp384_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +{ + int ret = 0; + NISTP384_PRE_COMP *pre = NULL; + int i, j; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[16]; +#ifndef FIPS_MODULE + BN_CTX *new_ctx = NULL; +#endif + + /* throw away old precomputation */ + EC_pre_comp_free(group); + +#ifndef FIPS_MODULE + if (ctx == NULL) + ctx = new_ctx = BN_CTX_new(); +#endif + if (ctx == NULL) + return 0; + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp384_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp384_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp384_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + goto done; + } + if ((!BN_to_felem(pre->g_pre_comp[1][0], group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[1][1], group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], group->generator->Z))) + goto err; + /* compute 2^95*G, 2^190*G, 2^285*G */ + for (i = 1; i <= 4; i <<= 1) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[i][0], pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 94; ++j) { + point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], + pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2]); + } + } + /* g_pre_comp[0] is the point at infinity */ + memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); + /* the remaining multiples */ + /* 2^95*G + 2^190*G */ + point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], pre->g_pre_comp[6][2], + pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], 0, + pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]); + /* 2^95*G + 2^285*G */ + point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], pre->g_pre_comp[10][2], + pre->g_pre_comp[8][0], pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 0, + pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]); + /* 2^190*G + 2^285*G */ + point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + pre->g_pre_comp[8][0], pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], 0, + pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], pre->g_pre_comp[4][2]); + /* 2^95*G + 2^190*G + 2^285*G */ + point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], pre->g_pre_comp[14][2], + pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], 0, + pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) { + /* odd multiples: add G */ + point_add(pre->g_pre_comp[2 * i + 1][0], pre->g_pre_comp[2 * i + 1][1], pre->g_pre_comp[2 * i + 1][2], + pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], 0, + pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], pre->g_pre_comp[1][2]); + } + make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); + + done: + SETPRECOMP(group, nistp384, pre); + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); +#ifndef FIPS_MODULE + BN_CTX_free(new_ctx); +#endif + ossl_ec_nistp384_pre_comp_free(pre); + return ret; +} + +int ossl_ec_GFp_nistp384_have_precompute_mult(const EC_GROUP *group) +{ + return HAVEPRECOMP(group, nistp384); +}
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