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.
This commit is contained in:
Bodo Möller
parent
7e9cfcd0dc
commit
9c37519b55
30
CHANGES
30
CHANGES
@ -4,6 +4,24 @@
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Changes between 1.0.0f and 1.0.1 [xx XXX xxxx]
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*) Add optional 64-bit optimized implementations of elliptic curves NIST-P224,
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NIST-P256, NIST-P521, with constant-time single point multiplication on
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typical inputs. Compiler support for the nonstandard type __uint128_t is
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required to use this. Code made available under Apache License version 2.0.
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To include this in your build of OpenSSL, use -DEC_NISTP_64_GCC_128 on
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the Configure (or config) command line, and run "make depend" (or "make
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update"). This enables the following EC_METHODs:
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EC_GFp_nistp224_method()
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EC_GFp_nistp256_method()
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EC_GFp_nistp521_method()
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EC_GROUP_new_by_curve_name() will automatically use these (while
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EC_GROUP_new_curve_GFp() currently prefers the more flexible
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implementations).
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[Emilia Käsper, Adam Langley, Bodo Moeller (Google)]
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*) Use type ossl_ssize_t instad of ssize_t which isn't available on
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all platforms. Move ssize_t definition from e_os.h to the public
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header file e_os2.h as it now appears in public header file cms.h
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@ -190,18 +208,6 @@
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*) Add functions to copy EVP_PKEY_METHOD and retrieve flags and id.
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[Steve Henson]
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*) Add EC_GFp_nistp224_method(), a 64-bit optimized implementation for
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elliptic curve NIST-P224 with constant-time single point multiplication on
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typical inputs. EC_GROUP_new_by_curve_name() will automatically use this
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(while EC_GROUP_new_curve_GFp() currently won't and prefers the more
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flexible implementations).
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The implementation requires support for the nonstandard type __uint128_t,
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and so is disabled by default. To include this in your build of OpenSSL,
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use -DEC_NISTP224_64_GCC_128 on the Configure (or config) command line,
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and run "make depend" (or "make update").
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[Emilia Käsper <emilia.kasper@esat.kuleuven.be> (Google)]
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*) Permit abbreviated handshakes when renegotiating using the function
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SSL_renegotiate_abbreviated().
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[Robin Seggelmann <seggelmann@fh-muenster.de>]
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@ -20,12 +20,14 @@ LIB=$(TOP)/libcrypto.a
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LIBSRC= ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c\
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ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c\
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ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c \
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ecp_nistp224.c ecp_oct.c ec2_oct.c ec_oct.c
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ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c \
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ecp_oct.c ec2_oct.c ec_oct.c
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LIBOBJ= ec_lib.o ecp_smpl.o ecp_mont.o ecp_nist.o ec_cvt.o ec_mult.o\
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ec_err.o ec_curve.o ec_check.o ec_print.o ec_asn1.o ec_key.o\
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ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o \
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ecp_nistp224.o ecp_oct.o ec2_oct.o ec_oct.o
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ecp_nistp224.o ecp_nistp256.o ecp_nistp521.o ecp_nistputil.o \
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ecp_oct.o ec2_oct.o ec_oct.o
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SRC= $(LIBSRC)
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@ -240,6 +242,9 @@ ecp_nist.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h
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ecp_nist.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h
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ecp_nist.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_nist.c
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ecp_nistp224.o: ../../include/openssl/opensslconf.h ecp_nistp224.c
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ecp_nistp256.o: ../../include/openssl/opensslconf.h ecp_nistp256.c
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ecp_nistp521.o: ../../include/openssl/opensslconf.h ecp_nistp521.c
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ecp_nistputil.o: ../../include/openssl/opensslconf.h ecp_nistputil.c
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ecp_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h
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ecp_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h
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ecp_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h
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@ -151,11 +151,21 @@ const EC_METHOD *EC_GFp_mont_method(void);
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*/
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const EC_METHOD *EC_GFp_nist_method(void);
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#ifndef OPENSSL_NO_EC_NISTP224_64_GCC_128
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#ifdef EC_NISTP_64_GCC_128
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/** Returns 64-bit optimized methods for nistp224
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* \return EC_METHOD object
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*/
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const EC_METHOD *EC_GFp_nistp224_method(void);
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/** Returns 64-bit optimized methods for nistp256
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* \return EC_METHOD object
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*/
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const EC_METHOD *EC_GFp_nistp256_method(void);
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/** Returns 64-bit optimized methods for nistp521
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* \return EC_METHOD object
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*/
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const EC_METHOD *EC_GFp_nistp521_method(void);
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#endif
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#ifndef OPENSSL_NO_EC2M
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@ -1003,6 +1013,12 @@ void ERR_load_EC_strings(void);
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#define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225
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#define EC_F_EC_GFP_NISTP224_POINTS_MUL 228
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#define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226
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#define EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE 230
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#define EC_F_EC_GFP_NISTP256_POINTS_MUL 231
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#define EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES 232
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#define EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE 233
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#define EC_F_EC_GFP_NISTP521_POINTS_MUL 234
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#define EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES 235
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#define EC_F_EC_GFP_NIST_FIELD_MUL 200
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#define EC_F_EC_GFP_NIST_FIELD_SQR 201
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#define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202
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@ -1077,6 +1093,8 @@ void ERR_load_EC_strings(void);
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#define EC_F_I2D_ECPRIVATEKEY 192
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#define EC_F_I2O_ECPUBLICKEY 151
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#define EC_F_NISTP224_PRE_COMP_NEW 227
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#define EC_F_NISTP256_PRE_COMP_NEW 236
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#define EC_F_NISTP521_PRE_COMP_NEW 237
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#define EC_F_O2I_ECPUBLICKEY 152
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#define EC_F_OLD_EC_PRIV_DECODE 222
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#define EC_F_PKEY_EC_CTRL 197
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@ -1841,16 +1841,19 @@ static const ec_list_element curve_list[] = {
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/* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */
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{ NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" },
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{ NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" },
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#ifdef EC_NISTP224_64_GCC_128
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{ NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field,\n"
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"\t\t64-bit optimized implementation." },
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#ifdef EC_NISTP_64_GCC_128
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{ NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" },
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#else
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{ NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" },
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#endif
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{ NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" },
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/* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */
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{ NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" },
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#ifdef EC_NISTP_64_GCC_128
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{ NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" },
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#else
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{ NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" },
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#endif
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/* X9.62 curves */
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{ NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" },
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{ NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" },
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@ -1858,7 +1861,11 @@ static const ec_list_element curve_list[] = {
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{ NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" },
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{ NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" },
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{ NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" },
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#ifdef EC_NISTP_64_GCC_128
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{ NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" },
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#else
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{ NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" },
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#endif
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#ifndef OPENSSL_NO_EC2M
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/* characteristic two field curves */
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/* NIST/SECG curves */
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@ -1,6 +1,6 @@
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/* crypto/ec/ec_err.c */
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/* ====================================================================
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* Copyright (c) 1999-2010 The OpenSSL Project. All rights reserved.
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* Copyright (c) 1999-2011 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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@ -116,6 +116,12 @@ static ERR_STRING_DATA EC_str_functs[]=
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{ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE), "ec_GFp_nistp224_group_set_curve"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL), "ec_GFp_nistp224_points_mul"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp224_point_get_affine_coordinates"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE), "ec_GFp_nistp256_group_set_curve"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINTS_MUL), "ec_GFp_nistp256_points_mul"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp256_point_get_affine_coordinates"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE), "ec_GFp_nistp521_group_set_curve"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINTS_MUL), "ec_GFp_nistp521_points_mul"},
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{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp521_point_get_affine_coordinates"},
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{ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"},
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{ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"},
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{ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE), "ec_GFp_nist_group_set_curve"},
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@ -190,6 +196,8 @@ static ERR_STRING_DATA EC_str_functs[]=
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{ERR_FUNC(EC_F_I2D_ECPRIVATEKEY), "i2d_ECPrivateKey"},
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{ERR_FUNC(EC_F_I2O_ECPUBLICKEY), "i2o_ECPublicKey"},
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{ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "NISTP224_PRE_COMP_NEW"},
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{ERR_FUNC(EC_F_NISTP256_PRE_COMP_NEW), "NISTP256_PRE_COMP_NEW"},
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{ERR_FUNC(EC_F_NISTP521_PRE_COMP_NEW), "NISTP521_PRE_COMP_NEW"},
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{ERR_FUNC(EC_F_O2I_ECPUBLICKEY), "o2i_ECPublicKey"},
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{ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE), "OLD_EC_PRIV_DECODE"},
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{ERR_FUNC(EC_F_PKEY_EC_CTRL), "PKEY_EC_CTRL"},
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@ -398,15 +398,49 @@ int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
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#ifdef EC_NISTP224_64_GCC_128
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#ifdef EC_NISTP_64_GCC_128
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/* method functions in ec2_mult.c */
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int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
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int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
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/* method functions in ecp_nistp224.c */
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int ec_GFp_nistp224_group_init(EC_GROUP *group);
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int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
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const BIGNUM *a, const BIGNUM *n, BN_CTX *);
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int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
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const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
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int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
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int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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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 *);
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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);
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int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
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/* method functions in ecp_nistp256.c */
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int ec_GFp_nistp256_group_init(EC_GROUP *group);
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int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
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int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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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 *);
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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);
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int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group);
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/* method functions in ecp_nistp521.c */
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int ec_GFp_nistp521_group_init(EC_GROUP *group);
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int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *);
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int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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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 *);
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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);
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int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group);
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/* utility functions in ecp_nistputil.c */
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void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
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size_t felem_size, void *tmp_felems,
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void (*felem_one)(void *out),
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int (*felem_is_zero)(const void *in),
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void (*felem_assign)(void *out, const void *in),
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void (*felem_square)(void *out, const void *in),
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void (*felem_mul)(void *out, const void *in1, const void *in2),
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void (*felem_inv)(void *out, const void *in),
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void (*felem_contract)(void *out, const void *in));
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void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in);
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#endif
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File diff suppressed because it is too large
Load Diff
2158
crypto/ec/ecp_nistp256.c
Normal file
2158
crypto/ec/ecp_nistp256.c
Normal file
File diff suppressed because it is too large
Load Diff
2017
crypto/ec/ecp_nistp521.c
Normal file
2017
crypto/ec/ecp_nistp521.c
Normal file
File diff suppressed because it is too large
Load Diff
196
crypto/ec/ecp_nistputil.c
Normal file
196
crypto/ec/ecp_nistputil.c
Normal file
@ -0,0 +1,196 @@
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/* crypto/ec/ecp_nistputil.c */
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/*
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* Written by Bodo Moeller for the OpenSSL project.
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*/
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/* Copyright 2011 Google Inc.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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*
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#ifdef EC_NISTP_64_GCC_128
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/*
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* Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c.
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*/
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#include <stddef.h>
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#include "ec_lcl.h"
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|
||||
/* Convert an array of points into affine coordinates.
|
||||
* (If the point at infinity is found (Z = 0), it remains unchanged.)
|
||||
* This function is essentially an equivalent to EC_POINTs_make_affine(), but
|
||||
* works with the internal representation of points as used by ecp_nistp###.c
|
||||
* rather than with (BIGNUM-based) EC_POINT data structures.
|
||||
*
|
||||
* point_array is the input/output buffer ('num' points in projective form,
|
||||
* i.e. three coordinates each), based on an internal representation of
|
||||
* field elements of size 'felem_size'.
|
||||
*
|
||||
* tmp_felems needs to point to a temporary array of 'num'+1 field elements
|
||||
* for storage of intermediate values.
|
||||
*/
|
||||
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))
|
||||
{
|
||||
int i = 0;
|
||||
|
||||
#define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size])
|
||||
#define X(I) (&((char *)point_array)[3*(I) * felem_size])
|
||||
#define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size])
|
||||
#define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size])
|
||||
|
||||
if (!felem_is_zero(Z(0)))
|
||||
felem_assign(tmp_felem(0), Z(0));
|
||||
else
|
||||
felem_one(tmp_felem(0));
|
||||
for (i = 1; i < (int)num; i++)
|
||||
{
|
||||
if (!felem_is_zero(Z(i)))
|
||||
felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i));
|
||||
else
|
||||
felem_assign(tmp_felem(i), tmp_felem(i-1));
|
||||
}
|
||||
/* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors:
|
||||
* if Z(i) = 0, we essentially pretend that Z(i) = 1 */
|
||||
|
||||
felem_inv(tmp_felem(num-1), tmp_felem(num-1));
|
||||
for (i = num - 1; i >= 0; i--)
|
||||
{
|
||||
if (i > 0)
|
||||
/* tmp_felem(i-1) is the product of Z(0) .. Z(i-1),
|
||||
* tmp_felem(i) is the inverse of the product of Z(0) .. Z(i)
|
||||
*/
|
||||
felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */
|
||||
else
|
||||
felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */
|
||||
|
||||
if (!felem_is_zero(Z(i)))
|
||||
{
|
||||
if (i > 0)
|
||||
/* For next iteration, replace tmp_felem(i-1) by its inverse */
|
||||
felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i));
|
||||
|
||||
/* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */
|
||||
felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */
|
||||
felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */
|
||||
felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */
|
||||
felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */
|
||||
felem_contract(X(i), X(i));
|
||||
felem_contract(Y(i), Y(i));
|
||||
felem_one(Z(i));
|
||||
}
|
||||
else
|
||||
{
|
||||
if (i > 0)
|
||||
/* For next iteration, replace tmp_felem(i-1) by its inverse */
|
||||
felem_assign(tmp_felem(i-1), tmp_felem(i));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/*
|
||||
* This function looks at 5+1 scalar bits (5 current, 1 adjacent less
|
||||
* significant bit), and recodes them into a signed digit for use in fast point
|
||||
* multiplication: the use of signed rather than unsigned digits means that
|
||||
* fewer points need to be precomputed, given that point inversion is easy
|
||||
* (a precomputed point dP makes -dP available as well).
|
||||
*
|
||||
* BACKGROUND:
|
||||
*
|
||||
* Signed digits for multiplication were introduced by Booth ("A signed binary
|
||||
* multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV,
|
||||
* pt. 2 (1951), pp. 236-240), in that case for multiplication of integers.
|
||||
* Booth's original encoding did not generally improve the density of nonzero
|
||||
* digits over the binary representation, and was merely meant to simplify the
|
||||
* handling of signed factors given in two's complement; but it has since been
|
||||
* shown to be the basis of various signed-digit representations that do have
|
||||
* further advantages, including the wNAF, using the following general approach:
|
||||
*
|
||||
* (1) Given a binary representation
|
||||
*
|
||||
* b_k ... b_2 b_1 b_0,
|
||||
*
|
||||
* of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1
|
||||
* by using bit-wise subtraction as follows:
|
||||
*
|
||||
* b_k b_(k-1) ... b_2 b_1 b_0
|
||||
* - b_k ... b_3 b_2 b_1 b_0
|
||||
* -------------------------------------
|
||||
* s_k b_(k-1) ... s_3 s_2 s_1 s_0
|
||||
*
|
||||
* A left-shift followed by subtraction of the original value yields a new
|
||||
* representation of the same value, using signed bits s_i = b_(i+1) - b_i.
|
||||
* This representation from Booth's paper has since appeared in the
|
||||
* literature under a variety of different names including "reversed binary
|
||||
* form", "alternating greedy expansion", "mutual opposite form", and
|
||||
* "sign-alternating {+-1}-representation".
|
||||
*
|
||||
* An interesting property is that among the nonzero bits, values 1 and -1
|
||||
* strictly alternate.
|
||||
*
|
||||
* (2) Various window schemes can be applied to the Booth representation of
|
||||
* integers: for example, right-to-left sliding windows yield the wNAF
|
||||
* (a signed-digit encoding independently discovered by various researchers
|
||||
* in the 1990s), and left-to-right sliding windows yield a left-to-right
|
||||
* equivalent of the wNAF (independently discovered by various researchers
|
||||
* around 2004).
|
||||
*
|
||||
* To prevent leaking information through side channels in point multiplication,
|
||||
* we need to recode the given integer into a regular pattern: sliding windows
|
||||
* as in wNAFs won't do, we need their fixed-window equivalent -- which is a few
|
||||
* decades older: we'll be using the so-called "modified Booth encoding" due to
|
||||
* MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49
|
||||
* (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five
|
||||
* signed bits into a signed digit:
|
||||
*
|
||||
* s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j)
|
||||
*
|
||||
* The sign-alternating property implies that the resulting digit values are
|
||||
* integers from -16 to 16.
|
||||
*
|
||||
* Of course, we don't actually need to compute the signed digits s_i as an
|
||||
* intermediate step (that's just a nice way to see how this scheme relates
|
||||
* to the wNAF): a direct computation obtains the recoded digit from the
|
||||
* six bits b_(4j + 4) ... b_(4j - 1).
|
||||
*
|
||||
* This function takes those five bits as an integer (0 .. 63), writing the
|
||||
* recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute
|
||||
* value, in the range 0 .. 8). Note that this integer essentially provides the
|
||||
* input bits "shifted to the left" by one position: for example, the input to
|
||||
* compute the least significant recoded digit, given that there's no bit b_-1,
|
||||
* has to be b_4 b_3 b_2 b_1 b_0 0.
|
||||
*
|
||||
*/
|
||||
void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in)
|
||||
{
|
||||
unsigned char s, d;
|
||||
|
||||
s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */
|
||||
d = (1 << 6) - in - 1;
|
||||
d = (d & s) | (in & ~s);
|
||||
d = (d >> 1) + (d & 1);
|
||||
|
||||
*sign = s & 1;
|
||||
*digit = d;
|
||||
}
|
||||
#else
|
||||
static void *dummy=&dummy;
|
||||
#endif
|
||||
@ -234,7 +234,7 @@ static void group_order_tests(EC_GROUP *group)
|
||||
BN_CTX_free(ctx);
|
||||
}
|
||||
|
||||
static void prime_field_tests()
|
||||
static void prime_field_tests(void)
|
||||
{
|
||||
BN_CTX *ctx = NULL;
|
||||
BIGNUM *p, *a, *b;
|
||||
@ -778,8 +778,8 @@ static void prime_field_tests()
|
||||
|
||||
#ifndef OPENSSL_NO_EC2M
|
||||
|
||||
static void char2_field_tests()
|
||||
{
|
||||
static void char2_field_tests(void)
|
||||
{
|
||||
BN_CTX *ctx = NULL;
|
||||
BIGNUM *p, *a, *b;
|
||||
EC_GROUP *group;
|
||||
@ -1262,15 +1262,76 @@ static void internal_curve_test(void)
|
||||
if (ok)
|
||||
fprintf(stdout, " ok\n\n");
|
||||
else
|
||||
{
|
||||
fprintf(stdout, " failed\n\n");
|
||||
ABORT;
|
||||
}
|
||||
OPENSSL_free(curves);
|
||||
return;
|
||||
}
|
||||
|
||||
#ifdef EC_NISTP224_64_GCC_128
|
||||
void nistp224_test()
|
||||
#ifdef EC_NISTP_64_GCC_128
|
||||
/* nistp_test_params contains magic numbers for testing our optimized
|
||||
* implementations of several NIST curves with characteristic > 3. */
|
||||
struct nistp_test_params
|
||||
{
|
||||
fprintf(stdout, "\nNIST curve P-224 (optimised implementation):\n");
|
||||
const EC_METHOD* (*meth) ();
|
||||
int degree;
|
||||
/* Qx, Qy and D are taken from
|
||||
* http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf
|
||||
* Otherwise, values are standard curve parameters from FIPS 180-3 */
|
||||
const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d;
|
||||
};
|
||||
|
||||
static const struct nistp_test_params nistp_tests_params[] =
|
||||
{
|
||||
{
|
||||
/* P-224 */
|
||||
EC_GFp_nistp224_method,
|
||||
224,
|
||||
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */
|
||||
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */
|
||||
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */
|
||||
"E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */
|
||||
"4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */
|
||||
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */
|
||||
"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */
|
||||
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */
|
||||
"3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */
|
||||
},
|
||||
{
|
||||
/* P-256 */
|
||||
EC_GFp_nistp256_method,
|
||||
256,
|
||||
"ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */
|
||||
"ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */
|
||||
"5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */
|
||||
"b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */
|
||||
"3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */
|
||||
"6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */
|
||||
"4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */
|
||||
"ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */
|
||||
"c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */
|
||||
},
|
||||
{
|
||||
/* P-521 */
|
||||
EC_GFp_nistp521_method,
|
||||
521,
|
||||
"1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */
|
||||
"1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */
|
||||
"051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */
|
||||
"0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */
|
||||
"0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */
|
||||
"c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */
|
||||
"11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */
|
||||
"1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */
|
||||
"0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */
|
||||
},
|
||||
};
|
||||
|
||||
void nistp_single_test(const struct nistp_test_params *test)
|
||||
{
|
||||
fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree);
|
||||
BIGNUM *p, *a, *b, *x, *y, *n, *m, *order;
|
||||
p = BN_new();
|
||||
a = BN_new();
|
||||
@ -1278,82 +1339,82 @@ void nistp224_test()
|
||||
x = BN_new(); y = BN_new();
|
||||
m = BN_new(); n = BN_new(); order = BN_new();
|
||||
BN_CTX *ctx = BN_CTX_new();
|
||||
EC_GROUP *NISTP224;
|
||||
EC_GROUP *NISTP;
|
||||
EC_POINT *G, *P, *Q, *Q_CHECK;
|
||||
|
||||
NISTP224 = EC_GROUP_new(EC_GFp_nistp224_method());
|
||||
if(!NISTP224) ABORT;
|
||||
if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) ABORT;
|
||||
NISTP = EC_GROUP_new(test->meth());
|
||||
if(!NISTP) ABORT;
|
||||
if (!BN_hex2bn(&p, test->p)) ABORT;
|
||||
if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT;
|
||||
if (!BN_hex2bn(&a, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE")) ABORT;
|
||||
if (!BN_hex2bn(&b, "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4")) ABORT;
|
||||
if (!EC_GROUP_set_curve_GFp(NISTP224, p, a, b, ctx)) ABORT;
|
||||
G = EC_POINT_new(NISTP224);
|
||||
P = EC_POINT_new(NISTP224);
|
||||
Q = EC_POINT_new(NISTP224);
|
||||
Q_CHECK = EC_POINT_new(NISTP224);
|
||||
if(!BN_hex2bn(&x, "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E")) ABORT;
|
||||
if(!BN_hex2bn(&y, "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555")) ABORT;
|
||||
if(!EC_POINT_set_affine_coordinates_GFp(NISTP224, Q_CHECK, x, y, ctx)) ABORT;
|
||||
if (!BN_hex2bn(&x, "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21")) ABORT;
|
||||
if (!BN_hex2bn(&y, "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34")) ABORT;
|
||||
if (!EC_POINT_set_affine_coordinates_GFp(NISTP224, G, x, y, ctx)) ABORT;
|
||||
if (!BN_hex2bn(&order, "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D")) ABORT;
|
||||
if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
|
||||
if (!BN_hex2bn(&a, test->a)) ABORT;
|
||||
if (!BN_hex2bn(&b, test->b)) ABORT;
|
||||
if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT;
|
||||
G = EC_POINT_new(NISTP);
|
||||
P = EC_POINT_new(NISTP);
|
||||
Q = EC_POINT_new(NISTP);
|
||||
Q_CHECK = EC_POINT_new(NISTP);
|
||||
if(!BN_hex2bn(&x, test->Qx)) ABORT;
|
||||
if(!BN_hex2bn(&y, test->Qy)) ABORT;
|
||||
if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT;
|
||||
if (!BN_hex2bn(&x, test->Gx)) ABORT;
|
||||
if (!BN_hex2bn(&y, test->Gy)) ABORT;
|
||||
if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT;
|
||||
if (!BN_hex2bn(&order, test->order)) ABORT;
|
||||
if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
|
||||
|
||||
fprintf(stdout, "verify degree ... ");
|
||||
if (EC_GROUP_get_degree(NISTP224) != 224) ABORT;
|
||||
if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT;
|
||||
fprintf(stdout, "ok\n");
|
||||
|
||||
fprintf(stdout, "NIST test vectors ... ");
|
||||
if (!BN_hex2bn(&n, "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8")) ABORT;
|
||||
if (!BN_hex2bn(&n, test->d)) ABORT;
|
||||
/* fixed point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
/* random point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
|
||||
/* set generator to P = 2*G, where G is the standard generator */
|
||||
if (!EC_POINT_dbl(NISTP224, P, G, ctx)) ABORT;
|
||||
if (!EC_GROUP_set_generator(NISTP224, P, order, BN_value_one())) ABORT;
|
||||
if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT;
|
||||
if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT;
|
||||
/* set the scalar to m=n/2, where n is the NIST test scalar */
|
||||
if (!BN_rshift(m, n, 1)) ABORT;
|
||||
|
||||
/* test the non-standard generator */
|
||||
/* fixed point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
/* random point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
|
||||
/* now repeat all tests with precomputation */
|
||||
if (!EC_GROUP_precompute_mult(NISTP224, ctx)) ABORT;
|
||||
if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT;
|
||||
|
||||
/* fixed point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, m, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
/* random point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, NULL, P, m, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
|
||||
/* reset generator */
|
||||
if (!EC_GROUP_set_generator(NISTP224, G, order, BN_value_one())) ABORT;
|
||||
if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT;
|
||||
/* fixed point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
/* random point multiplication */
|
||||
EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT;
|
||||
EC_POINT_mul(NISTP, Q, NULL, G, n, ctx);
|
||||
if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT;
|
||||
|
||||
fprintf(stdout, "ok\n");
|
||||
group_order_tests(NISTP224);
|
||||
group_order_tests(NISTP);
|
||||
#if 0
|
||||
timings(NISTP224, TIMING_BASE_PT, ctx);
|
||||
timings(NISTP224, TIMING_RAND_PT, ctx);
|
||||
timings(NISTP, TIMING_BASE_PT, ctx);
|
||||
timings(NISTP, TIMING_RAND_PT, ctx);
|
||||
#endif
|
||||
EC_GROUP_free(NISTP224);
|
||||
EC_GROUP_free(NISTP);
|
||||
EC_POINT_free(G);
|
||||
EC_POINT_free(P);
|
||||
EC_POINT_free(Q);
|
||||
@ -1368,6 +1429,16 @@ void nistp224_test()
|
||||
BN_free(order);
|
||||
BN_CTX_free(ctx);
|
||||
}
|
||||
|
||||
void nistp_tests()
|
||||
{
|
||||
unsigned i;
|
||||
|
||||
for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++)
|
||||
{
|
||||
nistp_single_test(&nistp_tests_params[i]);
|
||||
}
|
||||
}
|
||||
#endif
|
||||
|
||||
static const char rnd_seed[] = "string to make the random number generator think it has entropy";
|
||||
@ -1396,8 +1467,8 @@ int main(int argc, char *argv[])
|
||||
#ifndef OPENSSL_NO_EC2M
|
||||
char2_field_tests();
|
||||
#endif
|
||||
#ifdef EC_NISTP224_64_GCC_128
|
||||
nistp224_test();
|
||||
#ifdef EC_NISTP_64_GCC_128
|
||||
nistp_tests();
|
||||
#endif
|
||||
/* test the internal curves */
|
||||
internal_curve_test();
|
||||
|
||||
Loading…
Reference in New Issue
Block a user