From 48ce525d168a5f063a3346e8e3a30411367e4e2a Mon Sep 17 00:00:00 2001 From: =?utf8?q?Bodo=20M=C3=B6ller?= Date: Thu, 26 Aug 2010 14:29:27 +0000 Subject: [PATCH] New 64-bit optimized implementation EC_GFp_nistp224_method(). Binary compatibility is not affected as this will only be compiled in if explicitly requested (#ifdef EC_NISTP224_64_GCC_128). Submitted by: Emilia Kasper (Google) --- CHANGES | 12 + crypto/ec/Makefile | 5 +- crypto/ec/ec.h | 13 + crypto/ec/ec_curve.c | 175 +++-- crypto/ec/ec_err.c | 9 +- crypto/ec/ec_lcl.h | 15 +- crypto/ec/ecp_nistp224.c | 1471 ++++++++++++++++++++++++++++++++++++++ crypto/ec/ectest.c | 252 ++++--- 8 files changed, 1782 insertions(+), 170 deletions(-) create mode 100644 crypto/ec/ecp_nistp224.c diff --git a/CHANGES b/CHANGES index 1a9737a26c..4766671e6a 100644 --- a/CHANGES +++ b/CHANGES @@ -4,6 +4,18 @@ Changes between 1.0.0a and 1.0.1 [xx XXX xxxx] + *) Add EC_GFp_nistp224_method(), a 64-bit optimized implementation for + elliptic curve NIST-P224 with constant-time single point multiplication on + typical inputs. EC_GROUP_new_by_curve_name() will automatically use this + (while EC_GROUP_new_curve_GFp() currently won't and prefers the more + flexible implementations). + + The implementation requires support for the nonstandard type __uint128_t, + and so is disabled by default. To include this in your build of OpenSSL, + use -DEC_NISTP224_64_GCC_128 on the Configure (or config) command line, + and run "make depend" (or "make update"). + [Emilia Käsper (Google)] + *) Permit abbreviated handshakes when renegotiating using the function SSL_renegotiate_abbreviated(). [Robin Seggelmann ] diff --git a/crypto/ec/Makefile b/crypto/ec/Makefile index db380ed16f..51f56936fc 100644 --- a/crypto/ec/Makefile +++ b/crypto/ec/Makefile @@ -19,11 +19,11 @@ APPS= LIB=$(TOP)/libcrypto.a LIBSRC= ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c\ ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c\ - ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c + ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c ecp_nistp224.c LIBOBJ= ec_lib.o ecp_smpl.o ecp_mont.o ecp_nist.o ec_cvt.o ec_mult.o\ ec_err.o ec_curve.o ec_check.o ec_print.o ec_asn1.o ec_key.o\ - ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o + ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o ecp_nistp224.o SRC= $(LIBSRC) @@ -221,6 +221,7 @@ ecp_nist.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ecp_nist.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ecp_nist.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ecp_nist.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_nist.c +ecp_nistp224.o: ecp_nistp224.c ecp_smpl.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ecp_smpl.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ecp_smpl.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h index ee7078130c..1073c8c423 100644 --- a/crypto/ec/ec.h +++ b/crypto/ec/ec.h @@ -151,6 +151,12 @@ const EC_METHOD *EC_GFp_mont_method(void); */ const EC_METHOD *EC_GFp_nist_method(void); +#ifdef EC_NISTP224_64_GCC_128 +/** Returns 64-bit optimized methods for nistp224 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp224_method(void); +#endif /********************************************************************/ /* EC_METHOD for curves over GF(2^m) */ @@ -926,6 +932,7 @@ void ERR_load_EC_strings(void); /* Error codes for the EC functions. */ /* Function codes. */ +#define EC_F_BN_TO_FELEM 224 #define EC_F_COMPUTE_WNAF 143 #define EC_F_D2I_ECPARAMETERS 144 #define EC_F_D2I_ECPKPARAMETERS 145 @@ -968,6 +975,9 @@ void ERR_load_EC_strings(void); #define EC_F_EC_GFP_MONT_FIELD_SQR 132 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135 +#define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225 +#define EC_F_EC_GFP_NISTP224_POINTS_MUL 228 +#define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226 #define EC_F_EC_GFP_NIST_FIELD_MUL 200 #define EC_F_EC_GFP_NIST_FIELD_SQR 201 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202 @@ -1040,6 +1050,7 @@ void ERR_load_EC_strings(void); #define EC_F_I2D_ECPKPARAMETERS 191 #define EC_F_I2D_ECPRIVATEKEY 192 #define EC_F_I2O_ECPUBLICKEY 151 +#define EC_F_NISTP224_PRE_COMP_NEW 227 #define EC_F_O2I_ECPUBLICKEY 152 #define EC_F_OLD_EC_PRIV_DECODE 222 #define EC_F_PKEY_EC_CTRL 197 @@ -1052,6 +1063,7 @@ void ERR_load_EC_strings(void); /* Reason codes. */ #define EC_R_ASN1_ERROR 115 #define EC_R_ASN1_UNKNOWN_FIELD 116 +#define EC_R_BIGNUM_OUT_OF_RANGE 144 #define EC_R_BUFFER_TOO_SMALL 100 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117 #define EC_R_DECODE_ERROR 142 @@ -1092,6 +1104,7 @@ void ERR_load_EC_strings(void); #define EC_R_UNKNOWN_GROUP 129 #define EC_R_UNKNOWN_ORDER 114 #define EC_R_UNSUPPORTED_FIELD 131 +#define EC_R_WRONG_CURVE_PARAMETERS 145 #define EC_R_WRONG_ORDER 130 #ifdef __cplusplus diff --git a/crypto/ec/ec_curve.c b/crypto/ec/ec_curve.c index 23274e4031..56a44d0e9e 100644 --- a/crypto/ec/ec_curve.c +++ b/crypto/ec/ec_curve.c @@ -3,7 +3,7 @@ * Written by Nils Larsch for the OpenSSL project. */ /* ==================================================================== - * Copyright (c) 1998-2004 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -1300,7 +1300,7 @@ static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } { 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, /* seed */ 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD, - 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, 0x07, 0x01,0x08,0xB3,0x9E,0x77,0xC4,0xB1,0x08,0xBE,0xD9, /* a */ @@ -1820,100 +1820,110 @@ static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } typedef struct _ec_list_element_st { int nid; const EC_CURVE_DATA *data; + const EC_METHOD *(*meth)(void); const char *comment; } ec_list_element; static const ec_list_element curve_list[] = { - /* prime field curves */ + /* prime field curves */ /* secg curves */ - { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, "SECG/WTLS curve over a 112 bit prime field"}, - { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, "SECG curve over a 112 bit prime field"}, - { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, "SECG curve over a 128 bit prime field"}, - { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, "SECG curve over a 128 bit prime field"}, - { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, "SECG curve over a 160 bit prime field"}, - { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, "SECG curve over a 160 bit prime field"}, - { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, "SECG/WTLS curve over a 160 bit prime field"}, + { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field" }, + { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ - { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, "SECG curve over a 192 bit prime field"}, - { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, "SECG curve over a 224 bit prime field"}, - { NID_secp224r1, &_EC_NIST_PRIME_224.h, "NIST/SECG curve over a 224 bit prime field"}, - { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, "SECG curve over a 256 bit prime field"}, + { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, + { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, +#ifdef EC_NISTP224_64_GCC_128 + { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field,\n" + "\t\t64-bit optimized implementation." }, +#else + { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, +#endif + { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ - { NID_secp384r1, &_EC_NIST_PRIME_384.h, "NIST/SECG curve over a 384 bit prime field"}, - { NID_secp521r1, &_EC_NIST_PRIME_521.h, "NIST/SECG curve over a 521 bit prime field"}, + { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, + { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, /* X9.62 curves */ - { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, "NIST/X9.62/SECG curve over a 192 bit prime field"}, - { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, "X9.62 curve over a 192 bit prime field"}, - { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, "X9.62 curve over a 192 bit prime field"}, - { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, "X9.62 curve over a 239 bit prime field"}, - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, "X9.62/SECG curve over a 256 bit prime field"}, + { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, + { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, /* characteristic two field curves */ /* NIST/SECG curves */ - { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, "SECG curve over a 113 bit binary field"}, - { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, "SECG curve over a 113 bit binary field"}, - { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, "SECG/WTLS curve over a 131 bit binary field"}, - { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, "SECG curve over a 131 bit binary field"}, - { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, "NIST/SECG/WTLS curve over a 163 bit binary field" }, - { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, "SECG curve over a 163 bit binary field"}, - { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, "NIST/SECG curve over a 163 bit binary field" }, - { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, "SECG curve over a 193 bit binary field"}, - { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, "SECG curve over a 193 bit binary field"}, - { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, "NIST/SECG/WTLS curve over a 233 bit binary field" }, - { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, "SECG curve over a 239 bit binary field"}, - { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, "NIST/SECG curve over a 283 bit binary field" }, - { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, "NIST/SECG curve over a 409 bit binary field" }, - { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, "NIST/SECG curve over a 571 bit binary field" }, - { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, "NIST/SECG curve over a 571 bit binary field" }, + { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field" }, + { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field" }, + { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field" }, + { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field" }, + { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field" }, + { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field" }, + { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field" }, /* X9.62 curves */ - { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, "X9.62 curve over a 163 bit binary field"}, - { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, "X9.62 curve over a 176 bit binary field"}, - { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, "X9.62 curve over a 191 bit binary field"}, - { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, "X9.62 curve over a 208 bit binary field"}, - { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, "X9.62 curve over a 239 bit binary field"}, - { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, "X9.62 curve over a 272 bit binary field"}, - { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, "X9.62 curve over a 304 bit binary field"}, - { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, "X9.62 curve over a 359 bit binary field"}, - { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, "X9.62 curve over a 368 bit binary field"}, - { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, "X9.62 curve over a 431 bit binary field"}, + { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field" }, + { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field" }, + { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field" }, + { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field" }, + { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field" }, + { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field" }, + { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field" }, /* the WAP/WTLS curves * [unlike SECG, spec has its own OIDs for curves from X9.62] */ - { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, "WTLS curve over a 113 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, "NIST/SECG/WTLS curve over a 163 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, "SECG curve over a 113 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, "X9.62 curve over a 163 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, "SECG/WTLS curve over a 112 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, "SECG/WTLS curve over a 160 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, "WTLS curve over a 112 bit prime field"}, - { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, "WTLS curve over a 160 bit prime field" }, - { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, "NIST/SECG/WTLS curve over a 233 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, "NIST/SECG/WTLS curve over a 233 bit binary field"}, - { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, "WTLS curvs over a 224 bit prime field"}, + { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curvs over a 224 bit prime field" }, /* IPSec curves */ - { NID_ipsec3, &_EC_IPSEC_155_ID3.h, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n""\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, - { NID_ipsec4, &_EC_IPSEC_185_ID4.h, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n""\tNot suitable for ECDSA.\n\tQuestionable extension field!"}, + { NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, + { NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, }; #define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element)) -static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) +static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) { EC_GROUP *group=NULL; EC_POINT *P=NULL; BN_CTX *ctx=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; + BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; int ok=0; int seed_len,param_len; + const EC_METHOD *meth; + const EC_CURVE_DATA *data; const unsigned char *params; if ((ctx = BN_CTX_new()) == NULL) @@ -1922,10 +1932,11 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } + data = curve.data; seed_len = data->seed_len; param_len = data->param_len; - params = (const unsigned char *)(data+1); /* skip header */ - params += seed_len; /* skip seed */ + params = (const unsigned char *)(data+1); /* skip header */ + params += seed_len; /* skip seed */ if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL)) || !(a = BN_bin2bn(params+1*param_len, param_len, NULL)) @@ -1935,7 +1946,17 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } - if (data->field_type == NID_X9_62_prime_field) + if (curve.meth != 0) + { + meth = curve.meth(); + if (((group = EC_GROUP_new(meth)) == NULL) || + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) + { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } + else if (data->field_type == NID_X9_62_prime_field) { if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { @@ -1957,7 +1978,7 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } - + if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL)) || !(y = BN_bin2bn(params+4*param_len, param_len, NULL))) { @@ -2025,7 +2046,7 @@ EC_GROUP *EC_GROUP_new_by_curve_name(int nid) for (i=0; i +#include +#include +#include "ec_lcl.h" + +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ + +typedef uint8_t u8; + +static const u8 nistp224_curve_params[5*28] = { + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ + 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, + 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, + 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ + 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, + 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, + 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ + 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, + 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34 +}; + +/******************************************************************************/ +/* INTERNAL REPRESENTATION OF FIELD ELEMENTS + * + * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 + * where each slice a_i is a 64-bit word, i.e., a field element is an fslice + * array a with 4 elements, where a[i] = a_i. + * Outputs from multiplications are represented as unreduced polynomials + * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 + * where each b_i is a 128-bit word. We ensure that inputs to each field + * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, + * and fit into a 128-bit word without overflow. The coefficients are then + * again partially reduced to a_i < 2^57. We only reduce to the unique minimal + * representation at the end of the computation. + * + */ + +typedef uint64_t fslice; + +/* Field element size (and group order size), in bytes: 28*8 = 224 */ +static const unsigned fElemSize = 28; + +/* Precomputed multiples of the standard generator + * b_0*G + b_1*2^56*G + b_2*2^112*G + b_3*2^168*G for + * (b_3, b_2, b_1, b_0) in [0,15], i.e., gmul[0] = point_at_infinity, + * gmul[1] = G, gmul[2] = 2^56*G, gmul[3] = 2^56*G + G, etc. + * Points are given in Jacobian projective coordinates: words 0-3 represent the + * X-coordinate (slice a_0 is word 0, etc.), words 4-7 represent the + * Y-coordinate and words 8-11 represent the Z-coordinate. */ +static const fslice gmul[16][3][4] = { + {{0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, + {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, + {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}} +}; + +/* Precomputation for the group generator. */ +typedef struct { + fslice g_pre_comp[16][3][4]; + int references; +} NISTP224_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp224_method(void) + { + static const EC_METHOD ret = { + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + ec_GFp_simple_set_compressed_coordinates, + ec_GFp_simple_point2oct, + ec_GFp_simple_oct2point, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + +/* Helper functions to convert field elements to/from internal representation */ +static void bin28_to_felem(fslice out[4], const u8 in[28]) + { + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; + } + +static void felem_to_bin28(u8 out[28], const fslice in[4]) + { + unsigned i; + for (i = 0; i < 7; ++i) + { + out[i] = in[0]>>(8*i); + out[i+7] = in[1]>>(8*i); + out[i+14] = in[2]>>(8*i); + out[i+21] = in[3]>>(8*i); + } + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* From OpenSSL BIGNUM to internal representation */ +static int BN_to_felem(fslice out[4], const BIGNUM *bn) + { + u8 b_in[fElemSize]; + u8 b_out[fElemSize]; + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, fElemSize); + unsigned num_bytes = BN_num_bytes(bn); + if (num_bytes > fElemSize) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; + } + +/* From internal representation to OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4]) + { + u8 b_in[fElemSize], b_out[fElemSize]; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, fElemSize); + return BN_bin2bn(b_out, fElemSize, out); + } + +/******************************************************************************/ +/* FIELD OPERATIONS + * + * Field operations, using the internal representation of field elements. + * NB! These operations are specific to our point multiplication and cannot be + * expected to be correct in general - e.g., multiplication with a large scalar + * will cause an overflow. + * + */ + +/* Sum two field elements: out += in */ +static void felem_sum64(fslice out[4], const fslice in[4]) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* Subtract field elements: out -= in */ +/* Assumes in[i] < 2^57 */ +static void felem_diff64(fslice out[4], const fslice in[4]) + { + static const uint64_t two58p2 = (1l << 58) + (1l << 2); + static const uint64_t two58m2 = (1l << 58) - (1l << 2); + static const uint64_t two58m42m2 = (1l << 58) - (1l << 42) - (1l << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Subtract in unreduced 128-bit mode: out128 -= in128 */ +/* Assumes in[i] < 2^119 */ +static void felem_diff128(uint128_t out[7], const uint128_t in[4]) + { + static const uint128_t two120 = ((uint128_t) 1) << 120; + static const uint128_t two120m64 = (((uint128_t) 1) << 120) - + (((uint128_t) 1) << 64); + static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) - + (((uint128_t) 1) << 104) - (((uint128_t) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + } + +/* Subtract in mixed mode: out128 -= in64 */ +/* in[i] < 2^63 */ +static void felem_diff_128_64(uint128_t out[7], const fslice in[4]) + { + static const uint128_t two64p8 = (((uint128_t) 1) << 64) + + (((uint128_t) 1) << 8); + static const uint128_t two64m8 = (((uint128_t) 1) << 64) - + (((uint128_t) 1) << 8); + static const uint128_t two64m48m8 = (((uint128_t) 1) << 64) - + (((uint128_t) 1) << 48) - (((uint128_t) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Multiply a field element by a scalar: out64 = out64 * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void felem_scalar64(fslice out[4], const fslice scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + } + +/* Multiply an unreduced field element by a scalar: out128 = out128 * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void felem_scalar128(uint128_t out[7], const uint128_t scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + } + +/* Square a field element: out = in^2 */ +static void felem_square(uint128_t out[7], const fslice in[4]) + { + out[0] = ((uint128_t) in[0]) * in[0]; + out[1] = ((uint128_t) in[0]) * in[1] * 2; + out[2] = ((uint128_t) in[0]) * in[2] * 2 + ((uint128_t) in[1]) * in[1]; + out[3] = ((uint128_t) in[0]) * in[3] * 2 + + ((uint128_t) in[1]) * in[2] * 2; + out[4] = ((uint128_t) in[1]) * in[3] * 2 + ((uint128_t) in[2]) * in[2]; + out[5] = ((uint128_t) in[2]) * in[3] * 2; + out[6] = ((uint128_t) in[3]) * in[3]; + } + +/* Multiply two field elements: out = in1 * in2 */ +static void felem_mul(uint128_t out[7], const fslice in1[4], const fslice in2[4]) + { + 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[1]) * in2[3] + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1]; + out[5] = ((uint128_t) in1[2]) * in2[3] + ((uint128_t) in1[3]) * in2[2]; + out[6] = ((uint128_t) in1[3]) * in2[3]; + } + +/* Reduce 128-bit coefficients to 64-bit coefficients. Requires in[i] < 2^126, + * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] < 2^57 */ +static void felem_reduce(fslice out[4], const uint128_t in[7]) + { + static const uint128_t two127p15 = (((uint128_t) 1) << 127) + + (((uint128_t) 1) << 15); + static const uint128_t two127m71 = (((uint128_t) 1) << 127) - + (((uint128_t) 1) << 71); + static const uint128_t two127m71m55 = (((uint128_t) 1) << 127) - + (((uint128_t) 1) << 71) - (((uint128_t) 1) << 55); + uint128_t output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6]&0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5]&0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4]&0xffff) << 40; + output[0] -= output[4]; + output[4] = 0; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] += output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + output[1] += (output[4]&0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + out[2] = output[2] & 0x00ffffffffffffff; + + /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] < 2^57 (due to final carry) */ + out[3] = output[3]; + } + +/* Reduce to unique minimal representation */ +static void felem_contract(fslice out[4], const fslice in[4]) + { + static const int64_t two56 = (1l << 56); + /* 0 <= in < 2^225 */ + /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = (int64_t) in[0] - (in[3] >> 56); + tmp[1] = (int64_t) in[1] + ((in[3] >> 16) & 0x0000010000000000); + tmp[2] = (int64_t) in[2]; + tmp[3] = (int64_t) in[3] & 0x00ffffffffffffff; + + /* eliminate negative coefficients */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + a = tmp[1] >> 63; + tmp[1] += two56 & a; + tmp[2] -= 1 & a; + + a = tmp[2] >> 63; + tmp[2] += two56 & a; + tmp[3] -= 1 & a; + + a = tmp[3] >> 63; + tmp[3] += two56 & a; + tmp[0] += 1 & a; + tmp[1] -= (1 & a) << 40; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* 0 <= in < 2^224 + 2^96 - 1 */ + /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */ + tmp[0] -= (tmp[3] >> 56); + tmp[1] += ((tmp[3] >> 16) & 0x0000010000000000); + tmp[3] &= 0x00ffffffffffffff; + + /* eliminate negative coefficients */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + a = tmp[1] >> 63; + tmp[1] += two56 & a; + tmp[2] -= 1 & a; + + a = tmp[2] >> 63; + tmp[2] += two56 & a; + tmp[3] -= 1 & a; + + a = tmp[3] >> 63; + tmp[3] += two56 & a; + tmp[0] += 1 & a; + tmp[1] -= (1 & a) << 40; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= in < 2^224 */ + + /* if in > 2^224 - 2^96, reduce */ + /* a = 0 iff in > 2^224 - 2^96, i.e., + * the high 128 bits are all 1 and the lower part is non-zero */ + a = (tmp[3] + 1) | (tmp[2] + 1) | + ((tmp[1] | 0x000000ffffffffff) + 1) | + ((((tmp[1] & 0xffff) - 1) >> 63) & ((tmp[0] - 1) >> 63)); + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = ((a & 0x00ffffffffffffff) - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one*/ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + /* 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] += two56 & a; + tmp[1] -= 1 & a; + + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; + } + +/* Zero-check: returns 1 if input is 0, and 0 otherwise. + * We know that field elements are reduced to in < 2^225, + * so we only need to check three cases: 0, 2^224 - 2^96 + 1, + * and 2^225 - 2^97 + 2 */ +static fslice felem_is_zero(const fslice in[4]) + { + fslice zero = (in[0] | in[1] | in[2] | in[3]); + zero = (((int64_t)(zero) - 1) >> 63) & 1; + fslice two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; + fslice two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); + } + +/* Invert a field element */ +/* Computation chain copied from djb's code */ +static void felem_inv(fslice out[4], const fslice in[4]) + { + fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4]; + uint128_t tmp[7]; + unsigned i; + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ + { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ + } + +/* Copy in constant time: + * if icopy == 1, copy in to out, + * if icopy == 0, copy out to itself. */ +static void +copy_conditional(fslice *out, const fslice *in, unsigned len, fslice icopy) + { + unsigned i; + /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ + const fslice copy = -icopy; + for (i = 0; i < len; ++i) + { + const fslice tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/* Copy in constant time: + * if isel == 1, copy in2 to out, + * if isel == 0, copy in1 to out. */ +static void select_conditional(fslice *out, const fslice *in1, const fslice *in2, + unsigned len, fslice isel) + { + unsigned i; + /* isel is a (64-bit) 0 or 1, so sel is either all-zero or all-one */ + const fslice sel = -isel; + for (i = 0; i < len; ++i) + { + const fslice tmp = sel & (in1[i] ^ in2[i]); + out[i] = in1[i] ^ tmp; + } +} + +/******************************************************************************/ +/* ELLIPTIC CURVE POINT OPERATIONS + * + * Points are represented in Jacobian projective coordinates: + * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), + * or to the point at infinity if Z == 0. + * + */ + +/* Double an elliptic curve point: + * (X', Y', Z') = 2 * (X, Y, Z), where + * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 + * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 + * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z + * 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(fslice x_out[4], fslice y_out[4], fslice z_out[4], + const fslice x_in[4], const fslice y_in[4], const fslice z_in[4]) + { + uint128_t tmp[7], tmp2[7]; + fslice delta[4]; + fslice gamma[4]; + fslice beta[4]; + fslice alpha[4]; + fslice ftmp[4], ftmp2[4]; + memcpy(ftmp, x_in, 4 * sizeof(fslice)); + memcpy(ftmp2, x_in, 4 * sizeof(fslice)); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff64(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum64(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar64(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + memcpy(ftmp, beta, 4 * sizeof(fslice)); + felem_scalar64(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum64(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + memcpy(ftmp, y_in, 4 * sizeof(fslice)); + felem_sum64(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar64(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff64(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_scalar128(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); + } + +/* Add two elliptic curve points: + * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where + * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - + * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 + * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - + * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 + * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) */ + +/* This function is not entirely constant-time: + * it includes a branch for checking whether the two input points are equal, + * (while not equal to the point at infinity). + * This case never happens during single point multiplication, + * so there is no timing leak for ECDH or ECDSA signing. */ +static void point_add(fslice x3[4], fslice y3[4], fslice z3[4], + const fslice x1[4], const fslice y1[4], const fslice z1[4], + const fslice x2[4], const fslice y2[4], const fslice z2[4]) + { + fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4], ftmp5[4]; + uint128_t tmp[7], tmp2[7]; + fslice z1_is_zero, z2_is_zero, x_equal, y_equal; + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp3 = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* ftmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp2 =z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* the formulae are incorrect if the points are equal + * so we check for this and do doubling if this happens */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + + /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z3, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + memcpy(ftmp5, ftmp, 4 * sizeof(fslice)); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + memcpy(ftmp5, ftmp2, 4 * sizeof(fslice)); + felem_scalar64(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x3, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */ + felem_diff64(ftmp2, x3); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) - + z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_diff128(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y3, tmp2); + + /* the result (x3, y3, z3) is incorrect if one of the inputs is the + * point at infinity, so we need to check for this separately */ + + /* if point 1 is at infinity, copy point 2 to output, and vice versa */ + copy_conditional(x3, x2, 4, z1_is_zero); + copy_conditional(x3, x1, 4, z2_is_zero); + copy_conditional(y3, y2, 4, z1_is_zero); + copy_conditional(y3, y1, 4, z2_is_zero); + copy_conditional(z3, z2, 4, z1_is_zero); + copy_conditional(z3, z1, 4, z2_is_zero); + } + +/* Select a point from an array of 16 precomputed point multiples, + * in constant time: for bits = {b_0, b_1, b_2, b_3}, return the point + * pre_comp[8*b_3 + 4*b_2 + 2*b_1 + b_0] */ +static void select_point(const fslice bits[4], const fslice pre_comp[16][3][4], + fslice out[12]) + { + fslice tmp[5][12]; + select_conditional(tmp[0], pre_comp[7][0], pre_comp[15][0], 12, bits[3]); + select_conditional(tmp[1], pre_comp[3][0], pre_comp[11][0], 12, bits[3]); + select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]); + select_conditional(tmp[0], pre_comp[5][0], pre_comp[13][0], 12, bits[3]); + select_conditional(tmp[1], pre_comp[1][0], pre_comp[9][0], 12, bits[3]); + select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]); + select_conditional(tmp[4], tmp[3], tmp[2], 12, bits[1]); + select_conditional(tmp[0], pre_comp[6][0], pre_comp[14][0], 12, bits[3]); + select_conditional(tmp[1], pre_comp[2][0], pre_comp[10][0], 12, bits[3]); + select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]); + select_conditional(tmp[0], pre_comp[4][0], pre_comp[12][0], 12, bits[3]); + select_conditional(tmp[1], pre_comp[0][0], pre_comp[8][0], 12, bits[3]); + select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]); + select_conditional(tmp[1], tmp[3], tmp[2], 12, bits[1]); + select_conditional(out, tmp[1], tmp[4], 12, bits[0]); + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 15*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(fslice x_out[4], fslice y_out[4], fslice z_out[4], + const u8 scalars[][fElemSize], const unsigned num_points, const u8 *g_scalar, + const fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4]) + { + unsigned i, j, num; + unsigned gen_mul = (g_scalar != NULL); + fslice nq[12], nqt[12], tmp[12]; + /* set nq to the point at infinity */ + memset(nq, 0, 12 * sizeof(fslice)); + fslice bits[4]; + u8 byte; + + /* Loop over all scalars msb-to-lsb, 4 bits at a time: for each nibble, + * double 4 times, then add the precomputed point multiples. + * If we are also adding multiples of the generator, then interleave + * these additions with the last 56 doublings. */ + for (i = (num_points ? 28 : 7); i > 0; --i) + { + for (j = 0; j < 8; ++j) + { + /* double once */ + point_double(nq, nq+4, nq+8, nq, nq+4, nq+8); + /* add multiples of the generator */ + if ((gen_mul) && (i <= 7)) + { + bits[3] = (g_scalar[i+20] >> (7-j)) & 1; + bits[2] = (g_scalar[i+13] >> (7-j)) & 1; + bits[1] = (g_scalar[i+6] >> (7-j)) & 1; + bits[0] = (g_scalar[i-1] >> (7-j)) & 1; + /* select the point to add, in constant time */ + select_point(bits, g_pre_comp, tmp); + memcpy(nqt, nq, 12 * sizeof(fslice)); + point_add(nq, nq+4, nq+8, nqt, nqt+4, nqt+8, + tmp, tmp+4, tmp+8); + } + /* do an addition after every 4 doublings */ + if (j % 4 == 3) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + byte = scalars[num][i-1]; + bits[3] = (byte >> (10-j)) & 1; + bits[2] = (byte >> (9-j)) & 1; + bits[1] = (byte >> (8-j)) & 1; + bits[0] = (byte >> (7-j)) & 1; + /* select the point to add */ + select_point(bits, + pre_comp[num], tmp); + memcpy(nqt, nq, 12 * sizeof(fslice)); + point_add(nq, nq+4, nq+8, nqt, nqt+4, + nqt+8, tmp, tmp+4, tmp+8); + } + } + } + } + memcpy(x_out, nq, 4 * sizeof(fslice)); + memcpy(y_out, nq+4, 4 * sizeof(fslice)); + memcpy(z_out, nq+8, 4 * sizeof(fslice)); + } + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP224_PRE_COMP *nistp224_pre_comp_new() + { + NISTP224_PRE_COMP *ret = NULL; + ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP)); + if (!ret) + { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp224_pre_comp_dup(void *src_) + { + NISTP224_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp224_pre_comp_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp224_pre_comp_clear_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp224_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp224_curve_params, fElemSize, curve_p); + BN_bin2bn(nistp224_curve_params + 28, fElemSize, curve_a); + BN_bin2bn(nistp224_curve_params + 56, fElemSize, curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + fslice z1[4], z2[4], x_in[4], y_in[4], x_out[4], y_out[4]; + uint128_t tmp[7]; + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + 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)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + 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)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + u8 g_secret[fElemSize]; + u8 (*secrets)[fElemSize] = NULL; + fslice (*pre_comp)[16][3][4] = NULL; + u8 tmp[fElemSize]; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4]; + NISTP224_PRE_COMP *pre = NULL; + fslice (*g_pre_comp)[3][4] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp224_pre_comp_dup, nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = (fslice (*)[3][4]) 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])) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_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 = num_points + 1; + } + secrets = OPENSSL_malloc(num_points * fElemSize); + pre_comp = OPENSSL_malloc(num_points * 16 * 3 * 4 * sizeof(fslice)); + + if ((num_points) && ((secrets == NULL) || (pre_comp == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * fElemSize); + memset(pre_comp, 0, num_points * 16 * 3 * 4 * sizeof(fslice)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* 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)) + { + num_bytes = BN_num_bytes(p_scalar); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((num_bytes > fElemSize) || (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)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* 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, 4 * sizeof(fslice)); + memcpy(pre_comp[i][1][1], y_out, 4 * sizeof(fslice)); + memcpy(pre_comp[i][1][2], z_out, 4 * sizeof(fslice)); + for (j = 1; j < 8; ++j) + { + point_double(pre_comp[i][2*j][0], + pre_comp[i][2*j][1], + pre_comp[i][2*j][2], + pre_comp[i][j][0], + pre_comp[i][j][1], + pre_comp[i][j][2]); + point_add(pre_comp[i][2*j+1][0], + pre_comp[i][2*j+1][1], + pre_comp[i][2*j+1][2], + pre_comp[i][1][0], + pre_comp[i][1][1], + pre_comp[i][1][2], + pre_comp[i][2*j][0], + pre_comp[i][2*j][1], + pre_comp[i][2*j][2]); + } + } + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, fElemSize); + num_bytes = BN_num_bytes(scalar); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((num_bytes > fElemSize) || (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)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const u8 (*)[fElemSize]) secrets, num_points, + g_secret, (const fslice (*)[16][3][4]) pre_comp, + (const fslice (*)[3][4]) g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const u8 (*)[fElemSize]) secrets, num_points, + NULL, (const fslice (*)[16][3][4]) 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))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + return ret; + } + +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params + 84, fElemSize, x); + BN_bin2bn(nistp224_curve_params + 112, fElemSize, y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_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)); + ret = 1; + goto err; + } + 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 2^56*G, 2^112*G, 2^168*G */ + for (i = 1; i < 5; ++i) + { + 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 < 55; ++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 */ + /* 2^56*G + 2^112*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], + pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^56*G + 2^168*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], + pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^112*G + 2^168*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], + pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); + /* 2^56*G + 2^112*G + 2^168*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], + 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], + pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp224_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } +#endif diff --git a/crypto/ec/ectest.c b/crypto/ec/ectest.c index 7509cb9c7c..283d1bab49 100644 --- a/crypto/ec/ectest.c +++ b/crypto/ec/ectest.c @@ -107,10 +107,6 @@ int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); retur EXIT(1); \ } while (0) -void prime_field_tests(void); -void char2_field_tests(void); -void internal_curve_test(void); - #define TIMING_BASE_PT 0 #define TIMING_RAND_PT 1 #define TIMING_SIMUL 2 @@ -195,6 +191,48 @@ static void timings(EC_GROUP *group, int type, BN_CTX *ctx) } #endif +/* test multiplication with group order, long and negative scalars */ +static void group_order_tests(EC_GROUP *group) + { + BIGNUM *n1, *n2, *order; + EC_POINT *P = EC_POINT_new(group); + EC_POINT *Q = EC_POINT_new(group); + n1 = BN_new(); n2 = BN_new(); order = BN_new(); + BN_CTX *ctx = BN_CTX_new(); + fprintf(stdout, "verify group order ..."); + fflush(stdout); + if (!EC_GROUP_get_order(group, order, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, "."); + fflush(stdout); + if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, " ok\n"); + fprintf(stdout, "long/negative scalar tests ... "); + if (!BN_one(n1)) ABORT; + /* n1 = 1 - order */ + if (!BN_sub(n1, n1, order)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = 1 + order */ + if (!BN_add(n2, order, BN_value_one())) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = (1 - order) * (1 + order) */ + if (!BN_mul(n2, n1, n2, ctx)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + fprintf(stdout, "ok\n"); + EC_POINT_free(P); + EC_POINT_free(Q); + BN_free(n1); + BN_free(n2); + BN_free(order); + BN_CTX_free(ctx); + } + void prime_field_tests() { BN_CTX *ctx = NULL; @@ -321,21 +359,21 @@ void prime_field_tests() if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "Generator as octect string, compressed form:\n "); + fprintf(stdout, "Generator as octet string, compressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); + fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); + fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; @@ -381,17 +419,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 160) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_160, group)) ABORT; @@ -425,17 +453,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 192) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_192, group)) ABORT; @@ -469,17 +487,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 224) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_224, group)) ABORT; @@ -514,17 +522,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 256) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_256, group)) ABORT; @@ -563,18 +561,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 384) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_384, group)) ABORT; @@ -619,18 +607,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 521) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_521, group)) ABORT; @@ -659,6 +637,7 @@ void prime_field_tests() points[2] = Q; points[3] = Q; + if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!BN_add(y, z, BN_value_one())) ABORT; if (BN_is_odd(y)) ABORT; if (!BN_rshift1(y, y)) ABORT; @@ -792,19 +771,10 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); \ if (EC_GROUP_get_degree(group) != _degree) ABORT; \ fprintf(stdout, " ok\n"); \ - fprintf(stdout, "verify group order ..."); \ - fflush(stdout); \ - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, "."); \ - fflush(stdout); \ - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, " ok\n"); \ + group_order_tests(group); \ if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ - if (!EC_GROUP_copy(_variable, group)) ABORT; + if (!EC_GROUP_copy(_variable, group)) ABORT; \ + void char2_field_tests() { @@ -1287,13 +1257,114 @@ void internal_curve_test(void) EC_GROUP_free(group); } if (ok) - fprintf(stdout, " ok\n"); + fprintf(stdout, " ok\n\n"); else - fprintf(stdout, " failed\n"); + fprintf(stdout, " failed\n\n"); OPENSSL_free(curves); return; } +#ifdef EC_NISTP224_64_GCC_128 +void nistp224_test() + { + fprintf(stdout, "\nNIST curve P-224 (optimised implementation):\n"); + BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; + p = BN_new(); + a = BN_new(); + b = BN_new(); + x = BN_new(); y = BN_new(); + m = BN_new(); n = BN_new(); order = BN_new(); + BN_CTX *ctx = BN_CTX_new(); + EC_GROUP *NISTP224 = NULL; + NISTP224 = EC_GROUP_new(EC_GFp_nistp224_method()); + if(!NISTP224) ABORT; + if (!BN_hex2bn(&p, "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001")) 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; + EC_POINT *G = EC_POINT_new(NISTP224); + EC_POINT *P = EC_POINT_new(NISTP224); + EC_POINT *Q = EC_POINT_new(NISTP224); + EC_POINT *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; + + fprintf(stdout, "verify degree ... "); + if (EC_GROUP_get_degree(NISTP224) != 224) ABORT; + fprintf(stdout, "ok\n"); + + fprintf(stdout, "NIST test vectors ... "); + if (!BN_hex2bn(&n, "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8")) ABORT; + /* fixed point multiplication */ + EC_POINT_mul(NISTP224, Q, n, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP224, 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; + + /* 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; + /* 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; + /* random point multiplication */ + EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT; + + /* now repeat all tests with precomputation */ + if (!EC_GROUP_precompute_mult(NISTP224, 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; + /* random point multiplication */ + EC_POINT_mul(NISTP224, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT; + + /* reset generator */ + if (!EC_GROUP_set_generator(NISTP224, 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; + /* random point multiplication */ + EC_POINT_mul(NISTP224, Q, NULL, G, n, ctx); + if (0 != EC_POINT_cmp(NISTP224, Q, Q_CHECK, ctx)) ABORT; + + fprintf(stdout, "ok\n"); + group_order_tests(NISTP224); +#if 0 + timings(NISTP224, TIMING_BASE_PT, ctx); + timings(NISTP224, TIMING_RAND_PT, ctx); +#endif + EC_GROUP_free(NISTP224); + EC_POINT_free(G); + EC_POINT_free(P); + EC_POINT_free(Q); + EC_POINT_free(Q_CHECK); + BN_free(n); + BN_free(m); + BN_free(p); + BN_free(a); + BN_free(b); + BN_free(x); + BN_free(y); + BN_free(order); + BN_CTX_free(ctx); + } +#endif + static const char rnd_seed[] = "string to make the random number generator think it has entropy"; int main(int argc, char *argv[]) @@ -1318,6 +1389,9 @@ int main(int argc, char *argv[]) prime_field_tests(); puts(""); char2_field_tests(); +#ifdef EC_NISTP224_64_GCC_128 + nistp224_test(); +#endif /* test the internal curves */ internal_curve_test(); -- 2.25.1