* 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
{ 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 */
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)
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))
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)
{
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)))
{
for (i=0; i<curve_list_length; i++)
if (curve_list[i].nid == nid)
{
- ret = ec_group_new_from_data(curve_list[i].data);
+ ret = ec_group_new_from_data(curve_list[i]);
break;
}
--- /dev/null
+/* crypto/ec/ecp_nistp224.c */
+/*
+ * Written by Emilia Kasper (Google) for the OpenSSL project.
+ */
+/* ====================================================================
+ * Copyright (c) 2000-2010 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
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. All advertising materials mentioning features or use of this
+ * software must display the following acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
+ *
+ * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
+ * endorse or promote products derived from this software without
+ * prior written permission. For written permission, please contact
+ * licensing@OpenSSL.org.
+ *
+ * 5. Products derived from this software may not be called "OpenSSL"
+ * nor may "OpenSSL" appear in their names without prior written
+ * permission of the OpenSSL Project.
+ *
+ * 6. Redistributions of any form whatsoever must retain the following
+ * acknowledgment:
+ * "This product includes software developed by the OpenSSL Project
+ * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
+ * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
+ * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+ * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
+ * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
+ * OF THE POSSIBILITY OF SUCH DAMAGE.
+ * ====================================================================
+ *
+ * This product includes cryptographic software written by Eric Young
+ * (eay@cryptsoft.com). This product includes software written by Tim
+ * Hudson (tjh@cryptsoft.com).
+ *
+ */
+
+/*
+ * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication
+ *
+ * Inspired by Daniel J. Bernstein's public domain nistp224 implementation
+ * and Adam Langley's public domain 64-bit C implementation of curve25519
+ */
+#ifdef EC_NISTP224_64_GCC_128
+#include <stdint.h>
+#include <string.h>
+#include <openssl/err.h>
+#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
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
}
#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;
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;
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;
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;
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;
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;
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;
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;
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;
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()
{
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[])
prime_field_tests();
puts("");
char2_field_tests();
+#ifdef EC_NISTP224_64_GCC_128
+ nistp224_test();
+#endif
/* test the internal curves */
internal_curve_test();
projects / openssl / commitdiff