New 64-bit optimized implementation EC_GFp_nistp224_method().
authorBodo Möller <bodo@openssl.org>
Thu, 26 Aug 2010 14:29:55 +0000 (14:29 +0000)
committerBodo Möller <bodo@openssl.org>
Thu, 26 Aug 2010 14:29:55 +0000 (14:29 +0000)
This will only be compiled in if explicitly requested
(#ifdef EC_NISTP224_64_GCC_128).

Submitted by: Emilia Kasper (Google)

CHANGES
crypto/ec/Makefile
crypto/ec/ec.h
crypto/ec/ec_curve.c
crypto/ec/ec_err.c
crypto/ec/ec_lcl.h
crypto/ec/ecp_nistp224.c [new file with mode: 0644]
crypto/ec/ectest.c

diff --git a/CHANGES b/CHANGES
index bd5f02bab3391b0bc7457daad34f0fefedea5faa..8c6cfbe9d80394d084b492ae8facb52e2dbbb6e7 100644 (file)
--- a/CHANGES
+++ b/CHANGES
   
  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 <emilia.kasper@esat.kuleuven.be> (Google)]
+
   *) Permit abbreviated handshakes when renegotiating using the function
      SSL_renegotiate_abbreviated().
      [Robin Seggelmann <seggelmann@fh-muenster.de>]
index db380ed16f8425bf73b9d547116e1da0247f9f02..51f56936fc30ee0093a44d9350222bca25c1f5d8 100644 (file)
@@ -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
index ee7078130c5c3ae1c73d8b76e9f73a2fee40632a..1073c8c423353aa33b1e837e1f44363b6c09500e 100644 (file)
@@ -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
index 23274e4031c6fbeb00b1cf364c3bb250a011f2ae..56a44d0e9ee91419f2276994454103ece446890f 100644 (file)
@@ -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<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;
                        }
 
index 84b4833371ada24f1edc7209dd1b2285eae59d6c..1f8cbf538c1e46114165d7bdc3633a81d2b92534 100644 (file)
@@ -1,6 +1,6 @@
 /* crypto/ec/ec_err.c */
 /* ====================================================================
- * Copyright (c) 1999-2007 The OpenSSL Project.  All rights reserved.
+ * Copyright (c) 1999-2010 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
@@ -70,6 +70,7 @@
 
 static ERR_STRING_DATA EC_str_functs[]=
        {
+{ERR_FUNC(EC_F_BN_TO_FELEM),   "BN_TO_FELEM"},
 {ERR_FUNC(EC_F_COMPUTE_WNAF),  "COMPUTE_WNAF"},
 {ERR_FUNC(EC_F_D2I_ECPARAMETERS),      "d2i_ECParameters"},
 {ERR_FUNC(EC_F_D2I_ECPKPARAMETERS),    "d2i_ECPKParameters"},
@@ -112,6 +113,9 @@ static ERR_STRING_DATA EC_str_functs[]=
 {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_SQR), "ec_GFp_mont_field_sqr"},
 {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE),   "ec_GFp_mont_group_set_curve"},
 {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP),       "EC_GFP_MONT_GROUP_SET_CURVE_GFP"},
+{ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE),       "ec_GFp_nistp224_group_set_curve"},
+{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL),    "ec_GFp_nistp224_points_mul"},
+{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES),  "ec_GFp_nistp224_point_get_affine_coordinates"},
 {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"},
 {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"},
 {ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE),   "ec_GFp_nist_group_set_curve"},
@@ -184,6 +188,7 @@ static ERR_STRING_DATA EC_str_functs[]=
 {ERR_FUNC(EC_F_I2D_ECPKPARAMETERS),    "i2d_ECPKParameters"},
 {ERR_FUNC(EC_F_I2D_ECPRIVATEKEY),      "i2d_ECPrivateKey"},
 {ERR_FUNC(EC_F_I2O_ECPUBLICKEY),       "i2o_ECPublicKey"},
+{ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "NISTP224_PRE_COMP_NEW"},
 {ERR_FUNC(EC_F_O2I_ECPUBLICKEY),       "o2i_ECPublicKey"},
 {ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE),    "OLD_EC_PRIV_DECODE"},
 {ERR_FUNC(EC_F_PKEY_EC_CTRL),  "PKEY_EC_CTRL"},
@@ -199,6 +204,7 @@ static ERR_STRING_DATA EC_str_reasons[]=
        {
 {ERR_REASON(EC_R_ASN1_ERROR)             ,"asn1 error"},
 {ERR_REASON(EC_R_ASN1_UNKNOWN_FIELD)     ,"asn1 unknown field"},
+{ERR_REASON(EC_R_BIGNUM_OUT_OF_RANGE)    ,"bignum out of range"},
 {ERR_REASON(EC_R_BUFFER_TOO_SMALL)       ,"buffer too small"},
 {ERR_REASON(EC_R_D2I_ECPKPARAMETERS_FAILURE),"d2i ecpkparameters failure"},
 {ERR_REASON(EC_R_DECODE_ERROR)           ,"decode error"},
@@ -239,6 +245,7 @@ static ERR_STRING_DATA EC_str_reasons[]=
 {ERR_REASON(EC_R_UNKNOWN_GROUP)          ,"unknown group"},
 {ERR_REASON(EC_R_UNKNOWN_ORDER)          ,"unknown order"},
 {ERR_REASON(EC_R_UNSUPPORTED_FIELD)      ,"unsupported field"},
+{ERR_REASON(EC_R_WRONG_CURVE_PARAMETERS) ,"wrong curve parameters"},
 {ERR_REASON(EC_R_WRONG_ORDER)            ,"wrong order"},
 {0,NULL}
        };
index 3e2c34b0bc8474f75461efa4be14292dd3ee9e86..fd751e5eb18f6b754fa0af419c8851cad1851c2e 100644 (file)
@@ -3,7 +3,7 @@
  * Originally written by Bodo Moeller for the OpenSSL project.
  */
 /* ====================================================================
- * Copyright (c) 1998-2003 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
@@ -391,3 +391,16 @@ int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
        size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
 int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
 int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
+
+#ifdef EC_NISTP224_64_GCC_128
+/* method functions in ecp_nistp224.c */
+int ec_GFp_nistp224_group_init(EC_GROUP *group);
+int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p,
+       const BIGNUM *a, const BIGNUM *n, BN_CTX *);
+int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group,
+       const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
+int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+       size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
+int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
+int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group);
+#endif
diff --git a/crypto/ec/ecp_nistp224.c b/crypto/ec/ecp_nistp224.c
new file mode 100644 (file)
index 0000000..72ce299
--- /dev/null
@@ -0,0 +1,1471 @@
+/* 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
index 7509cb9c7cc7887a8d86f75a43b3a5b4ccc8da6a..283d1bab49906850bd7810d42669f116cf79b874 100644 (file)
@@ -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();