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mbedtls/library/ecp_curves.c
Manuel Pégourié-Gonnard 32b04c1237 Split ecp.c
2013-12-02 16:36:11 +01:00

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/*
* Elliptic curves over GF(p): curve-specific data and functions
*
* Copyright (C) 2006-2013, Brainspark B.V.
*
* This file is part of PolarSSL (http://www.polarssl.org)
* Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org>
*
* All rights reserved.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#include "polarssl/config.h"
#if defined(POLARSSL_ECP_C)
#include "polarssl/ecp.h"
/*
* Domain parameters for secp192r1
*/
#define SECP192R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF"
#define SECP192R1_B \
"64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1"
#define SECP192R1_GX \
"188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012"
#define SECP192R1_GY \
"07192B95FFC8DA78631011ED6B24CDD573F977A11E794811"
#define SECP192R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831"
/*
* Domain parameters for secp224r1
*/
#define SECP224R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001"
#define SECP224R1_B \
"B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4"
#define SECP224R1_GX \
"B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21"
#define SECP224R1_GY \
"BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34"
#define SECP224R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D"
/*
* Domain parameters for secp256r1
*/
#define SECP256R1_P \
"FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF"
#define SECP256R1_B \
"5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B"
#define SECP256R1_GX \
"6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296"
#define SECP256R1_GY \
"4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5"
#define SECP256R1_N \
"FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551"
/*
* Domain parameters for secp384r1
*/
#define SECP384R1_P \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF"
#define SECP384R1_B \
"B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \
"0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF"
#define SECP384R1_GX \
"AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \
"59F741E082542A385502F25DBF55296C3A545E3872760AB7"
#define SECP384R1_GY \
"3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \
"E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F"
#define SECP384R1_N \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973"
/*
* Domain parameters for secp521r1
*/
#define SECP521R1_P \
"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF"
#define SECP521R1_B \
"00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \
"99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \
"3BB1BF073573DF883D2C34F1EF451FD46B503F00"
#define SECP521R1_GX \
"000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \
"053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \
"A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66"
#define SECP521R1_GY \
"0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \
"579B446817AFBD17273E662C97EE72995EF42640C550B901" \
"3FAD0761353C7086A272C24088BE94769FD16650"
#define SECP521R1_N \
"000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \
"FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \
"F709A5D03BB5C9B8899C47AEBB6FB71E91386409"
/*
* Domain parameters for brainpoolP256r1 (RFC 5639 3.4)
*/
#define BP256R1_P \
"A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377"
#define BP256R1_A \
"7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9"
#define BP256R1_B \
"26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6"
#define BP256R1_GX \
"8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262"
#define BP256R1_GY \
"547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997"
#define BP256R1_N \
"A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7"
/*
* Domain parameters for brainpoolP384r1 (RFC 5639 3.6)
*/
#define BP384R1_P \
"8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711" \
"23ACD3A729901D1A71874700133107EC53"
#define BP384R1_A \
"7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9" \
"0F8AA5814A503AD4EB04A8C7DD22CE2826"
#define BP384R1_B \
"04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62" \
"D57CB4390295DBC9943AB78696FA504C11"
#define BP384R1_GX \
"1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10" \
"E8E826E03436D646AAEF87B2E247D4AF1E"
#define BP384R1_GY \
"8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129" \
"280E4646217791811142820341263C5315"
#define BP384R1_N \
"8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425" \
"A7CF3AB6AF6B7FC3103B883202E9046565"
/*
* Domain parameters for brainpoolP512r1 (RFC 5639 3.7)
*/
#define BP512R1_P \
"AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
"717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3"
#define BP512R1_A \
"7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863" \
"BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA"
#define BP512R1_B \
"3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117" \
"A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723"
#define BP512R1_GX \
"81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009" \
"8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822"
#define BP512R1_GY \
"7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81" \
"11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892"
#define BP512R1_N \
"AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
"70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069"
/*
* Import an ECP group from ASCII strings, general case (A used)
*/
static int ecp_group_read_string_gen( ecp_group *grp, int radix,
const char *p, const char *a, const char *b,
const char *gx, const char *gy, const char *n)
{
int ret;
MPI_CHK( mpi_read_string( &grp->P, radix, p ) );
MPI_CHK( mpi_read_string( &grp->A, radix, a ) );
MPI_CHK( mpi_read_string( &grp->B, radix, b ) );
MPI_CHK( ecp_point_read_string( &grp->G, radix, gx, gy ) );
MPI_CHK( mpi_read_string( &grp->N, radix, n ) );
grp->pbits = mpi_msb( &grp->P );
grp->nbits = mpi_msb( &grp->N );
cleanup:
if( ret != 0 )
ecp_group_free( grp );
return( ret );
}
#if defined(POLARSSL_ECP_NIST_OPTIM)
/* Forward declarations */
int ecp_mod_p192( mpi * );
int ecp_mod_p224( mpi * );
int ecp_mod_p256( mpi * );
int ecp_mod_p384( mpi * );
int ecp_mod_p521( mpi * );
#endif
/*
* Set a group using well-known domain parameters
*/
int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
{
grp->id = id;
switch( id )
{
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
case POLARSSL_ECP_DP_SECP192R1:
#if defined(POLARSSL_ECP_NIST_OPTIM)
grp->modp = ecp_mod_p192;
#endif
return( ecp_group_read_string( grp, 16,
SECP192R1_P, SECP192R1_B,
SECP192R1_GX, SECP192R1_GY, SECP192R1_N ) );
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
case POLARSSL_ECP_DP_SECP224R1:
#if defined(POLARSSL_ECP_NIST_OPTIM)
grp->modp = ecp_mod_p224;
#endif
return( ecp_group_read_string( grp, 16,
SECP224R1_P, SECP224R1_B,
SECP224R1_GX, SECP224R1_GY, SECP224R1_N ) );
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
case POLARSSL_ECP_DP_SECP256R1:
#if defined(POLARSSL_ECP_NIST_OPTIM)
grp->modp = ecp_mod_p256;
#endif
return( ecp_group_read_string( grp, 16,
SECP256R1_P, SECP256R1_B,
SECP256R1_GX, SECP256R1_GY, SECP256R1_N ) );
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
case POLARSSL_ECP_DP_SECP384R1:
#if defined(POLARSSL_ECP_NIST_OPTIM)
grp->modp = ecp_mod_p384;
#endif
return( ecp_group_read_string( grp, 16,
SECP384R1_P, SECP384R1_B,
SECP384R1_GX, SECP384R1_GY, SECP384R1_N ) );
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
case POLARSSL_ECP_DP_SECP521R1:
#if defined(POLARSSL_ECP_NIST_OPTIM)
grp->modp = ecp_mod_p521;
#endif
return( ecp_group_read_string( grp, 16,
SECP521R1_P, SECP521R1_B,
SECP521R1_GX, SECP521R1_GY, SECP521R1_N ) );
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
#if defined(POLARSSL_ECP_DP_BP256R1_ENABLED)
case POLARSSL_ECP_DP_BP256R1:
return( ecp_group_read_string_gen( grp, 16,
BP256R1_P, BP256R1_A, BP256R1_B,
BP256R1_GX, BP256R1_GY, BP256R1_N ) );
#endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */
#if defined(POLARSSL_ECP_DP_BP384R1_ENABLED)
case POLARSSL_ECP_DP_BP384R1:
return( ecp_group_read_string_gen( grp, 16,
BP384R1_P, BP384R1_A, BP384R1_B,
BP384R1_GX, BP384R1_GY, BP384R1_N ) );
#endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */
#if defined(POLARSSL_ECP_DP_BP512R1_ENABLED)
case POLARSSL_ECP_DP_BP512R1:
return( ecp_group_read_string_gen( grp, 16,
BP512R1_P, BP512R1_A, BP512R1_B,
BP512R1_GX, BP512R1_GY, BP512R1_N ) );
#endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */
default:
ecp_group_free( grp );
return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE );
}
}
#if defined(POLARSSL_ECP_NIST_OPTIM)
/*
* Fast reduction modulo the primes used by the NIST curves.
*
* These functions are critical for speed, but not needed for correct
* operations. So, we make the choice to heavily rely on the internals of our
* bignum library, which creates a tight coupling between these functions and
* our MPI implementation. However, the coupling between the ECP module and
* MPI remains loose, since these functions can be deactivated at will.
*/
#if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED)
/*
* Compared to the way things are presented in FIPS 186-3 D.2,
* we proceed in columns, from right (least significant chunk) to left,
* adding chunks to N in place, and keeping a carry for the next chunk.
* This avoids moving things around in memory, and uselessly adding zeros,
* compared to the more straightforward, line-oriented approach.
*
* For this prime we need to handle data in chunks of 64 bits.
* Since this is always a multiple of our basic t_uint, we can
* use a t_uint * to designate such a chunk, and small loops to handle it.
*/
/* Add 64-bit chunks (dst += src) and update carry */
static inline void add64( t_uint *dst, t_uint *src, t_uint *carry )
{
unsigned char i;
t_uint c = 0;
for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ )
{
*dst += c; c = ( *dst < c );
*dst += *src; c += ( *dst < *src );
}
*carry += c;
}
/* Add carry to a 64-bit chunk and update carry */
static inline void carry64( t_uint *dst, t_uint *carry )
{
unsigned char i;
for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ )
{
*dst += *carry;
*carry = ( *dst < *carry );
}
}
#define WIDTH 8 / sizeof( t_uint )
#define A( i ) N->p + i * WIDTH
#define ADD( i ) add64( p, A( i ), &c )
#define NEXT p += WIDTH; carry64( p, &c )
#define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0
/*
* Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
*/
int ecp_mod_p192( mpi *N )
{
int ret;
t_uint c = 0;
t_uint *p, *end;
/* Make sure we have enough blocks so that A(5) is legal */
MPI_CHK( mpi_grow( N, 6 * WIDTH ) );
p = N->p;
end = p + N->n;
ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5
ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5
ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5
cleanup:
return( ret );
}
#undef WIDTH
#undef A
#undef ADD
#undef NEXT
#undef LAST
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) || \
defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) || \
defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
/*
* The reader is advised to first understand ecp_mod_p192() since the same
* general structure is used here, but with additional complications:
* (1) chunks of 32 bits, and (2) subtractions.
*/
/*
* For these primes, we need to handle data in chunks of 32 bits.
* This makes it more complicated if we use 64 bits limbs in MPI,
* which prevents us from using a uniform access method as for p192.
*
* So, we define a mini abstraction layer to access 32 bit chunks,
* load them in 'cur' for work, and store them back from 'cur' when done.
*
* While at it, also define the size of N in terms of 32-bit chunks.
*/
#define LOAD32 cur = A( i );
#if defined(POLARSSL_HAVE_INT8) /* 8 bit */
#define MAX32 N->n / 4
#define A( j ) (uint32_t)( N->p[4*j+0] ) | \
( N->p[4*j+1] << 8 ) | \
( N->p[4*j+2] << 16 ) | \
( N->p[4*j+3] << 24 )
#define STORE32 N->p[4*i+0] = (t_uint)( cur ); \
N->p[4*i+1] = (t_uint)( cur >> 8 ); \
N->p[4*i+2] = (t_uint)( cur >> 16 ); \
N->p[4*i+3] = (t_uint)( cur >> 24 );
#elif defined(POLARSSL_HAVE_INT16) /* 16 bit */
#define MAX32 N->n / 2
#define A( j ) (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 )
#define STORE32 N->p[2*i+0] = (t_uint)( cur ); \
N->p[2*i+1] = (t_uint)( cur >> 16 );
#elif defined(POLARSSL_HAVE_INT32) /* 32 bit */
#define MAX32 N->n
#define A( j ) N->p[j]
#define STORE32 N->p[i] = cur;
#else /* 64-bit */
#define MAX32 N->n * 2
#define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] )
#define STORE32 \
if( i % 2 ) { \
N->p[i/2] &= 0x00000000FFFFFFFF; \
N->p[i/2] |= ((t_uint) cur) << 32; \
} else { \
N->p[i/2] &= 0xFFFFFFFF00000000; \
N->p[i/2] |= (t_uint) cur; \
}
#endif /* sizeof( t_uint ) */
/*
* Helpers for addition and subtraction of chunks, with signed carry.
*/
static inline void add32( uint32_t *dst, uint32_t src, signed char *carry )
{
*dst += src;
*carry += ( *dst < src );
}
static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry )
{
*carry -= ( *dst < src );
*dst -= src;
}
#define ADD( j ) add32( &cur, A( j ), &c );
#define SUB( j ) sub32( &cur, A( j ), &c );
/*
* Helpers for the main 'loop'
* (see fix_negative for the motivation of C)
*/
#define INIT( b ) \
int ret; \
signed char c = 0, cc; \
uint32_t cur; \
size_t i = 0, bits = b; \
mpi C; \
t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ]; \
\
C.s = 1; \
C.n = b / 8 / sizeof( t_uint) + 1; \
C.p = Cp; \
memset( Cp, 0, C.n * sizeof( t_uint ) ); \
\
MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \
LOAD32;
#define NEXT \
STORE32; i++; LOAD32; \
cc = c; c = 0; \
if( cc < 0 ) \
sub32( &cur, -cc, &c ); \
else \
add32( &cur, cc, &c ); \
#define LAST \
STORE32; i++; \
cur = c > 0 ? c : 0; STORE32; \
cur = 0; while( ++i < MAX32 ) { STORE32; } \
if( c < 0 ) fix_negative( N, c, &C, bits );
/*
* If the result is negative, we get it in the form
* c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits'
*/
static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits )
{
int ret;
/* C = - c * 2^(bits + 32) */
#if !defined(POLARSSL_HAVE_INT64)
((void) bits);
#else
if( bits == 224 )
C->p[ C->n - 1 ] = ((t_uint) -c) << 32;
else
#endif
C->p[ C->n - 1 ] = (t_uint) -c;
/* N = - ( C - N ) */
MPI_CHK( mpi_sub_abs( N, C, N ) );
N->s = -1;
cleanup:
return( ret );
}
#if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED)
/*
* Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2)
*/
int ecp_mod_p224( mpi *N )
{
INIT( 224 );
SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11
SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12
SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13
SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11
SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12
SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13
SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10
cleanup:
return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED)
/*
* Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3)
*/
int ecp_mod_p256( mpi *N )
{
INIT( 256 );
ADD( 8 ); ADD( 9 );
SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0
ADD( 9 ); ADD( 10 );
SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1
ADD( 10 ); ADD( 11 );
SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2
ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 );
SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3
ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 );
SUB( 9 ); SUB( 10 ); NEXT; // A4
ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 );
SUB( 10 ); SUB( 11 ); NEXT; // A5
ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 );
SUB( 8 ); SUB( 9 ); NEXT; // A6
ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 );
SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7
cleanup:
return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED)
/*
* Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4)
*/
int ecp_mod_p384( mpi *N )
{
INIT( 384 );
ADD( 12 ); ADD( 21 ); ADD( 20 );
SUB( 23 ); NEXT; // A0
ADD( 13 ); ADD( 22 ); ADD( 23 );
SUB( 12 ); SUB( 20 ); NEXT; // A2
ADD( 14 ); ADD( 23 );
SUB( 13 ); SUB( 21 ); NEXT; // A2
ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 );
SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3
ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 );
SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4
ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 );
SUB( 16 ); NEXT; // A5
ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 );
SUB( 17 ); NEXT; // A6
ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 );
SUB( 18 ); NEXT; // A7
ADD( 20 ); ADD( 17 ); ADD( 16 );
SUB( 19 ); NEXT; // A8
ADD( 21 ); ADD( 18 ); ADD( 17 );
SUB( 20 ); NEXT; // A9
ADD( 22 ); ADD( 19 ); ADD( 18 );
SUB( 21 ); NEXT; // A10
ADD( 23 ); ADD( 20 ); ADD( 19 );
SUB( 22 ); LAST; // A11
cleanup:
return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */
#undef A
#undef LOAD32
#undef STORE32
#undef MAX32
#undef INIT
#undef NEXT
#undef LAST
#endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED ||
POLARSSL_ECP_DP_SECP256R1_ENABLED ||
POLARSSL_ECP_DP_SECP384R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
/*
* Here we have an actual Mersenne prime, so things are more straightforward.
* However, chunks are aligned on a 'weird' boundary (521 bits).
*/
/* Size of p521 in terms of t_uint */
#define P521_WIDTH ( 521 / 8 / sizeof( t_uint ) + 1 )
/* Bits to keep in the most significant t_uint */
#if defined(POLARSSL_HAVE_INT8)
#define P521_MASK 0x01
#else
#define P521_MASK 0x01FF
#endif
/*
* Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
* Write N as A1 + 2^521 A0, return A0 + A1
*/
int ecp_mod_p521( mpi *N )
{
int ret;
size_t i;
mpi M;
t_uint Mp[P521_WIDTH + 1];
/* Worst case for the size of M is when t_uint is 16 bits:
* we need to hold bits 513 to 1056, which is 34 limbs, that is
* P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */
if( N->n < P521_WIDTH )
return( 0 );
/* M = A1 */
M.s = 1;
M.n = N->n - ( P521_WIDTH - 1 );
if( M.n > P521_WIDTH + 1 )
M.n = P521_WIDTH + 1;
M.p = Mp;
memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) );
MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) );
/* N = A0 */
N->p[P521_WIDTH - 1] &= P521_MASK;
for( i = P521_WIDTH; i < N->n; i++ )
N->p[i] = 0;
/* N = A0 + A1 */
MPI_CHK( mpi_add_abs( N, N, &M ) );
cleanup:
return( ret );
}
#undef P521_WIDTH
#undef P521_MASK
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
#endif /* POLARSSL_ECP_NIST_OPTIM */
#endif
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