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Merged optimizations for MODP NIST curves

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This commit is contained in:
Paul Bakker 2013-10-28 14:16:59 +01:00
commit 3f917e230d
7 changed files with 687 additions and 311 deletions
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756
library/ecp.c
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@ -111,6 +111,42 @@ const ecp_curve_info *ecp_curve_list( void )
return ecp_supported_curves;
}
/*
* Get the curve info for the internal identifer
*/
const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id )
{
const ecp_curve_info *curve_info;
for( curve_info = ecp_curve_list();
curve_info->grp_id != POLARSSL_ECP_DP_NONE;
curve_info++ )
{
if( curve_info->grp_id == grp_id )
return( curve_info );
}
return( NULL );
}
/*
* Get the curve info from the TLS identifier
*/
const ecp_curve_info *ecp_curve_info_from_tls_id( uint16_t tls_id )
{
const ecp_curve_info *curve_info;
for( curve_info = ecp_curve_list();
curve_info->grp_id != POLARSSL_ECP_DP_NONE;
curve_info++ )
{
if( curve_info->tls_id == tls_id )
return( curve_info );
}
return( NULL );
}
/*
* Initialize (the components of) a point
*/
@ -200,6 +236,29 @@ void ecp_keypair_free( ecp_keypair *key )
ecp_point_free( &key->Q );
}
/*
* Copy the contents of a point
*/
int ecp_copy( ecp_point *P, const ecp_point *Q )
{
int ret;
MPI_CHK( mpi_copy( &P->X, &Q->X ) );
MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
MPI_CHK( mpi_copy( &P->Z, &Q->Z ) );
cleanup:
return( ret );
}
/*
* Copy the contents of a group object
*/
int ecp_group_copy( ecp_group *dst, const ecp_group *src )
{
return ecp_use_known_dp( dst, src->id );
}
/*
* Set point to zero
*/
@ -223,29 +282,6 @@ int ecp_is_zero( ecp_point *pt )
return( mpi_cmp_int( &pt->Z, 0 ) == 0 );
}
/*
* Copy the contents of Q into P
*/
int ecp_copy( ecp_point *P, const ecp_point *Q )
{
int ret;
MPI_CHK( mpi_copy( &P->X, &Q->X ) );
MPI_CHK( mpi_copy( &P->Y, &Q->Y ) );
MPI_CHK( mpi_copy( &P->Z, &Q->Z ) );
cleanup:
return( ret );
}
/*
* Copy the contents of a group object
*/
int ecp_group_copy( ecp_group *dst, const ecp_group *src )
{
return ecp_use_known_dp( dst, src->id );
}
/*
* Import a non-zero point from ASCII strings
*/
@ -262,50 +298,6 @@ cleanup:
return( ret );
}
/*
* 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 );
}
/*
* Import an ECP group from ASCII strings, case A == -3
*/
int ecp_group_read_string( ecp_group *grp, int radix,
const char *p, const char *b,
const char *gx, const char *gy, const char *n)
{
int ret;
MPI_CHK( ecp_group_read_string_gen( grp, radix, p, "00", b, gx, gy, n ) );
MPI_CHK( mpi_add_int( &grp->A, &grp->P, -3 ) );
cleanup:
if( ret != 0 )
ecp_group_free( grp );
return( ret );
}
/*
* Export a point into unsigned binary data (SEC1 2.3.3)
*/
@ -449,150 +441,48 @@ int ecp_tls_write_point( const ecp_group *grp, const ecp_point *pt,
}
/*
* Wrapper around fast quasi-modp functions, with fall-back to mpi_mod_mpi.
* See the documentation of struct ecp_group.
* Import an ECP group from ASCII strings, general case (A used)
*/
static int ecp_modp( mpi *N, const ecp_group *grp )
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;
if( grp->modp == NULL )
return( mpi_mod_mpi( N, N, &grp->P ) );
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 ) );
if( mpi_cmp_int( N, 0 ) < 0 || mpi_msb( N ) > 2 * grp->pbits )
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
MPI_CHK( grp->modp( N ) );
while( mpi_cmp_int( N, 0 ) < 0 )
MPI_CHK( mpi_add_mpi( N, N, &grp->P ) );
while( mpi_cmp_mpi( N, &grp->P ) >= 0 )
MPI_CHK( mpi_sub_mpi( N, N, &grp->P ) );
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_DP_SECP192R1_ENABLED)
/*
* 192 bits in terms of t_uint
* Import an ECP group from ASCII strings, case A == -3
*/
#define P192_SIZE_INT ( 192 / CHAR_BIT / sizeof( t_uint ) )
/*
* Table to get S1, S2, S3 of FIPS 186-3 D.2.1:
* -1 means let this chunk be 0
* a positive value i means A_i.
*/
#define P192_CHUNKS 3
#define P192_CHUNK_CHAR ( 64 / CHAR_BIT )
#define P192_CHUNK_INT ( P192_CHUNK_CHAR / sizeof( t_uint ) )
const signed char p192_tbl[][P192_CHUNKS] = {
{ -1, 3, 3 }, /* S1 */
{ 4, 4, -1 }, /* S2 */
{ 5, 5, 5 }, /* S3 */
};
/*
* Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1)
*/
static int ecp_mod_p192( mpi *N )
int ecp_group_read_string( ecp_group *grp, int radix,
const char *p, const char *b,
const char *gx, const char *gy, const char *n)
{
int ret;
unsigned char i, j, offset;
signed char chunk;
mpi tmp, acc;
t_uint tmp_p[P192_SIZE_INT], acc_p[P192_SIZE_INT + 1];
tmp.s = 1;
tmp.n = sizeof( tmp_p ) / sizeof( tmp_p[0] );
tmp.p = tmp_p;
acc.s = 1;
acc.n = sizeof( acc_p ) / sizeof( acc_p[0] );
acc.p = acc_p;
MPI_CHK( mpi_grow( N, P192_SIZE_INT * 2 ) );
/*
* acc = T
*/
memset( acc_p, 0, sizeof( acc_p ) );
memcpy( acc_p, N->p, P192_CHUNK_CHAR * P192_CHUNKS );
for( i = 0; i < sizeof( p192_tbl ) / sizeof( p192_tbl[0] ); i++)
{
/*
* tmp = S_i
*/
memset( tmp_p, 0, sizeof( tmp_p ) );
for( j = 0, offset = P192_CHUNKS - 1; j < P192_CHUNKS; j++, offset-- )
{
chunk = p192_tbl[i][j];
if( chunk >= 0 )
memcpy( tmp_p + offset * P192_CHUNK_INT,
N->p + chunk * P192_CHUNK_INT,
P192_CHUNK_CHAR );
}
/*
* acc += tmp
*/
MPI_CHK( mpi_add_abs( &acc, &acc, &tmp ) );
}
MPI_CHK( mpi_copy( N, &acc ) );
MPI_CHK( ecp_group_read_string_gen( grp, radix, p, "00", b, gx, gy, n ) );
MPI_CHK( mpi_add_int( &grp->A, &grp->P, -3 ) );
cleanup:
if( ret != 0 )
ecp_group_free( grp );
return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */
#if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED)
/*
* Size of p521 in terms of t_uint
*/
#define P521_SIZE_INT ( 521 / CHAR_BIT / sizeof( t_uint ) + 1 )
/*
* Bits to keep in the most significant t_uint
*/
#if defined(POLARSS_HAVE_INT8)
#define P521_MASK 0x01
#else
#define P521_MASK 0x01FF
#endif
/*
* Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5)
*/
static int ecp_mod_p521( mpi *N )
{
int ret;
t_uint Mp[P521_SIZE_INT];
mpi M;
if( N->n < P521_SIZE_INT )
return( 0 );
memset( Mp, 0, P521_SIZE_INT * sizeof( t_uint ) );
memcpy( Mp, N->p, P521_SIZE_INT * sizeof( t_uint ) );
Mp[P521_SIZE_INT - 1] &= P521_MASK;
M.s = 1;
M.n = P521_SIZE_INT;
M.p = Mp;
MPI_CHK( mpi_shift_r( N, 521 ) );
MPI_CHK( mpi_add_abs( N, N, &M ) );
cleanup:
return( ret );
}
#endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */
/*
* Domain parameters for secp192r1
@ -739,6 +629,15 @@ cleanup:
"AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \
"70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069"
#if defined(POLARSSL_ECP_NIST_OPTIM)
/* Forward declarations */
static int ecp_mod_p192( mpi * );
static int ecp_mod_p224( mpi * );
static int ecp_mod_p256( mpi * );
static int ecp_mod_p384( mpi * );
static int ecp_mod_p521( mpi * );
#endif
/*
* Set a group using well-known domain parameters
*/
@ -750,7 +649,9 @@ int ecp_use_known_dp( ecp_group *grp, ecp_group_id 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 ) );
@ -758,6 +659,9 @@ int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
#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 ) );
@ -765,6 +669,9 @@ int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
#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 ) );
@ -772,6 +679,9 @@ int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
#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 ) );
@ -779,7 +689,9 @@ int ecp_use_known_dp( ecp_group *grp, ecp_group_id id )
#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 ) );
@ -878,39 +790,37 @@ int ecp_tls_write_group( const ecp_group *grp, size_t *olen,
}
/*
* Get the curve info from the TLS identifier
* Wrapper around fast quasi-modp functions, with fall-back to mpi_mod_mpi.
* See the documentation of struct ecp_group.
*
* This function is in the critial loop for ecp_mul, so pay attention to perf.
*/
const ecp_curve_info *ecp_curve_info_from_tls_id( uint16_t tls_id )
static int ecp_modp( mpi *N, const ecp_group *grp )
{
const ecp_curve_info *curve_info;
int ret;
for( curve_info = ecp_curve_list();
curve_info->grp_id != POLARSSL_ECP_DP_NONE;
curve_info++ )
if( grp->modp == NULL )
return( mpi_mod_mpi( N, N, &grp->P ) );
/* N->s < 0 is a much faster test, which fails only if N is 0 */
if( ( N->s < 0 && mpi_cmp_int( N, 0 ) != 0 ) ||
mpi_msb( N ) > 2 * grp->pbits )
{
if( curve_info->tls_id == tls_id )
return( curve_info );
return( POLARSSL_ERR_ECP_BAD_INPUT_DATA );
}
return( NULL );
}
MPI_CHK( grp->modp( N ) );
/*
* Get the curve info for the internal identifer
*/
const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id )
{
const ecp_curve_info *curve_info;
/* N->s < 0 is a much faster test, which fails only if N is 0 */
while( N->s < 0 && mpi_cmp_int( N, 0 ) != 0 )
MPI_CHK( mpi_add_mpi( N, N, &grp->P ) );
for( curve_info = ecp_curve_list();
curve_info->grp_id != POLARSSL_ECP_DP_NONE;
curve_info++ )
{
if( curve_info->grp_id == grp_id )
return( curve_info );
}
while( mpi_cmp_mpi( N, &grp->P ) >= 0 )
/* we known P, N and the result are positive */
MPI_CHK( mpi_sub_abs( N, N, &grp->P ) );
return( NULL );
cleanup:
return( ret );
}
/*
@ -930,17 +840,20 @@ const ecp_curve_info *ecp_curve_info_from_grp_id( ecp_group_id grp_id )
/*
* Reduce a mpi mod p in-place, to use after mpi_sub_mpi
* N->s < 0 is a very fast test, which fails only if N is 0
*/
#define MOD_SUB( N ) \
while( mpi_cmp_int( &N, 0 ) < 0 ) \
while( N.s < 0 && mpi_cmp_int( &N, 0 ) != 0 ) \
MPI_CHK( mpi_add_mpi( &N, &N, &grp->P ) )
/*
* Reduce a mpi mod p in-place, to use after mpi_add_mpi and mpi_mul_int
* Reduce a mpi mod p in-place, to use after mpi_add_mpi and mpi_mul_int.
* We known P, N and the result are positive, so sub_abs is correct, and
* a bit faster.
*/
#define MOD_ADD( N ) \
while( mpi_cmp_mpi( &N, &grp->P ) >= 0 ) \
MPI_CHK( mpi_sub_mpi( &N, &N, &grp->P ) )
MPI_CHK( mpi_sub_abs( &N, &N, &grp->P ) )
/*
* Normalize jacobian coordinates so that Z == 0 || Z == 1 (GECC 3.2.1)
@ -1117,7 +1030,7 @@ cleanup:
}
/*
* Addition or subtraction: R = P + Q or R = P + Q,
* Addition or subtraction: R = P + Q or R = P - Q,
* mixed affine-Jacobian coordinates (GECC 3.22)
*
* The coordinates of Q must be normalized (= affine),
@ -1667,6 +1580,409 @@ int ecp_gen_keypair( ecp_group *grp, mpi *d, ecp_point *Q,
return( ecp_mul( grp, Q, d, &grp->G, f_rng, p_rng ) );
}
#if defined(POLARSSL_ECP_NIST_OPTIM)
/*
* Fast reduction modulo the primes used by the NIST curves.
*
* These functions are: critical for speed, but not need 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)
*/
static 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] = (uint8_t)( cur ); \
N->p[4*i+1] = (uint8_t)( cur >> 8 ); \
N->p[4*i+2] = (uint8_t)( cur >> 16 ); \
N->p[4*i+3] = (uint8_t)( 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] = (uint16_t)( cur ); \
N->p[2*i+1] = (uint16_t)( 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] |= ((uint64_t) cur) << 32; \
} else { \
N->p[i/2] &= 0xFFFFFFFF00000000; \
N->p[i/2] |= (uint64_t) 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)
*/
static 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)
*/
static 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)
*/
static 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
*/
static 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 */
#if defined(POLARSSL_SELF_TEST)
/*