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Merge pull request #5377 from hanno-arm/ecp_add_mixed_fewer_mpis

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Minor improvements to ECC arithmetic subroutines
This commit is contained in:
Gilles Peskine 2022-02-17 10:27:18 +01:00 committed by GitHub
commit 57b1ff39c2
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GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 353 additions and 221 deletions
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574
library/ecp.c
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@ -342,6 +342,18 @@ int mbedtls_ecp_check_budget( const mbedtls_ecp_group *grp,
#endif /* MBEDTLS_ECP_RESTARTABLE */
static void mpi_init_many( mbedtls_mpi *arr, size_t size )
{
while( size-- )
mbedtls_mpi_init( arr++ );
}
static void mpi_free_many( mbedtls_mpi *arr, size_t size )
{
while( size-- )
mbedtls_mpi_free( arr++ );
}
/*
* List of supported curves:
* - internal ID
@ -1093,9 +1105,11 @@ cleanup:
* Reduce a mbedtls_mpi mod p in-place, to use after mbedtls_mpi_sub_mpi
* N->s < 0 is a very fast test, which fails only if N is 0
*/
#define MOD_SUB( N ) \
while( (N).s < 0 && mbedtls_mpi_cmp_int( &(N), 0 ) != 0 ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( &(N), &(N), &grp->P ) )
#define MOD_SUB( N ) \
do { \
while( (N)->s < 0 && mbedtls_mpi_cmp_int( (N), 0 ) != 0 ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( (N), (N), &grp->P ) ); \
} while( 0 )
#if ( defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
!( defined(MBEDTLS_ECP_NO_FALLBACK) && \
@ -1111,7 +1125,7 @@ static inline int mbedtls_mpi_sub_mod( const mbedtls_ecp_group *grp,
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( X, A, B ) );
MOD_SUB( *X );
MOD_SUB( X );
cleanup:
return( ret );
}
@ -1122,9 +1136,9 @@ cleanup:
* We known P, N and the result are positive, so sub_abs is correct, and
* a bit faster.
*/
#define MOD_ADD( N ) \
while( mbedtls_mpi_cmp_mpi( &(N), &grp->P ) >= 0 ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( &(N), &(N), &grp->P ) )
#define MOD_ADD( N ) \
while( mbedtls_mpi_cmp_mpi( (N), &grp->P ) >= 0 ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_abs( (N), (N), &grp->P ) )
static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
@ -1133,11 +1147,40 @@ static inline int mbedtls_mpi_add_mod( const mbedtls_ecp_group *grp,
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mpi( X, A, B ) );
MOD_ADD( *X );
MOD_ADD( X );
cleanup:
return( ret );
}
static inline int mbedtls_mpi_mul_int_mod( const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
const mbedtls_mpi *A,
mbedtls_mpi_uint c )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( X, A, c ) );
MOD_ADD( X );
cleanup:
return( ret );
}
static inline int mbedtls_mpi_sub_int_mod( const mbedtls_ecp_group *grp,
mbedtls_mpi *X,
const mbedtls_mpi *A,
mbedtls_mpi_uint c )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( X, A, c ) );
MOD_SUB( X );
cleanup:
return( ret );
}
#define MPI_ECP_SUB_INT( X, A, c ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int_mod( grp, X, A, c ) )
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED) && \
!( defined(MBEDTLS_ECP_NO_FALLBACK) && \
defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) && \
@ -1148,12 +1191,77 @@ static inline int mbedtls_mpi_shift_l_mod( const mbedtls_ecp_group *grp,
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l( X, count ) );
MOD_ADD( *X );
MOD_ADD( X );
cleanup:
return( ret );
}
#endif /* All functions referencing mbedtls_mpi_shift_l_mod() are alt-implemented without fallback */
/*
* Macro wrappers around ECP modular arithmetic
*
* Currently, these wrappers are defined via the bignum module.
*/
#define MPI_ECP_ADD( X, A, B ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, X, A, B ) )
#define MPI_ECP_SUB( X, A, B ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, X, A, B ) )
#define MPI_ECP_MUL( X, A, B ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, X, A, B ) )
#define MPI_ECP_SQR( X, A ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, X, A, A ) )
#define MPI_ECP_MUL_INT( X, A, c ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int_mod( grp, X, A, c ) )
#define MPI_ECP_INV( dst, src ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( (dst), (src), &grp->P ) )
#define MPI_ECP_MOV( X, A ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) )
#define MPI_ECP_SHIFT_L( X, count ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, X, count ) )
#define MPI_ECP_LSET( X, c ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, c ) )
#define MPI_ECP_CMP_INT( X, c ) \
mbedtls_mpi_cmp_int( X, c )
#define MPI_ECP_CMP( X, Y ) \
mbedtls_mpi_cmp_mpi( X, Y )
/* Needs f_rng, p_rng to be defined. */
#define MPI_ECP_RAND( X ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_random( (X), 2, &grp->P, f_rng, p_rng ) )
/* Conditional negation
* Needs grp and a temporary MPI tmp to be defined. */
#define MPI_ECP_COND_NEG( X, cond ) \
do \
{ \
unsigned char nonzero = mbedtls_mpi_cmp_int( (X), 0 ) != 0; \
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &tmp, &grp->P, (X) ) ); \
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( (X), &tmp, \
nonzero & cond ) ); \
} while( 0 )
#define MPI_ECP_NEG( X ) MPI_ECP_COND_NEG( (X), 1 )
#define MPI_ECP_VALID( X ) \
( (X)->p != NULL )
#define MPI_ECP_COND_ASSIGN( X, Y, cond ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( (X), (Y), (cond) ) )
#define MPI_ECP_COND_SWAP( X, Y, cond ) \
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( (X), (Y), (cond) ) )
#if defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
/*
* For curves in short Weierstrass form, we do all the internal operations in
@ -1169,7 +1277,7 @@ cleanup:
*/
static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *pt )
{
if( mbedtls_mpi_cmp_int( &pt->Z, 0 ) == 0 )
if( MPI_ECP_CMP_INT( &pt->Z, 0 ) == 0 )
return( 0 );
#if defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT)
@ -1181,30 +1289,20 @@ static int ecp_normalize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *p
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi Zi, ZZi;
mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
mbedtls_mpi T;
mbedtls_mpi_init( &T );
/*
* X = X / Z^2 mod p
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &Zi, &pt->Z, &grp->P ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ZZi ) );
MPI_ECP_INV( &T, &pt->Z ); /* T <- 1 / Z */
MPI_ECP_MUL( &pt->Y, &pt->Y, &T ); /* Y' <- Y*T = Y / Z */
MPI_ECP_SQR( &T, &T ); /* T <- T^2 = 1 / Z^2 */
MPI_ECP_MUL( &pt->X, &pt->X, &T ); /* X <- X * T = X / Z^2 */
MPI_ECP_MUL( &pt->Y, &pt->Y, &T ); /* Y'' <- Y' * T = Y / Z^3 */
/*
* Y = Y / Z^3 mod p
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ZZi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &Zi ) );
/*
* Z = 1
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
MPI_ECP_LSET( &pt->Z, 1 );
cleanup:
mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
mbedtls_mpi_free( &T );
return( ret );
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_NORMALIZE_JAC_ALT) */
@ -1237,52 +1335,58 @@ static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
size_t i;
mbedtls_mpi *c, u, Zi, ZZi;
mbedtls_mpi *c, t;
if( ( c = mbedtls_calloc( T_size, sizeof( mbedtls_mpi ) ) ) == NULL )
return( MBEDTLS_ERR_ECP_ALLOC_FAILED );
for( i = 0; i < T_size; i++ )
mbedtls_mpi_init( &c[i] );
mbedtls_mpi_init( &u ); mbedtls_mpi_init( &Zi ); mbedtls_mpi_init( &ZZi );
mbedtls_mpi_init( &t );
mpi_init_many( c, T_size );
/*
* c[i] = Z_0 * ... * Z_i
* c[i] = Z_0 * ... * Z_i, i = 0,..,n := T_size-1
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &c[0], &T[0]->Z ) );
MPI_ECP_MOV( &c[0], &T[0]->Z );
for( i = 1; i < T_size; i++ )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &c[i], &c[i-1], &T[i]->Z ) );
MPI_ECP_MUL( &c[i], &c[i-1], &T[i]->Z );
}
/*
* u = 1 / (Z_0 * ... * Z_n) mod P
* c[n] = 1 / (Z_0 * ... * Z_n) mod P
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &u, &c[T_size-1], &grp->P ) );
MPI_ECP_INV( &c[T_size-1], &c[T_size-1] );
for( i = T_size - 1; ; i-- )
{
/*
* Zi = 1 / Z_i mod p
* u = 1 / (Z_0 * ... * Z_i) mod P
/* At the start of iteration i (note that i decrements), we have
* - c[j] = Z_0 * .... * Z_j for j < i,
* - c[j] = 1 / (Z_0 * .... * Z_j) for j == i,
*
* This is maintained via
* - c[i-1] <- c[i] * Z_i
*
* We also derive 1/Z_i = c[i] * c[i-1] for i>0 and use that
* to do the actual normalization. For i==0, we already have
* c[0] = 1 / Z_0.
*/
if( i == 0 ) {
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &Zi, &u ) );
if( i > 0 )
{
/* Compute 1/Z_i and establish invariant for the next iteration. */
MPI_ECP_MUL( &t, &c[i], &c[i-1] );
MPI_ECP_MUL( &c[i-1], &c[i], &T[i]->Z );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Zi, &u, &c[i-1] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &u, &u, &T[i]->Z ) );
MPI_ECP_MOV( &t, &c[0] );
}
/*
* proceed as in normalize()
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ZZi, &Zi, &Zi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->X, &T[i]->X, &ZZi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &ZZi ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T[i]->Y, &T[i]->Y, &Zi ) );
/* Now t holds 1 / Z_i; normalize as in ecp_normalize_jac() */
MPI_ECP_MUL( &T[i]->Y, &T[i]->Y, &t );
MPI_ECP_SQR( &t, &t );
MPI_ECP_MUL( &T[i]->X, &T[i]->X, &t );
MPI_ECP_MUL( &T[i]->Y, &T[i]->Y, &t );
/*
* Post-precessing: reclaim some memory by shrinking coordinates
@ -1292,7 +1396,8 @@ static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->X, grp->P.n ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shrink( &T[i]->Y, grp->P.n ) );
mbedtls_mpi_free( &T[i]->Z );
MPI_ECP_LSET( &T[i]->Z, 1 );
if( i == 0 )
break;
@ -1300,9 +1405,8 @@ static int ecp_normalize_jac_many( const mbedtls_ecp_group *grp,
cleanup:
mbedtls_mpi_free( &u ); mbedtls_mpi_free( &Zi ); mbedtls_mpi_free( &ZZi );
for( i = 0; i < T_size; i++ )
mbedtls_mpi_free( &c[i] );
mbedtls_mpi_free( &t );
mpi_free_many( c, T_size );
mbedtls_free( c );
return( ret );
@ -1318,19 +1422,13 @@ static int ecp_safe_invert_jac( const mbedtls_ecp_group *grp,
unsigned char inv )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
unsigned char nonzero;
mbedtls_mpi mQY;
mbedtls_mpi tmp;
mbedtls_mpi_init( &tmp );
mbedtls_mpi_init( &mQY );
/* Use the fact that -Q.Y mod P = P - Q.Y unless Q.Y == 0 */
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &mQY, &grp->P, &Q->Y ) );
nonzero = mbedtls_mpi_cmp_int( &Q->Y, 0 ) != 0;
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &Q->Y, &mQY, inv & nonzero ) );
MPI_ECP_COND_NEG( &Q->Y, inv );
cleanup:
mbedtls_mpi_free( &mQY );
mbedtls_mpi_free( &tmp );
return( ret );
}
@ -1349,7 +1447,8 @@ cleanup:
* 3M + 6S + 1a otherwise
*/
static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point *P )
const mbedtls_ecp_point *P,
mbedtls_mpi tmp[4] )
{
#if defined(MBEDTLS_SELF_TEST)
dbl_count++;
@ -1364,67 +1463,64 @@ static int ecp_double_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi M, S, T, U;
mbedtls_mpi_init( &M ); mbedtls_mpi_init( &S ); mbedtls_mpi_init( &T ); mbedtls_mpi_init( &U );
/* Special case for A = -3 */
if( grp->A.p == NULL )
{
/* M = 3(X + Z^2)(X - Z^2) */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &T, &P->X, &S ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &U, &P->X, &S ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &U ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
/* tmp[0] <- M = 3(X + Z^2)(X - Z^2) */
MPI_ECP_SQR( &tmp[1], &P->Z );
MPI_ECP_ADD( &tmp[2], &P->X, &tmp[1] );
MPI_ECP_SUB( &tmp[3], &P->X, &tmp[1] );
MPI_ECP_MUL( &tmp[1], &tmp[2], &tmp[3] );
MPI_ECP_MUL_INT( &tmp[0], &tmp[1], 3 );
}
else
{
/* M = 3.X^2 */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &P->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_int( &M, &S, 3 ) ); MOD_ADD( M );
/* tmp[0] <- M = 3.X^2 + A.Z^4 */
MPI_ECP_SQR( &tmp[1], &P->X );
MPI_ECP_MUL_INT( &tmp[0], &tmp[1], 3 );
/* Optimize away for "koblitz" curves with A = 0 */
if( mbedtls_mpi_cmp_int( &grp->A, 0 ) != 0 )
if( MPI_ECP_CMP_INT( &grp->A, 0 ) != 0 )
{
/* M += A.Z^4 */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->Z, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &S, &S ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &T, &grp->A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &M, &M, &S ) );
MPI_ECP_SQR( &tmp[1], &P->Z );
MPI_ECP_SQR( &tmp[2], &tmp[1] );
MPI_ECP_MUL( &tmp[1], &tmp[2], &grp->A );
MPI_ECP_ADD( &tmp[0], &tmp[0], &tmp[1] );
}
}
/* S = 4.X.Y^2 */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &P->Y, &P->Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &P->X, &T ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &S, 1 ) );
/* tmp[1] <- S = 4.X.Y^2 */
MPI_ECP_SQR( &tmp[2], &P->Y );
MPI_ECP_SHIFT_L( &tmp[2], 1 );
MPI_ECP_MUL( &tmp[1], &P->X, &tmp[2] );
MPI_ECP_SHIFT_L( &tmp[1], 1 );
/* U = 8.Y^4 */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &T, &T ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
/* tmp[3] <- U = 8.Y^4 */
MPI_ECP_SQR( &tmp[3], &tmp[2] );
MPI_ECP_SHIFT_L( &tmp[3], 1 );
/* T = M^2 - 2.S */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T, &M, &M ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T, &T, &S ) );
/* tmp[2] <- T = M^2 - 2.S */
MPI_ECP_SQR( &tmp[2], &tmp[0] );
MPI_ECP_SUB( &tmp[2], &tmp[2], &tmp[1] );
MPI_ECP_SUB( &tmp[2], &tmp[2], &tmp[1] );
/* S = M(S - T) - U */
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &T ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S, &S, &M ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S, &S, &U ) );
/* tmp[1] <- S = M(S - T) - U */
MPI_ECP_SUB( &tmp[1], &tmp[1], &tmp[2] );
MPI_ECP_MUL( &tmp[1], &tmp[1], &tmp[0] );
MPI_ECP_SUB( &tmp[1], &tmp[1], &tmp[3] );
/* U = 2.Y.Z */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &U, &P->Y, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &U, 1 ) );
/* tmp[3] <- U = 2.Y.Z */
MPI_ECP_MUL( &tmp[3], &P->Y, &P->Z );
MPI_ECP_SHIFT_L( &tmp[3], 1 );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &T ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &S ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &U ) );
/* Store results */
MPI_ECP_MOV( &R->X, &tmp[2] );
MPI_ECP_MOV( &R->Y, &tmp[1] );
MPI_ECP_MOV( &R->Z, &tmp[3] );
cleanup:
mbedtls_mpi_free( &M ); mbedtls_mpi_free( &S ); mbedtls_mpi_free( &T ); mbedtls_mpi_free( &U );
return( ret );
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_JAC_ALT) */
@ -1436,6 +1532,10 @@ cleanup:
* The coordinates of Q must be normalized (= affine),
* but those of P don't need to. R is not normalized.
*
* P,Q,R may alias, but only at the level of EC points: they must be either
* equal as pointers, or disjoint (including the coordinate data buffers).
* Fine-grained aliasing at the level of coordinates is not supported.
*
* Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
* None of these cases can happen as intermediate step in ecp_mul_comb():
* - at each step, P, Q and R are multiples of the base point, the factor
@ -1444,12 +1544,11 @@ cleanup:
* due to the choice of precomputed points in the modified comb method.
* So branches for these cases do not leak secret information.
*
* We accept Q->Z being unset (saving memory in tables) as meaning 1.
*
* Cost: 1A := 8M + 3S
*/
static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q )
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
mbedtls_mpi tmp[4] )
{
#if defined(MBEDTLS_SELF_TEST)
add_count++;
@ -1464,39 +1563,45 @@ static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi T1, T2, T3, T4, X, Y, Z;
/* NOTE: Aliasing between input and output is allowed, so one has to make
* sure that at the point X,Y,Z are written, {P,Q}->{X,Y,Z} are no
* longer read from. */
mbedtls_mpi * const X = &R->X;
mbedtls_mpi * const Y = &R->Y;
mbedtls_mpi * const Z = &R->Z;
if( !MPI_ECP_VALID( &Q->Z ) )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
/*
* Trivial cases: P == 0 or Q == 0 (case 1)
*/
if( mbedtls_mpi_cmp_int( &P->Z, 0 ) == 0 )
if( MPI_ECP_CMP_INT( &P->Z, 0 ) == 0 )
return( mbedtls_ecp_copy( R, Q ) );
if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 0 ) == 0 )
if( MPI_ECP_CMP_INT( &Q->Z, 0 ) == 0 )
return( mbedtls_ecp_copy( R, P ) );
/*
* Make sure Q coordinates are normalized
*/
if( Q->Z.p != NULL && mbedtls_mpi_cmp_int( &Q->Z, 1 ) != 0 )
if( MPI_ECP_CMP_INT( &Q->Z, 1 ) != 0 )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 ); mbedtls_mpi_init( &T3 ); mbedtls_mpi_init( &T4 );
mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &P->Z, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T1, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T1, &T1, &Q->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T2, &T2, &Q->Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T1, &T1, &P->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T2, &T2, &P->Y ) );
MPI_ECP_SQR( &tmp[0], &P->Z );
MPI_ECP_MUL( &tmp[1], &tmp[0], &P->Z );
MPI_ECP_MUL( &tmp[0], &tmp[0], &Q->X );
MPI_ECP_MUL( &tmp[1], &tmp[1], &Q->Y );
MPI_ECP_SUB( &tmp[0], &tmp[0], &P->X );
MPI_ECP_SUB( &tmp[1], &tmp[1], &P->Y );
/* Special cases (2) and (3) */
if( mbedtls_mpi_cmp_int( &T1, 0 ) == 0 )
if( MPI_ECP_CMP_INT( &tmp[0], 0 ) == 0 )
{
if( mbedtls_mpi_cmp_int( &T2, 0 ) == 0 )
if( MPI_ECP_CMP_INT( &tmp[1], 0 ) == 0 )
{
ret = ecp_double_jac( grp, R, P );
ret = ecp_double_jac( grp, R, P, tmp );
goto cleanup;
}
else
@ -1506,29 +1611,27 @@ static int ecp_add_mixed( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
}
}
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &Z, &P->Z, &T1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T1, &T1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T3, &T1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &P->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &T1, &T3 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_shift_l_mod( grp, &T1, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &X, &T2, &T2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &X, &X, &T4 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &T3, &T3, &X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T3, &T3, &T2 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &T4, &T4, &P->Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &Y, &T3, &T4 ) );
/* {P,Q}->Z no longer used, so OK to write to Z even if there's aliasing. */
MPI_ECP_MUL( Z, &P->Z, &tmp[0] );
MPI_ECP_SQR( &tmp[2], &tmp[0] );
MPI_ECP_MUL( &tmp[3], &tmp[2], &tmp[0] );
MPI_ECP_MUL( &tmp[2], &tmp[2], &P->X );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->X, &X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Y, &Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &R->Z, &Z ) );
MPI_ECP_MOV( &tmp[0], &tmp[2] );
MPI_ECP_SHIFT_L( &tmp[0], 1 );
/* {P,Q}->X no longer used, so OK to write to X even if there's aliasing. */
MPI_ECP_SQR( X, &tmp[1] );
MPI_ECP_SUB( X, X, &tmp[0] );
MPI_ECP_SUB( X, X, &tmp[3] );
MPI_ECP_SUB( &tmp[2], &tmp[2], X );
MPI_ECP_MUL( &tmp[2], &tmp[2], &tmp[1] );
MPI_ECP_MUL( &tmp[3], &tmp[3], &P->Y );
/* {P,Q}->Y no longer used, so OK to write to Y even if there's aliasing. */
MPI_ECP_SUB( Y, &tmp[2], &tmp[3] );
cleanup:
mbedtls_mpi_free( &T1 ); mbedtls_mpi_free( &T2 ); mbedtls_mpi_free( &T3 ); mbedtls_mpi_free( &T4 );
mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
return( ret );
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_ADD_MIXED_ALT) */
}
@ -1552,26 +1655,28 @@ static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *p
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi l, ll;
mbedtls_mpi l;
mbedtls_mpi_init( &l ); mbedtls_mpi_init( &ll );
mbedtls_mpi_init( &l );
/* Generate l such that 1 < l < p */
MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
MPI_ECP_RAND( &l );
/* Z = l * Z */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Z, &pt->Z, &l ) );
/* Z' = l * Z */
MPI_ECP_MUL( &pt->Z, &pt->Z, &l );
/* X = l^2 * X */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &l, &l ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->X, &pt->X, &ll ) );
/* Y' = l * Y */
MPI_ECP_MUL( &pt->Y, &pt->Y, &l );
/* Y = l^3 * Y */
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &ll, &ll, &l ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &pt->Y, &pt->Y, &ll ) );
/* X' = l^2 * X */
MPI_ECP_SQR( &l, &l );
MPI_ECP_MUL( &pt->X, &pt->X, &l );
/* Y'' = l^2 * Y' = l^3 * Y */
MPI_ECP_MUL( &pt->Y, &pt->Y, &l );
cleanup:
mbedtls_mpi_free( &l ); mbedtls_mpi_free( &ll );
mbedtls_mpi_free( &l );
if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
@ -1714,6 +1819,10 @@ static int ecp_precompute_comb( const mbedtls_ecp_group *grp,
const unsigned char T_size = 1U << ( w - 1 );
mbedtls_ecp_point *cur, *TT[COMB_MAX_PRE - 1];
mbedtls_mpi tmp[4];
mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->rsm != NULL )
{
@ -1764,7 +1873,7 @@ dbl:
if( j % d == 0 )
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( cur, T + ( i >> 1 ) ) );
MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur ) );
MBEDTLS_MPI_CHK( ecp_double_jac( grp, cur, cur, tmp ) );
}
#if defined(MBEDTLS_ECP_RESTARTABLE)
@ -1774,8 +1883,11 @@ dbl:
norm_dbl:
#endif
/*
* Normalize current elements in T. As T has holes,
* use an auxiliary array of pointers to elements in T.
* Normalize current elements in T to allow them to be used in
* ecp_add_mixed() below, which requires one normalized input.
*
* As T has holes, use an auxiliary array of pointers to elements in T.
*
*/
j = 0;
for( i = 1; i < T_size; i <<= 1 )
@ -1801,7 +1913,7 @@ add:
{
j = i;
while( j-- )
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i] ) );
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, &T[i + j], &T[j], &T[i], tmp ) );
}
#if defined(MBEDTLS_ECP_RESTARTABLE)
@ -1822,7 +1934,18 @@ norm_add:
MBEDTLS_MPI_CHK( ecp_normalize_jac_many( grp, TT, j ) );
/* Free Z coordinate (=1 after normalization) to save RAM.
* This makes T[i] invalid as mbedtls_ecp_points, but this is OK
* since from this point onwards, they are only accessed indirectly
* via the getter function ecp_select_comb() which does set the
* target's Z coordinate to 1. */
for( i = 0; i < T_size; i++ )
mbedtls_mpi_free( &T[i].Z );
cleanup:
mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
ret == MBEDTLS_ERR_ECP_IN_PROGRESS )
@ -1853,13 +1976,15 @@ static int ecp_select_comb( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
/* Read the whole table to thwart cache-based timing attacks */
for( j = 0; j < T_size; j++ )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->X, &T[j].X, j == ii ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_assign( &R->Y, &T[j].Y, j == ii ) );
MPI_ECP_COND_ASSIGN( &R->X, &T[j].X, j == ii );
MPI_ECP_COND_ASSIGN( &R->Y, &T[j].Y, j == ii );
}
/* Safely invert result if i is "negative" */
MBEDTLS_MPI_CHK( ecp_safe_invert_jac( grp, R, i >> 7 ) );
MPI_ECP_LSET( &R->Z, 1 );
cleanup:
return( ret );
}
@ -1879,9 +2004,11 @@ static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_ecp_point Txi;
mbedtls_mpi tmp[4];
size_t i;
mbedtls_ecp_point_init( &Txi );
mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
#if !defined(MBEDTLS_ECP_RESTARTABLE)
(void) rs_ctx;
@ -1907,7 +2034,6 @@ static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R
/* Start with a non-zero point and randomize its coordinates */
i = d;
MBEDTLS_MPI_CHK( ecp_select_comb( grp, R, T, T_size, x[i] ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 1 ) );
if( f_rng != 0 )
MBEDTLS_MPI_CHK( ecp_randomize_jac( grp, R, f_rng, p_rng ) );
}
@ -1917,14 +2043,15 @@ static int ecp_mul_comb_core( const mbedtls_ecp_group *grp, mbedtls_ecp_point *R
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_DBL + MBEDTLS_ECP_OPS_ADD );
--i;
MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R ) );
MBEDTLS_MPI_CHK( ecp_double_jac( grp, R, R, tmp ) );
MBEDTLS_MPI_CHK( ecp_select_comb( grp, &Txi, T, T_size, x[i] ) );
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi ) );
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, R, R, &Txi, tmp ) );
}
cleanup:
mbedtls_ecp_point_free( &Txi );
mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->rsm != NULL &&
@ -2127,8 +2254,8 @@ static int ecp_mul_comb( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
/* Is P the base point ? */
#if MBEDTLS_ECP_FIXED_POINT_OPTIM == 1
p_eq_g = ( mbedtls_mpi_cmp_mpi( &P->Y, &grp->G.Y ) == 0 &&
mbedtls_mpi_cmp_mpi( &P->X, &grp->G.X ) == 0 );
p_eq_g = ( MPI_ECP_CMP( &P->Y, &grp->G.Y ) == 0 &&
MPI_ECP_CMP( &P->X, &grp->G.X ) == 0 );
#else
p_eq_g = 0;
#endif
@ -2258,9 +2385,9 @@ static int ecp_normalize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &P->Z, &P->Z, &grp->P ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &P->Z, 1 ) );
MPI_ECP_INV( &P->Z, &P->Z );
MPI_ECP_MUL( &P->X, &P->X, &P->Z );
MPI_ECP_LSET( &P->Z, 1 );
cleanup:
return( ret );
@ -2291,10 +2418,10 @@ static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P
mbedtls_mpi_init( &l );
/* Generate l such that 1 < l < p */
MBEDTLS_MPI_CHK( mbedtls_mpi_random( &l, 2, &grp->P, f_rng, p_rng ) );
MPI_ECP_RAND( &l );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->X, &P->X, &l ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &P->Z, &P->Z, &l ) );
MPI_ECP_MUL( &P->X, &P->X, &l );
MPI_ECP_MUL( &P->Z, &P->Z, &l );
cleanup:
mbedtls_mpi_free( &l );
@ -2323,7 +2450,8 @@ cleanup:
static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
mbedtls_ecp_point *R, mbedtls_ecp_point *S,
const mbedtls_ecp_point *P, const mbedtls_ecp_point *Q,
const mbedtls_mpi *d )
const mbedtls_mpi *d,
mbedtls_mpi T[4] )
{
#if defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT)
if( mbedtls_internal_ecp_grp_capable( grp ) )
@ -2334,35 +2462,27 @@ static int ecp_double_add_mxz( const mbedtls_ecp_group *grp,
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
#else
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi A, AA, B, BB, E, C, D, DA, CB;
mbedtls_mpi_init( &A ); mbedtls_mpi_init( &AA ); mbedtls_mpi_init( &B );
mbedtls_mpi_init( &BB ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &C );
mbedtls_mpi_init( &D ); mbedtls_mpi_init( &DA ); mbedtls_mpi_init( &CB );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &A, &P->X, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &AA, &A, &A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &B, &P->X, &P->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &BB, &B, &B ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &E, &AA, &BB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &C, &Q->X, &Q->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &D, &Q->X, &Q->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &DA, &D, &A ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &CB, &C, &B ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &S->X, &DA, &CB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->X, &S->X, &S->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mod( grp, &S->Z, &DA, &CB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, &S->Z, &S->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &S->Z, d, &S->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->X, &AA, &BB ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &grp->A, &E ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &R->Z, &BB, &R->Z ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &R->Z, &E, &R->Z ) );
MPI_ECP_ADD( &T[0], &P->X, &P->Z ); /* Pp := PX + PZ */
MPI_ECP_SUB( &T[1], &P->X, &P->Z ); /* Pm := PX - PZ */
MPI_ECP_ADD( &T[2], &Q->X, &Q->Z ); /* Qp := QX + XZ */
MPI_ECP_SUB( &T[3], &Q->X, &Q->Z ); /* Qm := QX - QZ */
MPI_ECP_MUL( &T[3], &T[3], &T[0] ); /* Qm * Pp */
MPI_ECP_MUL( &T[2], &T[2], &T[1] ); /* Qp * Pm */
MPI_ECP_SQR( &T[0], &T[0] ); /* Pp^2 */
MPI_ECP_SQR( &T[1], &T[1] ); /* Pm^2 */
MPI_ECP_MUL( &R->X, &T[0], &T[1] ); /* Pp^2 * Pm^2 */
MPI_ECP_SUB( &T[0], &T[0], &T[1] ); /* Pp^2 - Pm^2 */
MPI_ECP_MUL( &R->Z, &grp->A, &T[0] ); /* A * (Pp^2 - Pm^2) */
MPI_ECP_ADD( &R->Z, &T[1], &R->Z ); /* [ A * (Pp^2-Pm^2) ] + Pm^2 */
MPI_ECP_ADD( &S->X, &T[3], &T[2] ); /* Qm*Pp + Qp*Pm */
MPI_ECP_SQR( &S->X, &S->X ); /* (Qm*Pp + Qp*Pm)^2 */
MPI_ECP_SUB( &S->Z, &T[3], &T[2] ); /* Qm*Pp - Qp*Pm */
MPI_ECP_SQR( &S->Z, &S->Z ); /* (Qm*Pp - Qp*Pm)^2 */
MPI_ECP_MUL( &S->Z, d, &S->Z ); /* d * ( Qm*Pp - Qp*Pm )^2 */
MPI_ECP_MUL( &R->Z, &T[0], &R->Z ); /* [A*(Pp^2-Pm^2)+Pm^2]*(Pp^2-Pm^2) */
cleanup:
mbedtls_mpi_free( &A ); mbedtls_mpi_free( &AA ); mbedtls_mpi_free( &B );
mbedtls_mpi_free( &BB ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &C );
mbedtls_mpi_free( &D ); mbedtls_mpi_free( &DA ); mbedtls_mpi_free( &CB );
return( ret );
#endif /* !defined(MBEDTLS_ECP_NO_FALLBACK) || !defined(MBEDTLS_ECP_DOUBLE_ADD_MXZ_ALT) */
@ -2382,22 +2502,25 @@ static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
unsigned char b;
mbedtls_ecp_point RP;
mbedtls_mpi PX;
mbedtls_mpi tmp[4];
mbedtls_ecp_point_init( &RP ); mbedtls_mpi_init( &PX );
mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
if( f_rng == NULL )
return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
/* Save PX and read from P before writing to R, in case P == R */
MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &PX, &P->X ) );
MPI_ECP_MOV( &PX, &P->X );
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( &RP, P ) );
/* Set R to zero in modified x/z coordinates */
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->X, 1 ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &R->Z, 0 ) );
MPI_ECP_LSET( &R->X, 1 );
MPI_ECP_LSET( &R->Z, 0 );
mbedtls_mpi_free( &R->Y );
/* RP.X might be sligtly larger than P, so reduce it */
MOD_ADD( RP.X );
MOD_ADD( &RP.X );
/* Randomize coordinates of the starting point */
MBEDTLS_MPI_CHK( ecp_randomize_mxz( grp, &RP, f_rng, p_rng ) );
@ -2414,11 +2537,11 @@ static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
* else double_add( R, RP, R, RP )
* but using safe conditional swaps to avoid leaks
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->X, &RP.X, b ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_safe_cond_swap( &R->Z, &RP.Z, b ) );
MPI_ECP_COND_SWAP( &R->X, &RP.X, b );
MPI_ECP_COND_SWAP( &R->Z, &RP.Z, b );
MBEDTLS_MPI_CHK( ecp_double_add_mxz( grp, R, &RP, R, &RP, &PX, tmp ) );
MPI_ECP_COND_SWAP( &R->X, &RP.X, b );
MPI_ECP_COND_SWAP( &R->Z, &RP.Z, b );
}
/*
@ -2438,6 +2561,7 @@ static int ecp_mul_mxz( mbedtls_ecp_group *grp, mbedtls_ecp_point *R,
cleanup:
mbedtls_ecp_point_free( &RP ); mbedtls_mpi_free( &PX );
mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
return( ret );
}
@ -2566,23 +2690,23 @@ static int ecp_check_pubkey_sw( const mbedtls_ecp_group *grp, const mbedtls_ecp_
* YY = Y^2
* RHS = X (X^2 + A) + B = X^3 + A X + B
*/
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &YY, &pt->Y, &pt->Y ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &pt->X, &pt->X ) );
MPI_ECP_SQR( &YY, &pt->Y );
MPI_ECP_SQR( &RHS, &pt->X );
/* Special case for A = -3 */
if( grp->A.p == NULL )
{
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &RHS, &RHS, 3 ) ); MOD_SUB( RHS );
MPI_ECP_SUB_INT( &RHS, &RHS, 3 );
}
else
{
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->A ) );
MPI_ECP_ADD( &RHS, &RHS, &grp->A );
}
MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mod( grp, &RHS, &RHS, &pt->X ) );
MBEDTLS_MPI_CHK( mbedtls_mpi_add_mod( grp, &RHS, &RHS, &grp->B ) );
MPI_ECP_MUL( &RHS, &RHS, &pt->X );
MPI_ECP_ADD( &RHS, &RHS, &grp->B );
if( mbedtls_mpi_cmp_mpi( &YY, &RHS ) != 0 )
if( MPI_ECP_CMP( &YY, &RHS ) != 0 )
ret = MBEDTLS_ERR_ECP_INVALID_KEY;
cleanup:
@ -2605,6 +2729,8 @@ static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
mbedtls_ecp_restart_ctx *rs_ctx )
{
int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
mbedtls_mpi tmp;
mbedtls_mpi_init( &tmp );
if( mbedtls_mpi_cmp_int( m, 0 ) == 0 )
{
@ -2617,8 +2743,7 @@ static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
else if( mbedtls_mpi_cmp_int( m, -1 ) == 0 )
{
MBEDTLS_MPI_CHK( mbedtls_ecp_copy( R, P ) );
if( mbedtls_mpi_cmp_int( &R->Y, 0 ) != 0 )
MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
MPI_ECP_NEG( &R->Y );
}
else
{
@ -2627,6 +2752,8 @@ static int mbedtls_ecp_mul_shortcuts( mbedtls_ecp_group *grp,
}
cleanup:
mbedtls_mpi_free( &tmp );
return( ret );
}
@ -2644,6 +2771,7 @@ int mbedtls_ecp_muladd_restartable(
mbedtls_ecp_point mP;
mbedtls_ecp_point *pmP = &mP;
mbedtls_ecp_point *pR = R;
mbedtls_mpi tmp[4];
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
char is_grp_capable = 0;
#endif
@ -2658,6 +2786,7 @@ int mbedtls_ecp_muladd_restartable(
return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
mbedtls_ecp_point_init( &mP );
mpi_init_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
ECP_RS_ENTER( ma );
@ -2699,7 +2828,7 @@ mul2:
add:
#endif
MBEDTLS_ECP_BUDGET( MBEDTLS_ECP_OPS_ADD );
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR ) );
MBEDTLS_MPI_CHK( ecp_add_mixed( grp, pR, pmP, pR, tmp ) );
#if defined(MBEDTLS_ECP_RESTARTABLE)
if( rs_ctx != NULL && rs_ctx->ma != NULL )
rs_ctx->ma->state = ecp_rsma_norm;
@ -2715,6 +2844,9 @@ norm:
#endif
cleanup:
mpi_free_many( tmp, sizeof( tmp ) / sizeof( mbedtls_mpi ) );
#if defined(MBEDTLS_ECP_INTERNAL_ALT)
if( is_grp_capable )
mbedtls_internal_ecp_free( grp );