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https://github.com/yuzu-emu/mbedtls.git
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Made ecp_mul() faster and truly SPA resistant
This commit is contained in:
Manuel Pégourié-Gonnard
Paul Bakker
parent
7652a593d6
commit
b63f9e98f5
@ -97,17 +97,23 @@ ecp_group;
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#define POLARSSL_ECP_DP_SECP384R1 3
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#define POLARSSL_ECP_DP_SECP521R1 4
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/**
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* Maximum bit size of the groups (that is, of N)
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*/
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#define POLARSSL_ECP_MAX_N_BITS 521
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/*
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* Maximum NAF width used for point multipliation. Default: 7.
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* Maximum window size (actually, NAF width) used for point multipliation.
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* Default: 7.
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* Minimum value: 2. Maximum value: 8.
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*
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* Result is an array of at most ( 1 << ( POLARSSL_ECP_NAF_WIDTH - 1 ) )
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* Result is an array of at most ( 1 << ( POLARSSL_ECP_WINDOW_SIZE - 1 ) )
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* points used for point multiplication, so at most 64 by default.
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* In practice, most curves will use less precomputed points.
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*
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* Reduction in size may reduce speed for big curves.
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*/
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#define POLARSSL_ECP_NAF_WIDTH 7 /**< Maximum NAF width used. */
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#define POLARSSL_ECP_WINDOW_SIZE 7 /**< Maximum NAF width used. */
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#ifdef __cplusplus
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extern "C" {
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@ -236,7 +242,11 @@ int ecp_sub( const ecp_group *grp, ecp_point *R,
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*
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* \return 0 if successful,
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* POLARSSL_ERR_MPI_MALLOC_FAILED if memory allocation failed
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* POLARSSL_ERR_ECP_GENERIC if m < 0
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* POLARSSL_ERR_ECP_GENERIC if m < 0 of m has greater bit
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* length than N, the number of points in the group.
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*
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* \note This function executes a constant number of operations
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* for random m in the allowed range.
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*/
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int ecp_mul( const ecp_group *grp, ecp_point *R,
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const mpi *m, const ecp_point *P );
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171
library/ecp.c
171
library/ecp.c
@ -768,8 +768,9 @@ cleanup:
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* Precompute odd multiples of P up to (2 * t_len - 1) P.
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* The table is filled with T[i] = (2 * i + 1) P.
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*/
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static int ecp_precompute( ecp_point T[], size_t t_len,
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const ecp_group *grp, const ecp_point *P )
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static int ecp_precompute( const ecp_group *grp,
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ecp_point T[], size_t t_len,
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const ecp_point *P )
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{
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int ret;
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size_t i;
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@ -795,47 +796,114 @@ cleanup:
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}
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/*
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* Integer multiplication: R = m * P (GECC 5.7, SPA-resistant)
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* Maximum length of the precomputed table
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*/
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#define MAX_PRE_LEN ( 1 << (POLARSSL_ECP_WINDOW_SIZE - 1) )
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/*
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* Maximum length of the NAF: ceil( grp->nbits + 1 ) / w
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* (that is: grp->nbits / w + 1)
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* Allow p_bits + 1 bits in case M = grp->N + 1 is one bit longer than N.
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*/
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#define MAX_NAF_LEN ( POLARSSL_ECP_MAX_N_BITS / 2 + 1 )
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/*
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* Integer multiplication: R = m * P
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*
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* Based on fixed-pattern width-w NAF, see comments of ecp_w_naf_fixed()
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* and <http://rd.springer.com/chapter/10.1007/3-540-36563-X_23>.
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*
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* This function executes a fixed number of operations for
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* random m in the range 0 .. 2^nbits - 1.
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*/
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int ecp_mul( const ecp_group *grp, ecp_point *R,
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const mpi *m, const ecp_point *P )
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{
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int ret, cmp;
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size_t pos;
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ecp_point Q[2];
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int ret;
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unsigned char w, m_is_odd;
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size_t pre_len, naf_len, i, j;
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signed char naf[ MAX_NAF_LEN ];
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ecp_point Q, T[ MAX_PRE_LEN ];
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mpi M;
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cmp = mpi_cmp_int( m, 0 );
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if( cmp < 0 )
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if( mpi_cmp_int( m, 0 ) < 0 || mpi_msb( m ) > grp->nbits )
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return( POLARSSL_ERR_ECP_GENERIC );
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w = 3; // TODO: find optimal values once precompute() is optimized
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if( w < 2 )
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w = 2;
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if( w > POLARSSL_ECP_WINDOW_SIZE )
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w = POLARSSL_ECP_WINDOW_SIZE;
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pre_len = 1 << ( w - 1 );
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naf_len = grp->nbits / w + 1;
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mpi_init( &M );
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ecp_point_init( &Q );
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for( i = 0; i < pre_len; i++ )
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ecp_point_init( &T[i] );
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m_is_odd = ( mpi_get_bit( m, 0 ) == 1 );
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/*
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* The general method works only for m != 0
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* Make sure M is odd:
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* later we'll get m * P by subtracting * P or 2 * P to M * P.
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*/
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if( cmp == 0 ) {
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return( ecp_set_zero( R ) );
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}
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MPI_CHK( mpi_copy( &M, m ) );
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MPI_CHK( mpi_add_int( &M, &M, 1 + m_is_odd ) );
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ecp_point_init( &Q[0] ); ecp_point_init( &Q[1] );
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/*
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* Compute the fixed-pattern NAF and precompute odd multiples
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*/
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MPI_CHK( ecp_w_naf_fixed( naf, naf_len, w, &M ) );
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MPI_CHK( ecp_precompute( grp, T, pre_len, P ) );
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MPI_CHK( ecp_set_zero( &Q[0] ) );
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for( pos = mpi_msb( m ) - 1 ; ; pos-- )
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/*
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* Compute M * P, using a variant of left-to-right 2^w-ary multiplication:
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* at each step we add (2 * naf[i] + 1) P, then multiply by 2^w.
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*
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* If naf[i] >= 0, we have (2 * naf[i] + 1) P == T[ naf[i] ]
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* Otherwise, (2 * naf[i] + 1) P == - ( 2 * ( - naf[i] - 1 ) + 1) P
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* == T[ - naf[i] - 1 ]
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*/
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MPI_CHK( ecp_set_zero( &Q ) );
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i = naf_len - 1;
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while( 1 )
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{
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MPI_CHK( ecp_double_jac( grp, &Q[0], &Q[0] ) );
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MPI_CHK( ecp_add_mixed( grp, &Q[1], &Q[0], P, 1 ) );
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MPI_CHK( ecp_copy( &Q[0], &Q[ mpi_get_bit( m, pos ) ] ) );
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if( naf[i] < 0 )
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{
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MPI_CHK( ecp_add_mixed( grp, &Q, &Q, &T[ - naf[i] - 1 ], -1 ) );
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}
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else
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{
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MPI_CHK( ecp_add_mixed( grp, &Q, &Q, &T[ naf[i] ], +1 ) );
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}
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if( pos == 0 )
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if( i == 0 )
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break;
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i--;
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for( j = 0; j < w; j++ )
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{
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MPI_CHK( ecp_double_jac( grp, &Q, &Q ) );
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}
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}
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MPI_CHK( ecp_copy( R, &Q[0] ) );
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MPI_CHK( ecp_normalize( grp, R ) );
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/*
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* Now get m * P from M * P.
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* Since we don't need T[] any more, we can recycle it:
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* we already have T[0] = P, now set T[1] = 2 * P.
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*/
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MPI_CHK( ecp_add( grp, &T[1], P, P ) );
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MPI_CHK( ecp_sub( grp, R, &Q, &T[m_is_odd] ) );
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cleanup:
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ecp_point_free( &Q[0] ); ecp_point_free( &Q[1] );
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mpi_free( &M );
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ecp_point_free( &Q );
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for( i = 0; i < pre_len; i++ )
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ecp_point_free( &T[i] );
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return( ret );
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}
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@ -850,72 +918,25 @@ int ecp_self_test( int verbose )
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{
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int ret;
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size_t i;
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int j, jj;
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ecp_group grp;
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ecp_point R;
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mpi m;
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unsigned long add_c_prev, dbl_c_prev;
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char *exponents[] =
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{
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"000000000000000000000000000000000000000000000000", /* zero */
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"000000000000000000000000000000000000000000000001", /* one */
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"FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831", /* N */
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"5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25", /* random */
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"400000000000000000000000000000000000000000000000",
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"7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
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"555555555555555555555555555555555555555555555555",
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"5EA6F389A38B8BC81E767753B15AA5569E1782E30ABE7D25",
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/* "000000000000000000000000000000000000000000000010", TODO */
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};
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signed char x[3];
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ecp_group_init( &grp );
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ecp_point_init( &R );
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mpi_init( &m );
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if( verbose != 0 )
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printf( " ECP test #0 (naf): " );
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for( j = 1; j < 32; j += 2 )
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{
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mpi_lset( &m, j );
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x[0] = x[1] = x[2] = 0;
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MPI_CHK( ecp_w_naf_fixed( x, 3, 2, &m ) );
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jj = ( 2 * x[0] + 1 ) + 4 * ( 2 * x[1] + 1 ) + 16 * ( 2 * x[2] + 1 );
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if( j != jj ||
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x[0] > 1 || x[0] < -2 ||
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x[1] > 1 || x[1] < -2 ||
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x[2] > 1 || x[2] < -2 )
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{
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if( verbose != 0 )
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printf( "failed\n" );
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printf( "%i != %i (%i, %i, %i)\n", j, jj, x[0], x[1], x[2] );
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ret = 1;
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goto cleanup;
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}
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x[0] = x[1] = x[2] = 0;
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MPI_CHK( ecp_w_naf_fixed( x, 2, 3, &m ) );
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jj = ( 2 * x[0] + 1 ) + 8 * ( 2 * x[1] + 1 );
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if( j != jj ||
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x[0] > 3 || x[0] < -4 ||
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x[1] > 3 || x[1] < -4 ||
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x[2] != 0 )
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{
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if( verbose != 0 )
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printf( "failed\n" );
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printf( "%i != %i (%i, %i)\n", j, jj, x[0], x[1] );
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ret = 1;
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goto cleanup;
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}
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}
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if( verbose != 0 )
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printf( "passed\n" );
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MPI_CHK( ecp_use_known_dp( &grp, POLARSSL_ECP_DP_SECP192R1 ) );
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if( verbose != 0 )
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@ -94,6 +94,15 @@ ecp_small_mul:12:0:17:05:0
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ECP small multiplication #13
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ecp_small_mul:13:1:0:0:0
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ECP small multiplication #14
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ecp_small_mul:1:0:17:42:0
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ECP small multiplication #15
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ecp_small_mul:2:0:20:01:0
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ECP small multiplication too big
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ecp_small_mul:-1:0:0:0:POLARSSL_ERR_ECP_GENERIC
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ECP mod p192 readable
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ecp_fast_mod:SECP192R1:"000000000000010500000000000001040000000000000103000000000000010200000000000001010000000000000100"
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