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Improve comb method (less precomputed points)
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Manuel Pégourié-Gonnard
parent
d1c1ba90ca
commit
101a39f55f
121
library/ecp.c
121
library/ecp.c
@ -1515,27 +1515,33 @@ cleanup:
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* Compute the representation of m that will be used with the comb method.
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*
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* The basic comb method is described in GECC 3.44 for example. We use a
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* modified version [3] that provides resistance to SPA by avoiding zero
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* digits in the representation. We represent (K_i, s_i) from the paper as a
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* single signed char.
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* modified version that provides resistance to SPA by avoiding zero
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* digits in the representation as in [3]. We modify the method further by
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* requiring that all K_i be odd, which has the small cost that our
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* representation uses on more K, due to carries.
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*
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* Also, for the sake of compactness, only the seven low-order bits of x[i]
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* are used to represent K_i, and the msb of x[i] encodes the the sign (s_i in
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* the paper): it is set if and only if if s_i == -1;
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*
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* Calling conventions:
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* - x is an array of size d
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* - x is an array of size d + 1
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* - w is the size, ie number of teeth, of the comb
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* - m is the MPI, expected to be odd and such that, if l = bitlength(m):
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* ceil( l / w ) <= d (these two assumptions are not checked, an incorrect
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* result my be returned if they are not satisfied)
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* - m is the MPI, expected to be odd and such that bitlength(m) <= w * d
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* (the result will be incorrect if these assumptions are not satisfied)
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*/
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static void ecp_comb_fixed( signed char x[], size_t d,
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static void ecp_comb_fixed( unsigned char x[], size_t d,
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unsigned char w, const mpi *m )
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{
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size_t i, j;
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unsigned char c, cc, adjust;
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memset( x, 0, d );
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memset( x, 0, d+1 );
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/* For x[0] use the classical comb value without adjustement */
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for( j = 0; j < w; j++ )
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x[0] |= mpi_get_bit( m, d * j ) << j;
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c = 0;
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for( i = 1; i < d; i++ )
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{
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@ -1543,95 +1549,100 @@ static void ecp_comb_fixed( signed char x[], size_t d,
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for( j = 0; j < w; j++ )
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x[i] |= mpi_get_bit( m, i + d * j ) << j;
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/* Adjust if it's zero */
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if( x[i] == 0 )
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{
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x[i] = x[i-1];
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x[i-1] *= -1;
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}
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/* Add carry and update it */
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cc = x[i] & c;
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x[i] = x[i] ^ c;
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c = cc;
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/* Make sure x[i] is odd, avoiding if-branches */
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adjust = 1 - ( x[i] & 0x01 );
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c |= x[i] & ( x[i-1] * adjust );
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x[i] = x[i] ^ ( x[i-1] * adjust );
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x[i-1] |= adjust << 7;
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}
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/* Finish with the carry */
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x[i] = c;
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adjust = 1 - ( x[i] & 0x01 );
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c |= x[i] & ( x[i-1] * adjust );
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x[i] = x[i] ^ ( x[i-1] * adjust );
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x[i-1] |= adjust << 7;
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}
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/*
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* Precompute points for the comb method
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*
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* If i = i_{w-1} ... i_0 is the binary representation of i, then
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* T[i-1] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + i_0 P
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* If i = i_{w-1} ... i_1 is the binary representation of i, then
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* T[i] = i_{w-1} 2^{(w-1)d} P + ... + i_1 2^d P + P
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*
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* T must be able to hold at least 2^w - 1 elements
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* T must be able to hold at least 2^{w - 1} elements
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*/
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static int ecp_precompute_comb( const ecp_group *grp,
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ecp_point T[], const ecp_point *P,
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unsigned char w, size_t d )
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{
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int ret;
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unsigned char i, mask;
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size_t j, t_len = ( 1U << w ) - 1;
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ecp_point *cur, *TT[t_len - 1];
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unsigned char i, j, k;
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ecp_point *cur, *TT[200]; // TODO
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/*
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* Compute the 2^{di}
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* Set T[0] = P and
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* T[2^{l-1}] = 2^{dl} P for l = 1 .. w-1 (this is not the final value)
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*/
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MPI_CHK( ecp_copy( &T[0], P ) );
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for( i = 1; i < w; i++ )
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k = 0;
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for( i = 1; i < ( 1U << (w-1) ); i <<= 1 )
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{
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cur = T + ( 1 << i ) - 1;
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ecp_copy( cur, T + ( 1 << (i-1) ) - 1 );
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cur = T + i;
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MPI_CHK( ecp_copy( cur, T + ( i >> 1 ) ) );
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for( j = 0; j < d; j++ )
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MPI_CHK( ecp_double_jac( grp, cur, cur ) );
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TT[i-1] = cur;
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TT[k++] = cur;
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}
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/* P already normalized, so w - 1 points to do */
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ecp_normalize_many( grp, TT, w - 1);
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ecp_normalize_many( grp, TT, k );
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/*
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* Compute the remaining ones using the minimal number of additions
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* Be careful to update T[2^l] only after using it!
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*/
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j = 0;
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for( i = 3; i < (1U << w); i++ )
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k = 0;
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for( i = 1; i < ( 1U << (w-1) ); i <<= 1 )
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{
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if( T[i - 1].X.p != NULL )
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continue;
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/* Find the least significant non-zero bit of the index */
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for( mask = 1; mask != 0; mask <<=1 )
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if( ( i & mask ) != 0 )
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break;
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/* Use the previously computed values */
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ecp_add_mixed( grp, &T[i - 1], &T[i - mask - 1], &T[mask - 1], +1 );
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/* Register for normalisation */
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TT[j++] = &T[i - 1];
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j = i;
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while( j-- )
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{
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ecp_add_mixed( grp, &T[i + j], &T[j], &T[i], +1 );
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TT[k++] = &T[i + j];
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}
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}
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ecp_normalize_many( grp, TT, j );
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ecp_normalize_many( grp, TT, k );
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cleanup:
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return( ret );
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}
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/*
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* Select precomputed point: R = sign(i) * T[ abs(i) ]
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* Select precomputed point: R = sign(i) * T[ abs(i) / 2 ]
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*/
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static int ecp_select_comb( const ecp_group *grp, ecp_point *R,
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const ecp_point T[], signed char i )
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const ecp_point T[], unsigned char i )
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{
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int ret;
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if( i > 0 )
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return( ecp_copy( R, &T[i - 1] ) );
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MPI_CHK( ecp_copy( R, &T[-i - 1] ) );
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/* Ignore the "sign" bit */
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MPI_CHK( ecp_copy( R, &T[ ( i & 0x7Fu ) >> 1 ] ) );
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/*
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* -R = (R.X, -R.Y, R.Z), and
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* -R.Y mod P = P - R.Y unless R.Y == 0
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*/
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if( mpi_cmp_int( &R->Y, 0 ) != 0 )
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MPI_CHK( mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
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if( ( i & 0x80 ) != 0 )
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if( mpi_cmp_int( &R->Y, 0 ) != 0 )
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MPI_CHK( mpi_sub_mpi( &R->Y, &grp->P, &R->Y ) );
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cleanup:
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return( ret );
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@ -1642,7 +1653,7 @@ cleanup:
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* This part is actually common with the basic comb method (GECC 3.44)
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*/
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static int ecp_mul_comb_core( const ecp_group *grp, ecp_point *R,
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const ecp_point T[], const signed char x[],
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const ecp_point T[], const unsigned char x[],
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size_t d )
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{
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int ret;
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@ -1652,7 +1663,7 @@ static int ecp_mul_comb_core( const ecp_group *grp, ecp_point *R,
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ecp_point_init( &Txi );
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/* Avoid useless doubling/addition of 0 by better initialisation */
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i = d - 1;
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i = d;
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MPI_CHK( ecp_select_comb( grp, R, T, x[i] ) );
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while( i-- != 0 )
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@ -1678,7 +1689,7 @@ int ecp_mul_comb( ecp_group *grp, ecp_point *R,
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int ret;
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unsigned char w, m_is_odd, p_eq_g;
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size_t pre_len, d, i;
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signed char k[100]; // TODO
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unsigned char k[200]; // TODO
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ecp_point Q, *T = NULL, S[2];
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mpi M;
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