diff options
Diffstat (limited to 'mpi/mpi-mpow.c')
| -rw-r--r-- | mpi/mpi-mpow.c | 141 |
1 files changed, 122 insertions, 19 deletions
diff --git a/mpi/mpi-mpow.c b/mpi/mpi-mpow.c index 689a7600f..a8c561dd1 100644 --- a/mpi/mpi-mpow.c +++ b/mpi/mpi-mpow.c @@ -1,5 +1,5 @@ /* mpi-mpow.c - MPI functions - * Copyright (C) 1998 Free Software Foundation, Inc. + * Copyright (C) 1998, 1999 Free Software Foundation, Inc. * * This file is part of GnuPG. * @@ -25,6 +25,22 @@ #include "longlong.h" #include <assert.h> +/* Barrett is slower than the classical way. It can be tweaked by + * using partial multiplications + */ +/*#define USE_BARRETT*/ + + + +#ifdef USE_BARRETT +static void barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2 ); +static MPI init_barrett( MPI m, int *k, MPI *r1, MPI *r2 ); +static int calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2 ); +#else +#define barrett_mulm( w, u, v, m, y, k, r1, r2 ) mpi_mulm( (w), (u), (v), (m) ) +#endif + + static int build_index( MPI *exparray, int k, int i, int t ) { @@ -52,6 +68,10 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m) int i, j, idx; MPI *G; /* table with precomputed values of size 2^k */ MPI tmp; + #ifdef USE_BARRETT + MPI barrett_y, barrett_r1, barrett_r2; + int barrett_k; + #endif for(k=0; basearray[k]; k++ ) ; @@ -68,27 +88,15 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m) assert( k < 10 ); G = m_alloc_clear( (1<<k) * sizeof *G ); - #if 0 - /* do the precomputation */ - G[0] = mpi_alloc_set_ui( 1 ); - for(i=1; i < (1<<k); i++ ) { - for(j=0; j < k; j++ ) { - if( (i & (1<<j) ) ) { - if( !G[i] ) - G[i] = mpi_copy( basearray[j] ); - else - mpi_mulm( G[i], G[i], basearray[j], m ); - } - } - if( !G[i] ) - G[i] = mpi_alloc(0); - } + #ifdef USE_BARRETT + barrett_y = init_barrett( m, &barrett_k, &barrett_r1, &barrett_r2 ); #endif /* and calculate */ tmp = mpi_alloc( mpi_get_nlimbs(m)+1 ); mpi_set_ui( res, 1 ); for(i = 1; i <= t; i++ ) { - mpi_mulm(tmp, res, res, m ); + barrett_mulm(tmp, res, res, m, barrett_y, barrett_k, + barrett_r1, barrett_r2 ); idx = build_index( exparray, k, i, t ); assert( idx >= 0 && idx < (1<<k) ); if( !G[idx] ) { @@ -100,20 +108,115 @@ mpi_mulpowm( MPI res, MPI *basearray, MPI *exparray, MPI m) if( !G[idx] ) G[idx] = mpi_copy( basearray[j] ); else - mpi_mulm( G[idx], G[idx], basearray[j], m ); + barrett_mulm( G[idx], G[idx], basearray[j], + m, barrett_y, barrett_k, barrett_r1, barrett_r2 ); } } if( !G[idx] ) G[idx] = mpi_alloc(0); } } - mpi_mulm(res, tmp, G[idx], m ); + barrett_mulm(res, tmp, G[idx], m, barrett_y, barrett_k, barrett_r1, barrett_r2 ); } /* cleanup */ mpi_free(tmp); + #ifdef USE_BARRETT + mpi_free(barrett_y); + mpi_free(barrett_r1); + mpi_free(barrett_r2); + #endif for(i=0; i < (1<<k); i++ ) mpi_free(G[i]); m_free(G); } + + +#ifdef USE_BARRETT +static void +barrett_mulm( MPI w, MPI u, MPI v, MPI m, MPI y, int k, MPI r1, MPI r2 ) +{ + mpi_mul(w, u, v); + if( calc_barrett( w, w, m, y, k, r1, r2 ) ) + mpi_fdiv_r( w, w, m ); +} + +/**************** + * Barrett precalculation: y = floor(b^(2k) / m) + */ +static MPI +init_barrett( MPI m, int *k, MPI *r1, MPI *r2 ) +{ + MPI tmp; + + mpi_normalize( m ); + *k = mpi_get_nlimbs( m ); + tmp = mpi_alloc( *k + 1 ); + mpi_set_ui( tmp, 1 ); + mpi_lshift_limbs( tmp, 2 * *k ); + mpi_fdiv_q( tmp, tmp, m ); + *r1 = mpi_alloc( 2* *k + 1 ); + *r2 = mpi_alloc( 2* *k + 1 ); + return tmp; +} + +/**************** + * Barrett reduction: We assume that these conditions are met: + * Given x =(x_2k-1 ...x_0)_b + * m =(m_k-1 ....m_0)_b with m_k-1 != 0 + * Output r = x mod m + * Before using this function init_barret must be used to calucalte y and k. + * Returns: false = no error + * true = can't perform barret reduction + */ +static int +calc_barrett( MPI r, MPI x, MPI m, MPI y, int k, MPI r1, MPI r2 ) +{ + int xx = k > 3 ? k-3:0; + + mpi_normalize( x ); + if( mpi_get_nlimbs(x) > 2*k ) + return 1; /* can't do it */ + + /* 1. q1 = floor( x / b^k-1) + * q2 = q1 * y + * q3 = floor( q2 / b^k+1 ) + * Actually, we don't need qx, we can work direct on r2 + */ + mpi_set( r2, x ); + mpi_rshift_limbs( r2, k-1 ); + mpi_mul( r2, r2, y ); + mpi_rshift_limbs( r2, k+1 ); + + /* 2. r1 = x mod b^k+1 + * r2 = q3 * m mod b^k+1 + * r = r1 - r2 + * 3. if r < 0 then r = r + b^k+1 + */ + mpi_set( r1, x ); + if( r1->nlimbs > k+1 ) /* quick modulo operation */ + r1->nlimbs = k+1; + mpi_mul( r2, r2, m ); + if( r2->nlimbs > k+1 ) /* quick modulo operation */ + r2->nlimbs = k+1; + mpi_sub( r, r1, r2 ); + + if( mpi_is_neg( r ) ) { + MPI tmp; + + tmp = mpi_alloc( k + 2 ); + mpi_set_ui( tmp, 1 ); + mpi_lshift_limbs( tmp, k+1 ); + mpi_add( r, r, tmp ); + mpi_free(tmp); + } + + /* 4. while r >= m do r = r - m */ + while( mpi_cmp( r, m ) >= 0 ) + mpi_sub( r, r, m ); + + return 0; +} +#endif /* USE_BARRETT */ + |