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montmul improvement to lesser copies

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This commit is contained in:
NIIBE Yutaka
2013-12-16 10:40:15 +09:00
parent 0ae7ea05c3
commit a0438913b7
2 changed files with 90 additions and 43 deletions
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7
ChangeLog
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@@ -1,3 +1,10 @@
2013-12-16 Niibe Yutaka <gniibe@fsij.org>
* polarssl/library/bignum.c (mpi_cmp_abs_limbs): New.
(mpi_montmul): Change the signature and use the upper half of T.
(mpi_montred): Likewise.
(mpi_exp_mod): Use improved mpi_montmul and mpi_montred.
2013-12-13 Niibe Yutaka <gniibe@fsij.org>
* polarssl/library/bignum.c (mpi_exp_mod): Initialize lower

126
polarssl/library/bignum.c
View File

@@ -643,6 +643,39 @@ int mpi_shift_r( mpi *X, size_t count )
return( 0 );
}
/*
* Compare unsigned values
*/
static int mpi_cmp_abs_limbs (size_t n, const t_uint *p0, const t_uint *p1)
{
size_t i, j;
p0 += n;
for( i = n; i > 0; i-- )
if( *--p0 != 0 )
break;
p1 += n;
for( j = n; j > 0; j-- )
if( *--p1 != 0 )
break;
if( i == 0 && j == 0 )
return( 0 );
if( i > j ) return( 1 );
if( j > i ) return( -1 );
for( ; i > 0; i-- )
{
if( *p0 > *p1 ) return( 1 );
if( *p0 < *p1 ) return( -1 );
p0--; p1--;
}
return( 0 );
}
/*
* Compare unsigned values
*/
@@ -1349,8 +1382,9 @@ static void mpi_montg_init( t_uint *mm, const mpi *N )
/*
* Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36)
* A is placed at the upper half of T.
*/
static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm, const mpi *T )
static void mpi_montmul( const mpi *B, const mpi *N, t_uint mm, mpi *T )
{
size_t i, n, m;
t_uint u0, u1, *d, c = 0;
@@ -1361,11 +1395,11 @@ static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm, const mp
for( i = 0; i < n; i++ )
{
d[n] = c;
/*
* T = (T + u0*B + u1*N) / 2^biL
*/
u0 = A->p[i];
u0 = d[n];
d[n] = c;
u1 = ( d[0] + u0 * B->p[0] ) * mm;
mpi_mul_hlp( m, B->p, d, u0 );
@@ -1373,19 +1407,18 @@ static void mpi_montmul( mpi *A, const mpi *B, const mpi *N, t_uint mm, const mp
d++;
}
memcpy( A->p, d, n * ciL );
if( ((mpi_cmp_abs( A, N ) >= 0) | c) )
mpi_sub_hlp( n, N->p, A->p );
/* prevent timing attacks */
if( ((mpi_cmp_abs_limbs ( n, d, N->p ) >= 0) | c) )
mpi_sub_hlp( n, N->p, d );
else
/* prevent timing attacks */
mpi_sub_hlp( n, A->p, d);
mpi_sub_hlp( n, T->p, T->p);
}
/*
* Montgomery reduction: A = A * R^-1 mod N
* A is placed at the upper half of T.
*/
static void mpi_montred( mpi *A, const mpi *N, t_uint mm, const mpi *T )
static void mpi_montred( const mpi *N, t_uint mm, mpi *T )
{
size_t i, j, n;
t_uint u0, u1, *d, c = 0;
@@ -1395,31 +1428,29 @@ static void mpi_montred( mpi *A, const mpi *N, t_uint mm, const mpi *T )
for( i = 0; i < n; i++ )
{
d[n] = c;
/*
* T = (T + u0 + u1*N) / 2^biL
*/
u0 = A->p[i];
u0 = d[n];
d[n] = c;
u1 = (d[0] + u0) * mm;
d[0] += u0;
c = (d[0] < u0);
for (j = 1; j < n; j++)
{
d[j] += c; c = ( d[j] < c );
}
{
d[j] += c; c = ( d[j] < c );
}
c = mpi_mul_hlp( n, N->p, d, u1 );
d++;
}
memcpy( A->p, d, n * ciL );
if( ((mpi_cmp_abs( A, N ) >= 0) | c) )
mpi_sub_hlp( n, N->p, A->p );
/* prevent timing attacks */
if( ((mpi_cmp_abs_limbs ( n, d, N->p ) >= 0) | c) )
mpi_sub_hlp( n, N->p, d );
else
/* prevent timing attacks */
mpi_sub_hlp( n, A->p, d);
mpi_sub_hlp( n, T->p, T->p);
}
/*
@@ -1460,7 +1491,7 @@ int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
MPI_CHK( mpi_grow( X, j ) );
MPI_CHK( mpi_grow( &W[1], j ) );
MPI_CHK( mpi_grow( &T, j * 2 ) );
memset( T.p, 0, j * ciL ); /* Clear the lower half of T. */
memset( T.p, 0, j * ciL ); /* Clear the lower half of T. */
/*
* Compensate for negative A (and correct at the end)
@@ -1499,39 +1530,43 @@ int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
mpi_mod_mpi( &W[1], A, N );
else mpi_copy( &W[1], A );
mpi_montmul( &W[1], &RR, N, mm, &T );
/*
* X = R^2 * R^-1 mod N = R mod N
*/
MPI_CHK( mpi_copy( X, &RR ) );
mpi_montred( X, N, mm, &T );
memcpy ( T.p + N->n, W[1].p, N->n * ciL);
mpi_montmul( &RR, N, mm, &T );
memcpy ( W[1].p, T.p + N->n, N->n * ciL);
if( wsize > 1 )
{
/*
* W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
* W[1 << (wsize - 1)] = W[1] ^ ( 2 ^ (wsize - 1) )
*/
j = one << (wsize - 1);
MPI_CHK( mpi_grow( &W[j], N->n ) );
MPI_CHK( mpi_copy( &W[j], &W[1] ) );
for( i = 0; i < wsize - 1; i++ )
mpi_montmul( &W[j], &W[j], N, mm, &T );
for( i = 0; i < wsize - 1; i++ ) {
memcpy ( W[j].p, T.p + N->n, N->n * ciL);
mpi_montmul( &W[j], N, mm, &T );
}
memcpy ( W[j].p, T.p + N->n, N->n * ciL);
/*
* W[i] = W[i - 1] * W[1]
*/
for( i = j + 1; i < (one << wsize); i++ )
{
MPI_CHK( mpi_grow( &W[i], N->n ) );
MPI_CHK( mpi_copy( &W[i], &W[i - 1] ) );
mpi_montmul( &W[i], &W[1], N, mm, &T );
mpi_montmul( &W[1], N, mm, &T );
memcpy ( W[i].p, T.p + N->n, N->n * ciL);
}
}
/*
* X = R^2 * R^-1 mod N = R mod N
*/
memcpy ( T.p + N->n, RR.p, N->n * ciL);
mpi_montred( N, mm, &T );
nblimbs = E->n;
bufsize = 0;
nbits = 0;
@@ -1563,7 +1598,8 @@ int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
/*
* out of window, square X
*/
mpi_montmul( X, X, N, mm, &T );
memcpy ( X->p, T.p + N->n, N->n * ciL);
mpi_montmul( X, N, mm, &T );
continue;
}
@@ -1580,13 +1616,15 @@ int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
/*
* X = X^wsize R^-1 mod N
*/
for( i = 0; i < wsize; i++ )
mpi_montmul( X, X, N, mm, &T );
for( i = 0; i < wsize; i++ ) {
memcpy ( X->p, T.p + N->n, N->n * ciL);
mpi_montmul( X, N, mm, &T );
}
/*
* X = X * W[wbits] R^-1 mod N
*/
mpi_montmul( X, &W[wbits], N, mm, &T );
mpi_montmul( &W[wbits], N, mm, &T );
state--;
nbits = 0;
@@ -1599,18 +1637,20 @@ int mpi_exp_mod( mpi *X, const mpi *A, const mpi *E, const mpi *N, mpi *_RR )
*/
for( i = 0; i < nbits; i++ )
{
mpi_montmul( X, X, N, mm, &T );
memcpy ( X->p, T.p + N->n, N->n * ciL);
mpi_montmul( X, N, mm, &T );
wbits <<= 1;
if( (wbits & (one << wsize)) != 0 )
mpi_montmul( X, &W[1], N, mm, &T );
mpi_montmul( &W[1], N, mm, &T );
}
/*
* X = A^E * R * R^-1 mod N = A^E mod N
*/
mpi_montred( X, N, mm, &T );
mpi_montred( N, mm, &T );
memcpy ( X->p, T.p + N->n, N->n * ciL);
if( neg )
{