/****************
* RES = BASE ^ EXPO mod MOD
*/
void
gcry_mpi_powm( gcry_mpi_t res, gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod)
{
mpi_ptr_t rp, ep, mp, bp;
mpi_size_t esize, msize, bsize, rsize;
int esign, msign, bsign, rsign;
int esec, msec, bsec, rsec;
mpi_size_t size;
int mod_shift_cnt;
int negative_result;
mpi_ptr_t mp_marker=NULL, bp_marker=NULL, ep_marker=NULL;
mpi_ptr_t xp_marker=NULL;
unsigned int mp_nlimbs = 0, bp_nlimbs = 0, ep_nlimbs = 0;
unsigned int xp_nlimbs = 0;
int assign_rp = 0;
mpi_ptr_t tspace = NULL;
mpi_size_t tsize=0; /* to avoid compiler warning */
/* fixme: we should check that the warning is void*/
esize = expo->nlimbs;
msize = mod->nlimbs;
size = 2 * msize;
esign = expo->sign;
msign = mod->sign;
esec = mpi_is_secure(expo);
msec = mpi_is_secure(mod);
bsec = mpi_is_secure(base);
rsec = mpi_is_secure(res);
rp = res->d;
ep = expo->d;
if( !msize )
msize = 1 / msize; /* provoke a signal */
if( !esize ) {
/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0
* depending on if MOD equals 1. */
rp[0] = 1;
res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
res->sign = 0;
goto leave;
}
/* Normalize MOD (i.e. make its most significant bit set) as required by
* mpn_divrem. This will make the intermediate values in the calculation
* slightly larger, but the correct result is obtained after a final
* reduction using the original MOD value. */
mp_nlimbs = msec? msize:0;
mp = mp_marker = mpi_alloc_limb_space(msize, msec);
count_leading_zeros( mod_shift_cnt, mod->d[msize-1] );
if( mod_shift_cnt )
_gcry_mpih_lshift( mp, mod->d, msize, mod_shift_cnt );
else
MPN_COPY( mp, mod->d, msize );
bsize = base->nlimbs;
bsign = base->sign;
if( bsize > msize ) { /* The base is larger than the module. Reduce it. */
/* Allocate (BSIZE + 1) with space for remainder and quotient.
* (The quotient is (bsize - msize + 1) limbs.) */
bp_nlimbs = bsec ? (bsize + 1):0;
bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
MPN_COPY( bp, base->d, bsize );
/* We don't care about the quotient, store it above the remainder,
* at BP + MSIZE. */
_gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize );
bsize = msize;
/* Canonicalize the base, since we are going to multiply with it
* quite a few times. */
MPN_NORMALIZE( bp, bsize );
}
else
bp = base->d;
if( !bsize ) {
res->nlimbs = 0;
res->sign = 0;
goto leave;
}
if( res->alloced < size ) {
/* We have to allocate more space for RES. If any of the input
* parameters are identical to RES, defer deallocation of the old
* space. */
if( rp == ep || rp == mp || rp == bp ) {
rp = mpi_alloc_limb_space( size, rsec );
assign_rp = 1;
}
else {
mpi_resize( res, size );
rp = res->d;
}
}
else { /* Make BASE, EXPO and MOD not overlap with RES. */
if( rp == bp ) {
/* RES and BASE are identical. Allocate temp. space for BASE. */
assert( !bp_marker );
bp_nlimbs = bsec? bsize:0;
bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
MPN_COPY(bp, rp, bsize);
}
if( rp == ep ) {
/* RES and EXPO are identical. Allocate temp. space for EXPO. */
ep_nlimbs = esec? esize:0;
ep = ep_marker = mpi_alloc_limb_space( esize, esec );
MPN_COPY(ep, rp, esize);
}
if( rp == mp ) {
/* RES and MOD are identical. Allocate temporary space for MOD.*/
assert( !mp_marker );
mp_nlimbs = msec?msize:0;
mp = mp_marker = mpi_alloc_limb_space( msize, msec );
MPN_COPY(mp, rp, msize);
}
}
MPN_COPY( rp, bp, bsize );
rsize = bsize;
rsign = bsign;
{
mpi_size_t i;
mpi_ptr_t xp;
int c;
mpi_limb_t e;
mpi_limb_t carry_limb;
struct karatsuba_ctx karactx;
xp_nlimbs = msec? (2 * (msize + 1)):0;
xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );
memset( &karactx, 0, sizeof karactx );
negative_result = (ep[0] & 1) && base->sign;
i = esize - 1;
e = ep[i];
count_leading_zeros (c, e);
e = (e << c) << 1; /* shift the expo bits to the left, lose msb */
c = BITS_PER_MPI_LIMB - 1 - c;
/* Main loop.
*
* Make the result be pointed to alternately by XP and RP. This
* helps us avoid block copying, which would otherwise be necessary
* with the overlap restrictions of _gcry_mpih_divmod. With 50% probability
* the result after this loop will be in the area originally pointed
* by RP (==RES->d), and with 50% probability in the area originally
* pointed to by XP.
*/
for(;;) {
while( c ) {
mpi_ptr_t tp;
mpi_size_t xsize;
/*mpih_mul_n(xp, rp, rp, rsize);*/
if( rsize < KARATSUBA_THRESHOLD )
_gcry_mpih_sqr_n_basecase( xp, rp, rsize );
else {
if( !tspace ) {
tsize = 2 * rsize;
tspace = mpi_alloc_limb_space( tsize, 0 );
}
else if( tsize < (2*rsize) ) {
_gcry_mpi_free_limb_space (tspace, 0);
tsize = 2 * rsize;
tspace = mpi_alloc_limb_space( tsize, 0 );
}
_gcry_mpih_sqr_n( xp, rp, rsize, tspace );
}
xsize = 2 * rsize;
if( xsize > msize ) {
_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
xsize = msize;
}
tp = rp; rp = xp; xp = tp;
rsize = xsize;
if( (mpi_limb_signed_t)e < 0 ) {
/*mpih_mul( xp, rp, rsize, bp, bsize );*/
if( bsize < KARATSUBA_THRESHOLD ) {
_gcry_mpih_mul( xp, rp, rsize, bp, bsize );
}
else {
_gcry_mpih_mul_karatsuba_case(
xp, rp, rsize, bp, bsize, &karactx );
}
xsize = rsize + bsize;
if( xsize > msize ) {
_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
xsize = msize;
}
tp = rp; rp = xp; xp = tp;
rsize = xsize;
}
e <<= 1;
c--;
}
i--;
if( i < 0 )
break;
e = ep[i];
c = BITS_PER_MPI_LIMB;
}
/* We shifted MOD, the modulo reduction argument, left MOD_SHIFT_CNT
* steps. Adjust the result by reducing it with the original MOD.
*
* Also make sure the result is put in RES->d (where it already
* might be, see above).
*/
if( mod_shift_cnt ) {
carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt);
rp = res->d;
if( carry_limb ) {
rp[rsize] = carry_limb;
rsize++;
}
}
else {
MPN_COPY( res->d, rp, rsize);
rp = res->d;
}
if( rsize >= msize ) {
_gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize);
rsize = msize;
}
/* Remove any leading zero words from the result. */
if( mod_shift_cnt )
_gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt);
MPN_NORMALIZE (rp, rsize);
_gcry_mpih_release_karatsuba_ctx( &karactx );
}
if( negative_result && rsize ) {
if( mod_shift_cnt )
_gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt);
_gcry_mpih_sub( rp, mp, msize, rp, rsize);
rsize = msize;
rsign = msign;
MPN_NORMALIZE(rp, rsize);
}
res->nlimbs = rsize;
res->sign = rsign;
leave:
if( assign_rp ) _gcry_mpi_assign_limb_space( res, rp, size );
if( mp_marker ) _gcry_mpi_free_limb_space( mp_marker, mp_nlimbs );
if( bp_marker ) _gcry_mpi_free_limb_space( bp_marker, bp_nlimbs );
if( ep_marker ) _gcry_mpi_free_limb_space( ep_marker, ep_nlimbs );
if( xp_marker ) _gcry_mpi_free_limb_space( xp_marker, xp_nlimbs );
if( tspace ) _gcry_mpi_free_limb_space( tspace, 0 );
}
/****************
* RES = BASE ^ EXPO mod MOD
*/
void
gcry_mpi_powm (gcry_mpi_t res,
gcry_mpi_t base, gcry_mpi_t expo, gcry_mpi_t mod)
{
/* Pointer to the limbs of the arguments, their size and signs. */
mpi_ptr_t rp, ep, mp, bp;
mpi_size_t esize, msize, bsize, rsize;
int msign, bsign, rsign;
/* Flags telling the secure allocation status of the arguments. */
int esec, msec, bsec;
/* Size of the result including space for temporary values. */
mpi_size_t size;
/* Helper. */
int mod_shift_cnt;
int negative_result;
mpi_ptr_t mp_marker = NULL;
mpi_ptr_t bp_marker = NULL;
mpi_ptr_t ep_marker = NULL;
mpi_ptr_t xp_marker = NULL;
unsigned int mp_nlimbs = 0;
unsigned int bp_nlimbs = 0;
unsigned int ep_nlimbs = 0;
unsigned int xp_nlimbs = 0;
mpi_ptr_t tspace = NULL;
mpi_size_t tsize = 0;
esize = expo->nlimbs;
msize = mod->nlimbs;
size = 2 * msize;
msign = mod->sign;
esec = mpi_is_secure(expo);
msec = mpi_is_secure(mod);
bsec = mpi_is_secure(base);
rp = res->d;
ep = expo->d;
if (!msize)
grub_fatal ("mpi division by zero");
if (!esize)
{
/* Exponent is zero, result is 1 mod MOD, i.e., 1 or 0 depending
on if MOD equals 1. */
res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
if (res->nlimbs)
{
RESIZE_IF_NEEDED (res, 1);
rp = res->d;
rp[0] = 1;
}
res->sign = 0;
goto leave;
}
/* Normalize MOD (i.e. make its most significant bit set) as
required by mpn_divrem. This will make the intermediate values
in the calculation slightly larger, but the correct result is
obtained after a final reduction using the original MOD value. */
mp_nlimbs = msec? msize:0;
mp = mp_marker = mpi_alloc_limb_space(msize, msec);
count_leading_zeros (mod_shift_cnt, mod->d[msize-1]);
if (mod_shift_cnt)
_gcry_mpih_lshift (mp, mod->d, msize, mod_shift_cnt);
else
MPN_COPY( mp, mod->d, msize );
bsize = base->nlimbs;
bsign = base->sign;
if (bsize > msize)
{
/* The base is larger than the module. Reduce it.
Allocate (BSIZE + 1) with space for remainder and quotient.
(The quotient is (bsize - msize + 1) limbs.) */
bp_nlimbs = bsec ? (bsize + 1):0;
bp = bp_marker = mpi_alloc_limb_space( bsize + 1, bsec );
MPN_COPY ( bp, base->d, bsize );
/* We don't care about the quotient, store it above the
* remainder, at BP + MSIZE. */
_gcry_mpih_divrem( bp + msize, 0, bp, bsize, mp, msize );
bsize = msize;
/* Canonicalize the base, since we are going to multiply with it
quite a few times. */
MPN_NORMALIZE( bp, bsize );
}
else
bp = base->d;
if (!bsize)
{
res->nlimbs = 0;
res->sign = 0;
goto leave;
}
/* Make BASE, EXPO and MOD not overlap with RES. */
if ( rp == bp )
{
/* RES and BASE are identical. Allocate temp. space for BASE. */
gcry_assert (!bp_marker);
bp_nlimbs = bsec? bsize:0;
bp = bp_marker = mpi_alloc_limb_space( bsize, bsec );
MPN_COPY(bp, rp, bsize);
}
if ( rp == ep )
{
/* RES and EXPO are identical. Allocate temp. space for EXPO. */
ep_nlimbs = esec? esize:0;
ep = ep_marker = mpi_alloc_limb_space( esize, esec );
MPN_COPY(ep, rp, esize);
}
if ( rp == mp )
{
/* RES and MOD are identical. Allocate temporary space for MOD.*/
gcry_assert (!mp_marker);
mp_nlimbs = msec?msize:0;
mp = mp_marker = mpi_alloc_limb_space( msize, msec );
MPN_COPY(mp, rp, msize);
}
/* Copy base to the result. */
if (res->alloced < size)
{
mpi_resize (res, size);
rp = res->d;
}
MPN_COPY ( rp, bp, bsize );
rsize = bsize;
rsign = bsign;
/* Main processing. */
{
mpi_size_t i;
mpi_ptr_t xp;
int c;
mpi_limb_t e;
mpi_limb_t carry_limb;
struct karatsuba_ctx karactx;
xp_nlimbs = msec? (2 * (msize + 1)):0;
xp = xp_marker = mpi_alloc_limb_space( 2 * (msize + 1), msec );
memset( &karactx, 0, sizeof karactx );
negative_result = (ep[0] & 1) && base->sign;
i = esize - 1;
e = ep[i];
count_leading_zeros (c, e);
e = (e << c) << 1; /* Shift the expo bits to the left, lose msb. */
c = BITS_PER_MPI_LIMB - 1 - c;
/* Main loop.
Make the result be pointed to alternately by XP and RP. This
helps us avoid block copying, which would otherwise be
necessary with the overlap restrictions of
_gcry_mpih_divmod. With 50% probability the result after this
loop will be in the area originally pointed by RP (==RES->d),
and with 50% probability in the area originally pointed to by XP. */
for (;;)
{
while (c)
{
mpi_ptr_t tp;
mpi_size_t xsize;
/*mpih_mul_n(xp, rp, rp, rsize);*/
if ( rsize < KARATSUBA_THRESHOLD )
_gcry_mpih_sqr_n_basecase( xp, rp, rsize );
else
{
if ( !tspace )
{
tsize = 2 * rsize;
tspace = mpi_alloc_limb_space( tsize, 0 );
}
else if ( tsize < (2*rsize) )
{
_gcry_mpi_free_limb_space (tspace, 0);
tsize = 2 * rsize;
tspace = mpi_alloc_limb_space (tsize, 0 );
}
_gcry_mpih_sqr_n (xp, rp, rsize, tspace);
}
xsize = 2 * rsize;
if ( xsize > msize )
{
_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
xsize = msize;
}
tp = rp; rp = xp; xp = tp;
rsize = xsize;
/* To mitigate the Yarom/Falkner flush+reload cache
* side-channel attack on the RSA secret exponent, we do
* the multiplication regardless of the value of the
* high-bit of E. But to avoid this performance penalty
* we do it only if the exponent has been stored in secure
* memory and we can thus assume it is a secret exponent. */
if (esec || (mpi_limb_signed_t)e < 0)
{
/*mpih_mul( xp, rp, rsize, bp, bsize );*/
if( bsize < KARATSUBA_THRESHOLD )
_gcry_mpih_mul ( xp, rp, rsize, bp, bsize );
else
_gcry_mpih_mul_karatsuba_case (xp, rp, rsize, bp, bsize,
&karactx);
xsize = rsize + bsize;
if ( xsize > msize )
{
_gcry_mpih_divrem(xp + msize, 0, xp, xsize, mp, msize);
xsize = msize;
}
}
if ( (mpi_limb_signed_t)e < 0 )
{
tp = rp; rp = xp; xp = tp;
rsize = xsize;
}
e <<= 1;
c--;
}
i--;
if ( i < 0 )
break;
e = ep[i];
c = BITS_PER_MPI_LIMB;
}
/* We shifted MOD, the modulo reduction argument, left
MOD_SHIFT_CNT steps. Adjust the result by reducing it with the
original MOD.
Also make sure the result is put in RES->d (where it already
might be, see above). */
if ( mod_shift_cnt )
{
carry_limb = _gcry_mpih_lshift( res->d, rp, rsize, mod_shift_cnt);
rp = res->d;
if ( carry_limb )
{
rp[rsize] = carry_limb;
rsize++;
}
}
else if (res->d != rp)
{
MPN_COPY (res->d, rp, rsize);
rp = res->d;
}
if ( rsize >= msize )
{
_gcry_mpih_divrem(rp + msize, 0, rp, rsize, mp, msize);
rsize = msize;
}
/* Remove any leading zero words from the result. */
if ( mod_shift_cnt )
_gcry_mpih_rshift( rp, rp, rsize, mod_shift_cnt);
MPN_NORMALIZE (rp, rsize);
_gcry_mpih_release_karatsuba_ctx (&karactx );
}
/* Fixup for negative results. */
if ( negative_result && rsize )
{
if ( mod_shift_cnt )
_gcry_mpih_rshift( mp, mp, msize, mod_shift_cnt);
_gcry_mpih_sub( rp, mp, msize, rp, rsize);
rsize = msize;
rsign = msign;
MPN_NORMALIZE(rp, rsize);
}
gcry_assert (res->d == rp);
res->nlimbs = rsize;
res->sign = rsign;
leave:
if (mp_marker)
_gcry_mpi_free_limb_space( mp_marker, mp_nlimbs );
if (bp_marker)
_gcry_mpi_free_limb_space( bp_marker, bp_nlimbs );
if (ep_marker)
_gcry_mpi_free_limb_space( ep_marker, ep_nlimbs );
if (xp_marker)
_gcry_mpi_free_limb_space( xp_marker, xp_nlimbs );
if (tspace)
_gcry_mpi_free_limb_space( tspace, 0 );
}
void
gcry_mpi_add(gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v)
{
mpi_ptr_t wp, up, vp;
mpi_size_t usize, vsize, wsize;
int usign, vsign, wsign;
if( u->nlimbs < v->nlimbs ) { /* Swap U and V. */
usize = v->nlimbs;
usign = v->sign;
vsize = u->nlimbs;
vsign = u->sign;
wsize = usize + 1;
RESIZE_IF_NEEDED(w, wsize);
/* These must be after realloc (u or v may be the same as w). */
up = v->d;
vp = u->d;
}
else {
usize = u->nlimbs;
usign = u->sign;
vsize = v->nlimbs;
vsign = v->sign;
wsize = usize + 1;
RESIZE_IF_NEEDED(w, wsize);
/* These must be after realloc (u or v may be the same as w). */
up = u->d;
vp = v->d;
}
wp = w->d;
wsign = 0;
if( !vsize ) { /* simple */
MPN_COPY(wp, up, usize );
wsize = usize;
wsign = usign;
}
else if( usign != vsign ) { /* different sign */
/* This test is right since USIZE >= VSIZE */
if( usize != vsize ) {
_gcry_mpih_sub(wp, up, usize, vp, vsize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
wsign = usign;
}
else if( _gcry_mpih_cmp(up, vp, usize) < 0 ) {
_gcry_mpih_sub_n(wp, vp, up, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if( !usign )
wsign = 1;
}
else {
_gcry_mpih_sub_n(wp, up, vp, usize);
wsize = usize;
MPN_NORMALIZE(wp, wsize);
if( usign )
wsign = 1;
}
}
else { /* U and V have same sign. Add them. */
mpi_limb_t cy = _gcry_mpih_add(wp, up, usize, vp, vsize);
wp[usize] = cy;
wsize = usize + cy;
if( usign )
wsign = 1;
}
w->nlimbs = wsize;
w->sign = wsign;
}