int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
{
mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
mpi_ptr_t xp_marker = NULL;
mpi_ptr_t tspace = NULL;
mpi_ptr_t rp, ep, mp, bp;
mpi_size_t esize, msize, bsize, rsize;
int esign, msign, bsign, rsign;
mpi_size_t size;
int mod_shift_cnt;
int negative_result;
int assign_rp = 0;
mpi_size_t tsize = 0;
int rc = -ENOMEM;
esize = exp->nlimbs;
msize = mod->nlimbs;
size = 2 * msize;
esign = exp->sign;
msign = mod->sign;
rp = res->d;
ep = exp->d;
if (!msize)
return -EINVAL;
if (!esize) {
rp[0] = 1;
res->nlimbs = (msize == 1 && mod->d[0] == 1) ? 0 : 1;
res->sign = 0;
goto leave;
}
mp = mp_marker = mpi_alloc_limb_space(msize);
if (!mp)
goto enomem;
count_leading_zeros(mod_shift_cnt, mod->d[msize - 1]);
if (mod_shift_cnt)
mpihelp_lshift(mp, mod->d, msize, mod_shift_cnt);
else
MPN_COPY(mp, mod->d, msize);
bsize = base->nlimbs;
bsign = base->sign;
if (bsize > msize) {
bp = bp_marker = mpi_alloc_limb_space(bsize + 1);
if (!bp)
goto enomem;
MPN_COPY(bp, base->d, bsize);
mpihelp_divrem(bp + msize, 0, bp, bsize, mp, msize);
bsize = msize;
MPN_NORMALIZE(bp, bsize);
} else
bp = base->d;
if (!bsize) {
res->nlimbs = 0;
res->sign = 0;
goto leave;
}
if (res->alloced < size) {
if (rp == ep || rp == mp || rp == bp) {
rp = mpi_alloc_limb_space(size);
if (!rp)
goto enomem;
assign_rp = 1;
} else {
if (mpi_resize(res, size) < 0)
goto enomem;
rp = res->d;
}
} else {
if (rp == bp) {
BUG_ON(bp_marker);
bp = bp_marker = mpi_alloc_limb_space(bsize);
if (!bp)
goto enomem;
MPN_COPY(bp, rp, bsize);
}
if (rp == ep) {
ep = ep_marker = mpi_alloc_limb_space(esize);
if (!ep)
goto enomem;
MPN_COPY(ep, rp, esize);
}
if (rp == mp) {
BUG_ON(mp_marker);
mp = mp_marker = mpi_alloc_limb_space(msize);
if (!mp)
goto enomem;
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 = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
if (!xp)
goto enomem;
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;
c = BITS_PER_MPI_LIMB - 1 - c;
for (;;) {
while (c) {
mpi_ptr_t tp;
mpi_size_t xsize;
if (rsize < KARATSUBA_THRESHOLD)
mpih_sqr_n_basecase(xp, rp, rsize);
else {
if (!tspace) {
tsize = 2 * rsize;
tspace =
mpi_alloc_limb_space(tsize);
if (!tspace)
goto enomem;
} else if (tsize < (2 * rsize)) {
mpi_free_limb_space(tspace);
tsize = 2 * rsize;
tspace =
mpi_alloc_limb_space(tsize);
if (!tspace)
goto enomem;
}
mpih_sqr_n(xp, rp, rsize, tspace);
}
xsize = 2 * rsize;
if (xsize > msize) {
mpihelp_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) {
if (bsize < KARATSUBA_THRESHOLD) {
mpi_limb_t tmp;
if (mpihelp_mul
(xp, rp, rsize, bp, bsize,
&tmp) < 0)
goto enomem;
} else {
if (mpihelp_mul_karatsuba_case
(xp, rp, rsize, bp, bsize,
&karactx) < 0)
goto enomem;
}
xsize = rsize + bsize;
if (xsize > msize) {
mpihelp_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;
}
if (mod_shift_cnt) {
carry_limb =
mpihelp_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) {
mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
rsize = msize;
}
if (mod_shift_cnt)
mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
MPN_NORMALIZE(rp, rsize);
mpihelp_release_karatsuba_ctx(&karactx);
}
if (negative_result && rsize) {
if (mod_shift_cnt)
mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
mpihelp_sub(rp, mp, msize, rp, rsize);
rsize = msize;
rsign = msign;
MPN_NORMALIZE(rp, rsize);
}
res->nlimbs = rsize;
res->sign = rsign;
leave:
rc = 0;
enomem:
if (assign_rp)
mpi_assign_limb_space(res, rp, size);
if (mp_marker)
mpi_free_limb_space(mp_marker);
if (bp_marker)
mpi_free_limb_space(bp_marker);
if (ep_marker)
mpi_free_limb_space(ep_marker);
if (xp_marker)
mpi_free_limb_space(xp_marker);
if (tspace)
mpi_free_limb_space(tspace);
return rc;
}
void
mpi_tdiv_qr( MPI quot, MPI rem, MPI num, MPI den)
{
mpi_ptr_t np, dp;
mpi_ptr_t qp, rp;
mpi_size_t nsize = num->nlimbs;
mpi_size_t dsize = den->nlimbs;
mpi_size_t qsize, rsize;
mpi_size_t sign_remainder = num->sign;
mpi_size_t sign_quotient = num->sign ^ den->sign;
unsigned normalization_steps;
mpi_limb_t q_limb;
mpi_ptr_t marker[5];
int markidx=0;
/* Ensure space is enough for quotient and remainder.
* We need space for an extra limb in the remainder, because it's
* up-shifted (normalized) below. */
rsize = nsize + 1;
mpi_resize( rem, rsize);
qsize = rsize - dsize; /* qsize cannot be bigger than this. */
if( qsize <= 0 ) {
if( num != rem ) {
rem->nlimbs = num->nlimbs;
rem->sign = num->sign;
MPN_COPY(rem->d, num->d, nsize);
}
if( quot ) {
/* This needs to follow the assignment to rem, in case the
* numerator and quotient are the same. */
quot->nlimbs = 0;
quot->sign = 0;
}
return;
}
if( quot )
mpi_resize( quot, qsize);
/* Read pointers here, when reallocation is finished. */
np = num->d;
dp = den->d;
rp = rem->d;
/* Optimize division by a single-limb divisor. */
if( dsize == 1 ) {
mpi_limb_t rlimb;
if( quot ) {
qp = quot->d;
rlimb = mpihelp_divmod_1( qp, np, nsize, dp[0] );
qsize -= qp[qsize - 1] == 0;
quot->nlimbs = qsize;
quot->sign = sign_quotient;
}
else
rlimb = mpihelp_mod_1( np, nsize, dp[0] );
rp[0] = rlimb;
rsize = rlimb != 0?1:0;
rem->nlimbs = rsize;
rem->sign = sign_remainder;
return;
}
if( quot ) {
qp = quot->d;
/* Make sure QP and NP point to different objects. Otherwise the
* numerator would be gradually overwritten by the quotient limbs. */
if(qp == np) { /* Copy NP object to temporary space. */
np = marker[markidx++] = mpi_alloc_limb_space(nsize,
mpi_is_secure(quot));
MPN_COPY(np, qp, nsize);
}
}
else /* Put quotient at top of remainder. */
qp = rp + dsize;
count_leading_zeros( normalization_steps, dp[dsize - 1] );
/* Normalize the denominator, i.e. make its most significant bit set by
* shifting it NORMALIZATION_STEPS bits to the left. Also shift the
* numerator the same number of steps (to keep the quotient the same!).
*/
if( normalization_steps ) {
mpi_ptr_t tp;
mpi_limb_t nlimb;
/* Shift up the denominator setting the most significant bit of
* the most significant word. Use temporary storage not to clobber
* the original contents of the denominator. */
tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den));
mpihelp_lshift( tp, dp, dsize, normalization_steps );
dp = tp;
/* Shift up the numerator, possibly introducing a new most
* significant word. Move the shifted numerator in the remainder
* meanwhile. */
nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
if( nlimb ) {
rp[nsize] = nlimb;
rsize = nsize + 1;
}
else
rsize = nsize;
}
else {
/* The denominator is already normalized, as required. Copy it to
* temporary space if it overlaps with the quotient or remainder. */
if( dp == rp || (quot && (dp == qp))) {
mpi_ptr_t tp;
tp = marker[markidx++] = mpi_alloc_limb_space(dsize, mpi_is_secure(den));
MPN_COPY( tp, dp, dsize );
dp = tp;
}
/* Move the numerator to the remainder. */
if( rp != np )
MPN_COPY(rp, np, nsize);
rsize = nsize;
}
q_limb = mpihelp_divrem( qp, 0, rp, rsize, dp, dsize );
if( quot ) {
qsize = rsize - dsize;
if(q_limb) {
qp[qsize] = q_limb;
qsize += 1;
}
quot->nlimbs = qsize;
quot->sign = sign_quotient;
}
rsize = dsize;
MPN_NORMALIZE (rp, rsize);
if( normalization_steps && rsize ) {
mpihelp_rshift(rp, rp, rsize, normalization_steps);
rsize -= rp[rsize - 1] == 0?1:0;
}
rem->nlimbs = rsize;
rem->sign = sign_remainder;
while( markidx )
mpi_free_gpg_limb_space(marker[--markidx]);
}
/****************
* RES = BASE ^ EXP mod MOD
*/
int mpi_powm(MPI res, MPI base, MPI exp, MPI mod)
{
mpi_ptr_t mp_marker = NULL, bp_marker = NULL, ep_marker = NULL;
mpi_ptr_t xp_marker = NULL;
mpi_ptr_t tspace = NULL;
mpi_ptr_t rp, ep, mp, bp;
mpi_size_t esize, msize, bsize, rsize;
int esign, msign, bsign, rsign;
mpi_size_t size;
int mod_shift_cnt;
int negative_result;
int assign_rp = 0;
mpi_size_t tsize = 0; /* to avoid compiler warning */
/* fixme: we should check that the warning is void */
int rc = -ENOMEM;
esize = exp->nlimbs;
msize = mod->nlimbs;
size = 2 * msize;
esign = exp->sign;
msign = mod->sign;
rp = res->d;
ep = exp->d;
if (!msize)
return -EINVAL;
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 = mp_marker = mpi_alloc_limb_space(msize);
if (!mp)
goto enomem;
count_leading_zeros(mod_shift_cnt, mod->d[msize - 1]);
if (mod_shift_cnt)
mpihelp_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 = bp_marker = mpi_alloc_limb_space(bsize + 1);
if (!bp)
goto enomem;
MPN_COPY(bp, base->d, bsize);
/* We don't care about the quotient, store it above the remainder,
* at BP + MSIZE. */
mpihelp_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);
if (!rp)
goto enomem;
assign_rp = 1;
} else {
if (mpi_resize(res, size) < 0)
goto enomem;
rp = res->d;
}
} else { /* Make BASE, EXP and MOD not overlap with RES. */
if (rp == bp) {
/* RES and BASE are identical. Allocate temp. space for BASE. */
BUG_ON(bp_marker);
bp = bp_marker = mpi_alloc_limb_space(bsize);
if (!bp)
goto enomem;
MPN_COPY(bp, rp, bsize);
}
if (rp == ep) {
/* RES and EXP are identical. Allocate temp. space for EXP. */
ep = ep_marker = mpi_alloc_limb_space(esize);
if (!ep)
goto enomem;
MPN_COPY(ep, rp, esize);
}
if (rp == mp) {
/* RES and MOD are identical. Allocate temporary space for MOD. */
BUG_ON(mp_marker);
mp = mp_marker = mpi_alloc_limb_space(msize);
if (!mp)
goto enomem;
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 = xp_marker = mpi_alloc_limb_space(2 * (msize + 1));
if (!xp)
goto enomem;
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 exp 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 mpihelp_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;
/*if (mpihelp_mul_n(xp, rp, rp, rsize) < 0) goto enomem */
if (rsize < KARATSUBA_THRESHOLD)
mpih_sqr_n_basecase(xp, rp, rsize);
else {
if (!tspace) {
tsize = 2 * rsize;
tspace =
mpi_alloc_limb_space(tsize);
if (!tspace)
goto enomem;
} else if (tsize < (2 * rsize)) {
mpi_free_limb_space(tspace);
tsize = 2 * rsize;
tspace =
mpi_alloc_limb_space(tsize);
if (!tspace)
goto enomem;
}
mpih_sqr_n(xp, rp, rsize, tspace);
}
xsize = 2 * rsize;
if (xsize > msize) {
mpihelp_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) {
/*mpihelp_mul( xp, rp, rsize, bp, bsize ); */
if (bsize < KARATSUBA_THRESHOLD) {
mpi_limb_t tmp;
if (mpihelp_mul
(xp, rp, rsize, bp, bsize,
&tmp) < 0)
goto enomem;
} else {
if (mpihelp_mul_karatsuba_case
(xp, rp, rsize, bp, bsize,
&karactx) < 0)
goto enomem;
}
xsize = rsize + bsize;
if (xsize > msize) {
mpihelp_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 =
mpihelp_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) {
mpihelp_divrem(rp + msize, 0, rp, rsize, mp, msize);
rsize = msize;
}
/* Remove any leading zero words from the result. */
if (mod_shift_cnt)
mpihelp_rshift(rp, rp, rsize, mod_shift_cnt);
MPN_NORMALIZE(rp, rsize);
mpihelp_release_karatsuba_ctx(&karactx);
}
if (negative_result && rsize) {
if (mod_shift_cnt)
mpihelp_rshift(mp, mp, msize, mod_shift_cnt);
mpihelp_sub(rp, mp, msize, rp, rsize);
rsize = msize;
rsign = msign;
MPN_NORMALIZE(rp, rsize);
}
res->nlimbs = rsize;
res->sign = rsign;
leave:
rc = 0;
enomem:
if (assign_rp)
mpi_assign_limb_space(res, rp, size);
if (mp_marker)
mpi_free_limb_space(mp_marker);
if (bp_marker)
mpi_free_limb_space(bp_marker);
if (ep_marker)
mpi_free_limb_space(ep_marker);
if (xp_marker)
mpi_free_limb_space(xp_marker);
if (tspace)
mpi_free_limb_space(tspace);
return rc;
}
