void
mpi_mul_ui( MPI prod, MPI mult, unsigned long small_mult )
{
mpi_size_t size, prod_size;
mpi_ptr_t prod_ptr;
mpi_limb_t cy;
int sign;
size = mult->nlimbs;
sign = mult->sign;
if( !size || !small_mult ) {
prod->nlimbs = 0;
prod->sign = 0;
return;
}
prod_size = size + 1;
if( prod->alloced < prod_size )
mpi_resize( prod, prod_size );
prod_ptr = prod->d;
cy = mpihelp_mul_1( prod_ptr, mult->d, size, (mpi_limb_t)small_mult );
if( cy )
prod_ptr[size++] = cy;
prod->nlimbs = size;
prod->sign = sign;
}
/****************
* Set bit N of A.
*/
void
mpi_set_bit( MPI a, unsigned n )
{
unsigned limbno, bitno;
limbno = n / BITS_PER_MPI_LIMB;
bitno = n % BITS_PER_MPI_LIMB;
if( limbno >= a->nlimbs ) { /* resize */
if( a->alloced >= limbno )
mpi_resize(a, limbno+1 );
a->nlimbs = limbno+1;
}
a->d[limbno] |= (A_LIMB_1<<bitno);
}
/****************
* Set bit N of A.
*/
void
gcry_mpi_set_bit( gcry_mpi_t a, unsigned int n )
{
unsigned int limbno, bitno;
limbno = n / BITS_PER_MPI_LIMB;
bitno = n % BITS_PER_MPI_LIMB;
if ( limbno >= a->nlimbs )
{
mpi_resize (a, limbno+1 );
a->nlimbs = limbno+1;
}
a->d[limbno] |= (A_LIMB_1<<bitno);
}
/****************
* Subtract the unsigned integer V from the mpi-integer U and store the
* result in W.
*/
void
mpi_sub_ui(MPI w, MPI u, unsigned long v )
{
mpi_ptr_t wp, up;
mpi_size_t usize, wsize;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
wsign = 0;
/* If not space for W (and possible carry), increase space. */
wsize = usize + 1;
if( w->alloced < wsize )
mpi_resize(w, wsize);
/* These must be after realloc (U may be the same as W). */
up = u->d;
wp = w->d;
if( !usize ) { /* simple */
wp[0] = v;
wsize = v? 1:0;
wsign = 1;
}
else if( usign ) { /* mpi and v are negative */
mpi_limb_t cy;
cy = mpihelp_add_1(wp, up, usize, v);
wp[usize] = cy;
wsize = usize + cy;
}
else { /* The signs are different. Need exact comparison to determine
* which operand to subtract from which. */
if( usize == 1 && up[0] < v ) {
wp[0] = v - up[0];
wsize = 1;
wsign = 1;
}
else {
mpihelp_sub_1(wp, up, usize, v);
/* Size can decrease with at most one limb. */
wsize = usize - (wp[usize-1]==0);
}
}
w->nlimbs = wsize;
w->sign = wsign;
}
int mpi_sub_ui(MPI w, MPI u, unsigned long v)
{
mpi_ptr_t wp, up;
mpi_size_t usize, wsize;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
wsign = 0;
wsize = usize + 1;
if (w->alloced < wsize)
if (mpi_resize(w, wsize) < 0)
return -ENOMEM;
up = u->d;
wp = w->d;
if (!usize) {
wp[0] = v;
wsize = v ? 1 : 0;
wsign = 1;
} else if (usign) {
mpi_limb_t cy;
cy = mpihelp_add_1(wp, up, usize, v);
wp[usize] = cy;
wsize = usize + cy;
} else {
if (usize == 1 && up[0] < v) {
wp[0] = v - up[0];
wsize = 1;
wsign = 1;
} else {
mpihelp_sub_1(wp, up, usize, v);
wsize = usize - (wp[usize - 1] == 0);
}
}
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
void
mpi_mul_2exp( MPI w, MPI u, unsigned long cnt)
{
mpi_size_t usize, wsize, limb_cnt;
mpi_ptr_t wp;
mpi_limb_t wlimb;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
if( !usize ) {
w->nlimbs = 0;
w->sign = 0;
return;
}
limb_cnt = cnt / BITS_PER_MPI_LIMB;
wsize = usize + limb_cnt + 1;
if( w->alloced < wsize )
mpi_resize(w, wsize );
wp = w->d;
wsize = usize + limb_cnt;
wsign = usign;
cnt %= BITS_PER_MPI_LIMB;
if( cnt ) {
wlimb = mpihelp_lshift( wp + limb_cnt, u->d, usize, cnt );
if( wlimb ) {
wp[wsize] = wlimb;
wsize++;
}
}
else {
MPN_COPY_DECR( wp + limb_cnt, u->d, usize );
}
/* Zero all whole limbs at low end. Do it here and not before calling
* mpn_lshift, not to lose for U == W. */
MPN_ZERO( wp, limb_cnt );
w->nlimbs = wsize;
w->sign = wsign;
}
int mpi_mul_2exp(MPI w, MPI u, unsigned long cnt)
{
mpi_size_t usize, wsize, limb_cnt;
mpi_ptr_t wp;
mpi_limb_t wlimb;
int usign, wsign;
usize = u->nlimbs;
usign = u->sign;
if (!usize) {
w->nlimbs = 0;
w->sign = 0;
return 0;
}
limb_cnt = cnt / BITS_PER_MPI_LIMB;
wsize = usize + limb_cnt + 1;
if (w->alloced < wsize)
if (mpi_resize(w, wsize) < 0)
return -ENOMEM;
wp = w->d;
wsize = usize + limb_cnt;
wsign = usign;
cnt %= BITS_PER_MPI_LIMB;
if (cnt) {
wlimb = mpihelp_lshift(wp + limb_cnt, u->d, usize, cnt);
if (wlimb) {
wp[wsize] = wlimb;
wsize++;
}
} else {
MPN_COPY_DECR(wp + limb_cnt, u->d, usize);
}
/*
*/
MPN_ZERO(wp, limb_cnt);
w->nlimbs = wsize;
w->sign = wsign;
return 0;
}
static void
ec_mulm (gcry_mpi_t w, gcry_mpi_t u, gcry_mpi_t v, mpi_ec_t ctx)
{
#if 0
/* NOTE: This code works only for limb sizes of 32 bit. */
mpi_limb_t *wp, *sp;
if (ctx->nist_nbits == 192)
{
mpi_mul (w, u, v);
mpi_resize (w, 12);
wp = w->d;
sp = ctx->s[0]->d;
sp[0*2+0] = wp[0*2+0];
sp[0*2+1] = wp[0*2+1];
sp[1*2+0] = wp[1*2+0];
sp[1*2+1] = wp[1*2+1];
sp[2*2+0] = wp[2*2+0];
sp[2*2+1] = wp[2*2+1];
sp = ctx->s[1]->d;
sp[0*2+0] = wp[3*2+0];
sp[0*2+1] = wp[3*2+1];
sp[1*2+0] = wp[3*2+0];
sp[1*2+1] = wp[3*2+1];
sp[2*2+0] = 0;
sp[2*2+1] = 0;
sp = ctx->s[2]->d;
sp[0*2+0] = 0;
sp[0*2+1] = 0;
sp[1*2+0] = wp[4*2+0];
sp[1*2+1] = wp[4*2+1];
sp[2*2+0] = wp[4*2+0];
sp[2*2+1] = wp[4*2+1];
sp = ctx->s[3]->d;
sp[0*2+0] = wp[5*2+0];
sp[0*2+1] = wp[5*2+1];
sp[1*2+0] = wp[5*2+0];
sp[1*2+1] = wp[5*2+1];
sp[2*2+0] = wp[5*2+0];
sp[2*2+1] = wp[5*2+1];
ctx->s[0]->nlimbs = 6;
ctx->s[1]->nlimbs = 6;
ctx->s[2]->nlimbs = 6;
ctx->s[3]->nlimbs = 6;
mpi_add (ctx->c, ctx->s[0], ctx->s[1]);
mpi_add (ctx->c, ctx->c, ctx->s[2]);
mpi_add (ctx->c, ctx->c, ctx->s[3]);
while ( mpi_cmp (ctx->c, ctx->p ) >= 0 )
mpi_sub ( ctx->c, ctx->c, ctx->p );
mpi_set (w, ctx->c);
}
else if (ctx->nist_nbits == 384)
{
int i;
mpi_mul (w, u, v);
mpi_resize (w, 24);
wp = w->d;
#define NEXT(a) do { ctx->s[(a)]->nlimbs = 12; \
sp = ctx->s[(a)]->d; \
i = 0; } while (0)
#define X(a) do { sp[i++] = wp[(a)];} while (0)
#define X0(a) do { sp[i++] = 0; } while (0)
NEXT(0);
X(0);X(1);X(2);X(3);X(4);X(5);X(6);X(7);X(8);X(9);X(10);X(11);
NEXT(1);
X0();X0();X0();X0();X(21);X(22);X(23);X0();X0();X0();X0();X0();
NEXT(2);
X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);X(21);X(22);X(23);
NEXT(3);
X(21);X(22);X(23);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);
NEXT(4);
X0();X(23);X0();X(20);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);
NEXT(5);
X0();X0();X0();X0();X(20);X(21);X(22);X(23);X0();X0();X0();X0();
NEXT(6);
X(20);X0();X0();X(21);X(22);X(23);X0();X0();X0();X0();X0();X0();
NEXT(7);
X(23);X(12);X(13);X(14);X(15);X(16);X(17);X(18);X(19);X(20);X(21);X(22);
NEXT(8);
X0();X(20);X(21);X(22);X(23);X0();X0();X0();X0();X0();X0();X0();
NEXT(9);
X0();X0();X0();X(23);X(23);X0();X0();X0();X0();X0();X0();X0();
#undef X0
#undef X
#undef NEXT
mpi_add (ctx->c, ctx->s[0], ctx->s[1]);
mpi_add (ctx->c, ctx->c, ctx->s[1]);
mpi_add (ctx->c, ctx->c, ctx->s[2]);
mpi_add (ctx->c, ctx->c, ctx->s[3]);
mpi_add (ctx->c, ctx->c, ctx->s[4]);
mpi_add (ctx->c, ctx->c, ctx->s[5]);
mpi_add (ctx->c, ctx->c, ctx->s[6]);
mpi_sub (ctx->c, ctx->c, ctx->s[7]);
mpi_sub (ctx->c, ctx->c, ctx->s[8]);
mpi_sub (ctx->c, ctx->c, ctx->s[9]);
while ( mpi_cmp (ctx->c, ctx->p ) >= 0 )
mpi_sub ( ctx->c, ctx->c, ctx->p );
while ( ctx->c->sign )
mpi_add ( ctx->c, ctx->c, ctx->p );
mpi_set (w, ctx->c);
}
else
#endif /*0*/
mpi_mulm (w, u, v, ctx->p);
}
void
mpi_mul( MPI w, MPI u, MPI v)
{
mpi_size_t usize, vsize, wsize;
mpi_ptr_t up, vp, wp;
mpi_limb_t cy;
int usign, vsign, usecure, vsecure, sign_product;
int assign_wp=0;
mpi_ptr_t tmp_limb=NULL;
if( u->nlimbs < v->nlimbs ) { /* Swap U and V. */
usize = v->nlimbs;
usign = v->sign;
usecure = mpi_is_secure(v);
up = v->d;
vsize = u->nlimbs;
vsign = u->sign;
vsecure = mpi_is_secure(u);
vp = u->d;
}
else {
usize = u->nlimbs;
usign = u->sign;
usecure = mpi_is_secure(u);
up = u->d;
vsize = v->nlimbs;
vsign = v->sign;
vsecure = mpi_is_secure(v);
vp = v->d;
}
sign_product = usign ^ vsign;
wp = w->d;
/* Ensure W has space enough to store the result. */
wsize = usize + vsize;
if ( !mpi_is_secure (w) && (mpi_is_secure (u) || mpi_is_secure (v)) ) {
/* w is not allocated in secure space but u or v is. To make sure
* that no temporray results are stored in w, we temporary use
* a newly allocated limb space for w */
wp = mpi_alloc_limb_space( wsize, 1 );
assign_wp = 2; /* mark it as 2 so that we can later copy it back to
* mormal memory */
}
else if( w->alloced < wsize ) {
if( wp == up || wp == vp ) {
wp = mpi_alloc_limb_space( wsize, mpi_is_secure(w) );
assign_wp = 1;
}
else {
mpi_resize(w, wsize );
wp = w->d;
}
}
else { /* Make U and V not overlap with W. */
if( wp == up ) {
/* W and U are identical. Allocate temporary space for U. */
up = tmp_limb = mpi_alloc_limb_space( usize, usecure );
/* Is V identical too? Keep it identical with U. */
if( wp == vp )
vp = up;
/* Copy to the temporary space. */
MPN_COPY( up, wp, usize );
}
else if( wp == vp ) {
/* W and V are identical. Allocate temporary space for V. */
vp = tmp_limb = mpi_alloc_limb_space( vsize, vsecure );
/* Copy to the temporary space. */
MPN_COPY( vp, wp, vsize );
}
}
if( !vsize )
wsize = 0;
else {
cy = mpihelp_mul( wp, up, usize, vp, vsize );
wsize -= cy? 0:1;
}
if( assign_wp ) {
if (assign_wp == 2) {
/* copy the temp wp from secure memory back to normal memory */
mpi_ptr_t tmp_wp = mpi_alloc_limb_space (wsize, 0);
MPN_COPY (tmp_wp, wp, wsize);
mpi_free_limb_space (wp);
wp = tmp_wp;
}
mpi_assign_limb_space( w, wp, wsize );
}
w->nlimbs = wsize;
w->sign = sign_product;
if( tmp_limb )
mpi_free_limb_space( tmp_limb );
}
int mpi_fromstr(MPI val, const char *str)
{
int hexmode = 0, sign = 0, prepend_zero = 0, i, j, c, c1, c2;
unsigned nbits, nbytes, nlimbs;
mpi_limb_t a;
if (*str == '-') {
sign = 1;
str++;
}
if (*str == '0' && str[1] == 'x')
hexmode = 1;
else
return -EINVAL;
str += 2;
nbits = strlen(str) * 4;
if (nbits % 8)
prepend_zero = 1;
nbytes = (nbits + 7) / 8;
nlimbs = (nbytes + BYTES_PER_MPI_LIMB - 1) / BYTES_PER_MPI_LIMB;
if (val->alloced < nlimbs)
if (!mpi_resize(val, nlimbs))
return -ENOMEM;
i = BYTES_PER_MPI_LIMB - nbytes % BYTES_PER_MPI_LIMB;
i %= BYTES_PER_MPI_LIMB;
j = val->nlimbs = nlimbs;
val->sign = sign;
for (; j > 0; j--) {
a = 0;
for (; i < BYTES_PER_MPI_LIMB; i++) {
if (prepend_zero) {
c1 = '0';
prepend_zero = 0;
} else
c1 = *str++;
assert(c1);
c2 = *str++;
assert(c2);
if (c1 >= '0' && c1 <= '9')
c = c1 - '0';
else if (c1 >= 'a' && c1 <= 'f')
c = c1 - 'a' + 10;
else if (c1 >= 'A' && c1 <= 'F')
c = c1 - 'A' + 10;
else {
mpi_clear(val);
return 1;
}
c <<= 4;
if (c2 >= '0' && c2 <= '9')
c |= c2 - '0';
else if (c2 >= 'a' && c2 <= 'f')
c |= c2 - 'a' + 10;
else if (c2 >= 'A' && c2 <= 'F')
c |= c2 - 'A' + 10;
else {
mpi_clear(val);
return 1;
}
a <<= 8;
a |= c;
}
i = 0;
val->d[j - 1] = a;
}
return 0;
}
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 ^ 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 );
}
/****************
* 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 );
}
/****************
* Fill the mpi VAL from the hex string in STR.
*/
static int
mpi_fromstr (gcry_mpi_t val, const char *str)
{
int sign = 0;
int prepend_zero = 0;
int i, j, c, c1, c2;
unsigned int nbits, nbytes, nlimbs;
mpi_limb_t a;
if ( *str == '-' )
{
sign = 1;
str++;
}
/* Skip optional hex prefix. */
if ( *str == '0' && str[1] == 'x' )
str += 2;
nbits = 4 * strlen (str);
if ((nbits % 8))
prepend_zero = 1;
nbytes = (nbits+7) / 8;
nlimbs = (nbytes+BYTES_PER_MPI_LIMB-1) / BYTES_PER_MPI_LIMB;
if ( val->alloced < nlimbs )
mpi_resize (val, nlimbs);
i = BYTES_PER_MPI_LIMB - (nbytes % BYTES_PER_MPI_LIMB);
i %= BYTES_PER_MPI_LIMB;
j = val->nlimbs = nlimbs;
val->sign = sign;
for (; j > 0; j--)
{
a = 0;
for (; i < BYTES_PER_MPI_LIMB; i++)
{
if (prepend_zero)
{
c1 = '0';
prepend_zero = 0;
}
else
c1 = *str++;
if (!c1)
{
mpi_clear (val);
return 1; /* Error. */
}
c2 = *str++;
if (!c2)
{
mpi_clear (val);
return 1; /* Error. */
}
if ( c1 >= '0' && c1 <= '9' )
c = c1 - '0';
else if ( c1 >= 'a' && c1 <= 'f' )
c = c1 - 'a' + 10;
else if ( c1 >= 'A' && c1 <= 'F' )
c = c1 - 'A' + 10;
else
{
mpi_clear (val);
return 1; /* Error. */
}
c <<= 4;
if ( c2 >= '0' && c2 <= '9' )
c |= c2 - '0';
else if( c2 >= 'a' && c2 <= 'f' )
c |= c2 - 'a' + 10;
else if( c2 >= 'A' && c2 <= 'F' )
c |= c2 - 'A' + 10;
else
{
mpi_clear(val);
return 1; /* Error. */
}
a <<= 8;
a |= c;
}
i = 0;
val->d[j-1] = a;
}
return 0; /* Okay. */
}
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;
}
int mpi_mul(MPI w, MPI u, MPI v)
{
int rc = -ENOMEM;
mpi_size_t usize, vsize, wsize;
mpi_ptr_t up, vp, wp;
mpi_limb_t cy;
int usign, vsign, sign_product;
int assign_wp = 0;
mpi_ptr_t tmp_limb = NULL;
if (u->nlimbs < v->nlimbs) { /* */
usize = v->nlimbs;
usign = v->sign;
up = v->d;
vsize = u->nlimbs;
vsign = u->sign;
vp = u->d;
} else {
usize = u->nlimbs;
usign = u->sign;
up = u->d;
vsize = v->nlimbs;
vsign = v->sign;
vp = v->d;
}
sign_product = usign ^ vsign;
wp = w->d;
/* */
wsize = usize + vsize;
if (w->alloced < (size_t) wsize) {
if (wp == up || wp == vp) {
wp = mpi_alloc_limb_space(wsize);
if (!wp)
goto nomem;
assign_wp = 1;
} else {
if (mpi_resize(w, wsize) < 0)
goto nomem;
wp = w->d;
}
} else { /* */
if (wp == up) {
/* */
up = tmp_limb = mpi_alloc_limb_space(usize);
if (!up)
goto nomem;
/* */
if (wp == vp)
vp = up;
/* */
MPN_COPY(up, wp, usize);
} else if (wp == vp) {
/* */
vp = tmp_limb = mpi_alloc_limb_space(vsize);
if (!vp)
goto nomem;
/* */
MPN_COPY(vp, wp, vsize);
}
}
if (!vsize)
wsize = 0;
else {
if (mpihelp_mul(wp, up, usize, vp, vsize, &cy) < 0)
goto nomem;
wsize -= cy ? 0 : 1;
}
if (assign_wp)
mpi_assign_limb_space(w, wp, wsize);
w->nlimbs = wsize;
w->sign = sign_product;
rc = 0;
nomem:
if (tmp_limb)
mpi_free_limb_space(tmp_limb);
return rc;
}
