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Nearly forgot. Reinstate the original unoptimised modpow, as a

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fallback for when Montgomery is inapplicable.

(I may also at some point switch to using it for small exponents, if
speed testing should reveal that there's a noticeable threshold beyond
which preparing the Montgomery setup is uneconomical.)

[originally from svn r9099]
This commit is contained in:
Simon Tatham 2011-02-20 15:14:02 +00:00
parent 260cee498e
commit 1b47322c3b
1 changed files with 129 additions and 7 deletions
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136
sshbn.c
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@ -704,9 +704,130 @@ static void internal_mod(BignumInt *a, int alen,
}
}
/*
* Compute (base ^ exp) % mod, the pedestrian way.
*/
Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)
{
BignumInt *a, *b, *n, *m;
int mshift;
int mlen, i, j;
Bignum base, result;
/*
* The most significant word of mod needs to be non-zero. It
* should already be, but let's make sure.
*/
assert(mod[mod[0]] != 0);
/*
* Make sure the base is smaller than the modulus, by reducing
* it modulo the modulus if not.
*/
base = bigmod(base_in, mod);
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
m = snewn(mlen, BignumInt);
for (j = 0; j < mlen; j++)
m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
if ((m[0] << mshift) & BIGNUM_TOP_BIT)
break;
if (mshift) {
for (i = 0; i < mlen - 1; i++)
m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
m[mlen - 1] = m[mlen - 1] << mshift;
}
/* Allocate n of size mlen, copy base to n */
n = snewn(mlen, BignumInt);
i = mlen - base[0];
for (j = 0; j < i; j++)
n[j] = 0;
for (j = 0; j < (int)base[0]; j++)
n[i + j] = base[base[0] - j];
/* Allocate a and b of size 2*mlen. Set a = 1 */
a = snewn(2 * mlen, BignumInt);
b = snewn(2 * mlen, BignumInt);
for (i = 0; i < 2 * mlen; i++)
a[i] = 0;
a[2 * mlen - 1] = 1;
/* Skip leading zero bits of exp. */
i = 0;
j = BIGNUM_INT_BITS-1;
while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
j--;
if (j < 0) {
i++;
j = BIGNUM_INT_BITS-1;
}
}
/* Main computation */
while (i < (int)exp[0]) {
while (j >= 0) {
internal_mul(a + mlen, a + mlen, b, mlen);
internal_mod(b, mlen * 2, m, mlen, NULL, 0);
if ((exp[exp[0] - i] & (1 << j)) != 0) {
internal_mul(b + mlen, n, a, mlen);
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
} else {
BignumInt *t;
t = a;
a = b;
b = t;
}
j--;
}
i++;
j = BIGNUM_INT_BITS-1;
}
/* Fixup result in case the modulus was shifted */
if (mshift) {
for (i = mlen - 1; i < 2 * mlen - 1; i++)
a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
for (i = 2 * mlen - 1; i >= mlen; i--)
a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
}
/* Copy result to buffer */
result = newbn(mod[0]);
for (i = 0; i < mlen; i++)
result[result[0] - i] = a[i + mlen];
while (result[0] > 1 && result[result[0]] == 0)
result[0]--;
/* Free temporary arrays */
for (i = 0; i < 2 * mlen; i++)
a[i] = 0;
sfree(a);
for (i = 0; i < 2 * mlen; i++)
b[i] = 0;
sfree(b);
for (i = 0; i < mlen; i++)
m[i] = 0;
sfree(m);
for (i = 0; i < mlen; i++)
n[i] = 0;
sfree(n);
freebn(base);
return result;
}
/*
* Compute (base ^ exp) % mod. Uses the Montgomery multiplication
* technique.
* technique where possible, falling back to modpow_simple otherwise.
*/
Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
{
@ -720,18 +841,19 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
*/
assert(mod[mod[0]] != 0);
/*
* mod had better be odd, or we can't do Montgomery multiplication
* using a power of two at all.
*/
if (!(mod[1] & 1))
return modpow_simple(base_in, exp, mod);
/*
* Make sure the base is smaller than the modulus, by reducing
* it modulo the modulus if not.
*/
base = bigmod(base_in, mod);
/*
* mod had better be odd, or we can't do Montgomery multiplication
* using a power of two at all.
*/
assert(mod[1] & 1);
/*
* Compute the inverse of n mod r, for monty_reduce. (In fact we
* want the inverse of _minus_ n mod r, but we'll sort that out