#include <assert.h>
#include <stdlib.h>
#include <string.h>
+#include <limits.h>
#include "misc.h"
static Bignum newbn(int length)
{
- Bignum b = snewn(length + 1, BignumInt);
+ Bignum b;
+
+ assert(length >= 0 && length < INT_MAX / BIGNUM_INT_BITS);
+
+ b = snewn(length + 1, BignumInt);
if (!b)
abort(); /* FIXME */
memset(b, 0, (length + 1) * sizeof(*b));
/*
* Burn the evidence, just in case.
*/
- memset(b, 0, sizeof(b[0]) * (b[0] + 1));
+ smemclr(b, sizeof(b[0]) * (b[0] + 1));
sfree(b);
}
Bignum bn_power_2(int n)
{
- Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
+ Bignum ret;
+
+ assert(n >= 0);
+
+ ret = newbn(n / BIGNUM_INT_BITS + 1);
bignum_set_bit(ret, n, 1);
return ret;
}
* Compute c = a * b.
* Input is in the first len words of a and b.
* Result is returned in the first 2*len words of c.
+ *
+ * 'scratch' must point to an array of BignumInt of size at least
+ * mul_compute_scratch(len). (This covers the needs of internal_mul
+ * and all its recursive calls to itself.)
*/
#define KARATSUBA_THRESHOLD 50
+static int mul_compute_scratch(int len)
+{
+ int ret = 0;
+ while (len > KARATSUBA_THRESHOLD) {
+ int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
+ int midlen = botlen + 1;
+ ret += 4*midlen;
+ len = midlen;
+ }
+ return ret;
+}
static void internal_mul(const BignumInt *a, const BignumInt *b,
- BignumInt *c, int len)
+ BignumInt *c, int len, BignumInt *scratch)
{
- int i, j;
- BignumDblInt t;
-
if (len > KARATSUBA_THRESHOLD) {
+ int i;
/*
* Karatsuba divide-and-conquer algorithm. Cut each input in
int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
int midlen = botlen + 1;
- BignumInt *scratch;
BignumDblInt carry;
+#ifdef KARA_DEBUG
+ int i;
+#endif
/*
* The coefficients a_1 b_1 and a_0 b_0 just avoid overlapping
* place.
*/
+#ifdef KARA_DEBUG
+ printf("a1,a0 = 0x");
+ for (i = 0; i < len; i++) {
+ if (i == toplen) printf(", 0x");
+ printf("%0*x", BIGNUM_INT_BITS/4, a[i]);
+ }
+ printf("\n");
+ printf("b1,b0 = 0x");
+ for (i = 0; i < len; i++) {
+ if (i == toplen) printf(", 0x");
+ printf("%0*x", BIGNUM_INT_BITS/4, b[i]);
+ }
+ printf("\n");
+#endif
+
/* a_1 b_1 */
- internal_mul(a, b, c, toplen);
+ internal_mul(a, b, c, toplen, scratch);
+#ifdef KARA_DEBUG
+ printf("a1b1 = 0x");
+ for (i = 0; i < 2*toplen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, c[i]);
+ }
+ printf("\n");
+#endif
/* a_0 b_0 */
- internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen);
-
- /*
- * We must allocate scratch space for the central coefficient,
- * and also for the two input values that we multiply when
- * computing it. Since either or both may carry into the
- * (botlen+1)th word, we must use a slightly longer length
- * 'midlen'.
- */
- scratch = snewn(4 * midlen, BignumInt);
+ internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch);
+#ifdef KARA_DEBUG
+ printf("a0b0 = 0x");
+ for (i = 0; i < 2*botlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, c[2*toplen+i]);
+ }
+ printf("\n");
+#endif
/* Zero padding. midlen exceeds toplen by at most 2, so just
* zero the first two words of each input and the rest will be
* copied over. */
scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0;
- for (j = 0; j < toplen; j++) {
- scratch[midlen - toplen + j] = a[j]; /* a_1 */
- scratch[2*midlen - toplen + j] = b[j]; /* b_1 */
+ for (i = 0; i < toplen; i++) {
+ scratch[midlen - toplen + i] = a[i]; /* a_1 */
+ scratch[2*midlen - toplen + i] = b[i]; /* b_1 */
}
/* compute a_1 + a_0 */
scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen);
+#ifdef KARA_DEBUG
+ printf("a1plusa0 = 0x");
+ for (i = 0; i < midlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
+ }
+ printf("\n");
+#endif
/* compute b_1 + b_0 */
scratch[midlen] = internal_add(scratch+midlen+1, b+toplen,
scratch+midlen+1, botlen);
+#ifdef KARA_DEBUG
+ printf("b1plusb0 = 0x");
+ for (i = 0; i < midlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]);
+ }
+ printf("\n");
+#endif
/*
* Now we can do the third multiplication.
*/
- internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen);
+ internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen,
+ scratch + 4*midlen);
+#ifdef KARA_DEBUG
+ printf("a1plusa0timesb1plusb0 = 0x");
+ for (i = 0; i < 2*midlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);
+ }
+ printf("\n");
+#endif
/*
* Now we can reuse the first half of 'scratch' to compute the
* product to obtain the middle one.
*/
scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0;
- for (j = 0; j < 2*toplen; j++)
- scratch[2*midlen - 2*toplen + j] = c[j];
+ for (i = 0; i < 2*toplen; i++)
+ scratch[2*midlen - 2*toplen + i] = c[i];
scratch[1] = internal_add(scratch+2, c + 2*toplen,
scratch+2, 2*botlen);
+#ifdef KARA_DEBUG
+ printf("a1b1plusa0b0 = 0x");
+ for (i = 0; i < 2*midlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
+ }
+ printf("\n");
+#endif
internal_sub(scratch + 2*midlen, scratch,
scratch + 2*midlen, 2*midlen);
+#ifdef KARA_DEBUG
+ printf("a1b0plusa0b1 = 0x");
+ for (i = 0; i < 2*midlen; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);
+ }
+ printf("\n");
+#endif
/*
* And now all we need to do is to add that middle coefficient
carry = internal_add(c + 2*len - botlen - 2*midlen,
scratch + 2*midlen,
c + 2*len - botlen - 2*midlen, 2*midlen);
- j = 2*len - botlen - 2*midlen - 1;
+ i = 2*len - botlen - 2*midlen - 1;
while (carry) {
- assert(j >= 0);
- carry += c[j];
- c[j] = (BignumInt)carry;
+ assert(i >= 0);
+ carry += c[i];
+ c[i] = (BignumInt)carry;
carry >>= BIGNUM_INT_BITS;
+ i--;
}
-
- /* Free scratch. */
- for (j = 0; j < 4 * midlen; j++)
- scratch[j] = 0;
- sfree(scratch);
+#ifdef KARA_DEBUG
+ printf("ab = 0x");
+ for (i = 0; i < 2*len; i++) {
+ printf("%0*x", BIGNUM_INT_BITS/4, c[i]);
+ }
+ printf("\n");
+#endif
} else {
+ int i;
+ BignumInt carry;
+ BignumDblInt t;
+ const BignumInt *ap, *bp;
+ BignumInt *cp, *cps;
/*
* Multiply in the ordinary O(N^2) way.
*/
- for (j = 0; j < 2 * len; j++)
- c[j] = 0;
+ for (i = 0; i < 2 * len; i++)
+ c[i] = 0;
- for (i = len - 1; i >= 0; i--) {
- t = 0;
- for (j = len - 1; j >= 0; j--) {
- t += MUL_WORD(a[i], (BignumDblInt) b[j]);
- t += (BignumDblInt) c[i + j + 1];
- c[i + j + 1] = (BignumInt) t;
- t = t >> BIGNUM_INT_BITS;
+ for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) {
+ carry = 0;
+ for (cp = cps, bp = b + len; cp--, bp-- > b ;) {
+ t = (MUL_WORD(*ap, *bp) + carry) + *cp;
+ *cp = (BignumInt) t;
+ carry = (BignumInt)(t >> BIGNUM_INT_BITS);
}
- c[i] = (BignumInt) t;
+ *cp = carry;
}
}
}
* (everything above that is thrown away).
*/
static void internal_mul_low(const BignumInt *a, const BignumInt *b,
- BignumInt *c, int len)
+ BignumInt *c, int len, BignumInt *scratch)
{
- int i, j;
- BignumDblInt t;
-
if (len > KARATSUBA_THRESHOLD) {
+ int i;
/*
* Karatsuba-aware version of internal_mul_low. As before, we
*/
int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
- BignumInt *scratch;
/*
- * Allocate scratch space for the various bits and pieces
- * we're going to be adding together. We need botlen*2 words
- * for a_0 b_0 (though we may end up throwing away its topmost
- * word), and toplen words for each of a_1 b_0 and a_0 b_1.
- * That adds up to exactly 2*len.
+ * Scratch space for the various bits and pieces we're going
+ * to be adding together: we need botlen*2 words for a_0 b_0
+ * (though we may end up throwing away its topmost word), and
+ * toplen words for each of a_1 b_0 and a_0 b_1. That adds up
+ * to exactly 2*len.
*/
- scratch = snewn(len*2, BignumInt);
/* a_0 b_0 */
- internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen);
+ internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen,
+ scratch + 2*len);
/* a_1 b_0 */
- internal_mul_low(a, b + len - toplen, scratch + toplen, toplen);
+ internal_mul_low(a, b + len - toplen, scratch + toplen, toplen,
+ scratch + 2*len);
/* a_0 b_1 */
- internal_mul_low(a + len - toplen, b, scratch, toplen);
+ internal_mul_low(a + len - toplen, b, scratch, toplen,
+ scratch + 2*len);
/* Copy the bottom half of the big coefficient into place */
- for (j = 0; j < botlen; j++)
- c[toplen + j] = scratch[2*toplen + botlen + j];
+ for (i = 0; i < botlen; i++)
+ c[toplen + i] = scratch[2*toplen + botlen + i];
/* Add the two small coefficients, throwing away the returned carry */
internal_add(scratch, scratch + toplen, scratch, toplen);
internal_add(scratch, scratch + 2*toplen + botlen - toplen,
c, toplen);
- /* Free scratch. */
- for (j = 0; j < len*2; j++)
- scratch[j] = 0;
- sfree(scratch);
-
} else {
+ int i;
+ BignumInt carry;
+ BignumDblInt t;
+ const BignumInt *ap, *bp;
+ BignumInt *cp, *cps;
- for (j = 0; j < len; j++)
- c[j] = 0;
+ /*
+ * Multiply in the ordinary O(N^2) way.
+ */
- for (i = len - 1; i >= 0; i--) {
- t = 0;
- for (j = len - 1; j >= len - i - 1; j--) {
- t += MUL_WORD(a[i], (BignumDblInt) b[j]);
- t += (BignumDblInt) c[i + j + 1 - len];
- c[i + j + 1 - len] = (BignumInt) t;
- t = t >> BIGNUM_INT_BITS;
+ for (i = 0; i < len; i++)
+ c[i] = 0;
+
+ for (cps = c + len, ap = a + len; ap-- > a; cps--) {
+ carry = 0;
+ for (cp = cps, bp = b + len; bp--, cp-- > c ;) {
+ t = (MUL_WORD(*ap, *bp) + carry) + *cp;
+ *cp = (BignumInt) t;
+ carry = (BignumInt)(t >> BIGNUM_INT_BITS);
}
}
-
}
}
* each, containing respectively n and the multiplicative inverse of
* -n mod r.
*
- * 'tmp' is an array of at least '3*len' BignumInts used as scratch
- * space.
+ * 'tmp' is an array of BignumInt used as scratch space, of length at
+ * least 3*len + mul_compute_scratch(len).
*/
static void monty_reduce(BignumInt *x, const BignumInt *n,
const BignumInt *mninv, BignumInt *tmp, int len)
* that mn is congruent to -x mod r. Hence, mn+x is an exact
* multiple of r, and is also (obviously) congruent to x mod n.
*/
- internal_mul_low(x + len, mninv, tmp, len);
+ internal_mul_low(x + len, mninv, tmp, len, tmp + 3*len);
/*
* Compute t = (mn+x)/r in ordinary, non-modular, integer
* significant half of the 'x' array, so then we must shift it
* down.
*/
- internal_mul(tmp, n, tmp+len, len);
+ internal_mul(tmp, n, tmp+len, len, tmp + 3*len);
carry = internal_add(x, tmp+len, x, 2*len);
for (i = 0; i < len; i++)
x[len + i] = x[i], x[i] = 0;
addend = (BignumDblInt)n << bshift;
while (addend) {
+ assert(word <= number[0]);
addend += number[word];
number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
addend >>= BIGNUM_INT_BITS;
int i, k;
m0 = m[0];
+ assert(m0 >> (BIGNUM_INT_BITS-1) == 1);
if (mlen > 1)
m1 = m[1];
else
}
/*
- * Compute (base ^ exp) % mod. Uses the Montgomery multiplication
- * technique.
+ * Compute (base ^ exp) % mod, the pedestrian way.
*/
-Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
+Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)
{
- BignumInt *a, *b, *x, *n, *mninv, *tmp;
- int len, i, j;
- Bignum base, base2, r, rn, inv, result;
+ BignumInt *a, *b, *n, *m, *scratch;
+ int mshift;
+ int mlen, scratchlen, i, j;
+ Bignum base, result;
/*
* The most significant word of mod needs to be non-zero. It
*/
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;
+
+ /* Scratch space for multiplies */
+ scratchlen = mul_compute_scratch(mlen);
+ scratch = snewn(scratchlen, BignumInt);
+
+ /* 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, scratch);
+ internal_mod(b, mlen * 2, m, mlen, NULL, 0);
+ if ((exp[exp[0] - i] & (1 << j)) != 0) {
+ internal_mul(b + mlen, n, a, mlen, scratch);
+ 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 */
+ smemclr(a, 2 * mlen * sizeof(*a));
+ sfree(a);
+ smemclr(scratch, scratchlen * sizeof(*scratch));
+ sfree(scratch);
+ smemclr(b, 2 * mlen * sizeof(*b));
+ sfree(b);
+ smemclr(m, mlen * sizeof(*m));
+ sfree(m);
+ smemclr(n, mlen * sizeof(*n));
+ sfree(n);
+
+ freebn(base);
+
+ return result;
+}
+
+/*
+ * Compute (base ^ exp) % mod. Uses the Montgomery multiplication
+ * technique where possible, falling back to modpow_simple otherwise.
+ */
+Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
+{
+ BignumInt *a, *b, *x, *n, *mninv, *scratch;
+ int len, scratchlen, i, j;
+ Bignum base, base2, r, rn, inv, 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);
+
/*
* mod had better be odd, or we can't do Montgomery multiplication
* using a power of two at all.
*/
- assert(mod[1] & 1);
+ 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);
/*
* Compute the inverse of n mod r, for monty_reduce. (In fact we
len = mod[0];
r = bn_power_2(BIGNUM_INT_BITS * len);
inv = modinv(mod, r);
+ assert(inv); /* cannot fail, since mod is odd and r is a power of 2 */
/*
* Multiply the base by r mod n, to get it into Montgomery
mninv = snewn(len, BignumInt);
for (j = 0; j < len; j++)
- mninv[len - 1 - j] = (j < inv[0] ? inv[j + 1] : 0);
+ mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0);
freebn(inv); /* we don't need this copy of it any more */
/* Now negate mninv mod r, so it's the inverse of -n rather than +n. */
x = snewn(len, BignumInt);
/* x = snewn(len, BignumInt); */ /* already done above */
for (j = 0; j < len; j++)
- x[len - 1 - j] = (j < base[0] ? base[j + 1] : 0);
+ x[len - 1 - j] = (j < (int)base[0] ? base[j + 1] : 0);
freebn(base); /* we don't need this copy of it any more */
a = snewn(2*len, BignumInt);
b = snewn(2*len, BignumInt);
for (j = 0; j < len; j++)
- a[2*len - 1 - j] = (j < rn[0] ? rn[j + 1] : 0);
+ a[2*len - 1 - j] = (j < (int)rn[0] ? rn[j + 1] : 0);
freebn(rn);
- tmp = snewn(3*len, BignumInt);
+ /* Scratch space for multiplies */
+ scratchlen = 3*len + mul_compute_scratch(len);
+ scratch = snewn(scratchlen, BignumInt);
/* Skip leading zero bits of exp. */
i = 0;
/* Main computation */
while (i < (int)exp[0]) {
while (j >= 0) {
- internal_mul(a + len, a + len, b, len);
- monty_reduce(b, n, mninv, tmp, len);
+ internal_mul(a + len, a + len, b, len, scratch);
+ monty_reduce(b, n, mninv, scratch, len);
if ((exp[exp[0] - i] & (1 << j)) != 0) {
- internal_mul(b + len, x, a, len);
- monty_reduce(a, n, mninv, tmp, len);
+ internal_mul(b + len, x, a, len, scratch);
+ monty_reduce(a, n, mninv, scratch, len);
} else {
BignumInt *t;
t = a;
* Final monty_reduce to get back from the adjusted Montgomery
* representation.
*/
- monty_reduce(a, n, mninv, tmp, len);
+ monty_reduce(a, n, mninv, scratch, len);
/* Copy result to buffer */
result = newbn(mod[0]);
result[0]--;
/* Free temporary arrays */
- for (i = 0; i < 3 * len; i++)
- tmp[i] = 0;
- sfree(tmp);
- for (i = 0; i < 2 * len; i++)
- a[i] = 0;
+ smemclr(scratch, scratchlen * sizeof(*scratch));
+ sfree(scratch);
+ smemclr(a, 2 * len * sizeof(*a));
sfree(a);
- for (i = 0; i < 2 * len; i++)
- b[i] = 0;
+ smemclr(b, 2 * len * sizeof(*b));
sfree(b);
- for (i = 0; i < len; i++)
- mninv[i] = 0;
+ smemclr(mninv, len * sizeof(*mninv));
sfree(mninv);
- for (i = 0; i < len; i++)
- n[i] = 0;
+ smemclr(n, len * sizeof(*n));
sfree(n);
- for (i = 0; i < len; i++)
- x[i] = 0;
+ smemclr(x, len * sizeof(*x));
sfree(x);
return result;
*/
Bignum modmul(Bignum p, Bignum q, Bignum mod)
{
- BignumInt *a, *n, *m, *o;
- int mshift;
+ BignumInt *a, *n, *m, *o, *scratch;
+ int mshift, scratchlen;
int pqlen, mlen, rlen, i, j;
Bignum 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);
+
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
pqlen = (p[0] > q[0] ? p[0] : q[0]);
+ /*
+ * Make sure that we're allowing enough space. The shifting below
+ * will underflow the vectors we allocate if pqlen is too small.
+ */
+ if (2*pqlen <= mlen)
+ pqlen = mlen/2 + 1;
+
/* Allocate n of size pqlen, copy p to n */
n = snewn(pqlen, BignumInt);
i = pqlen - p[0];
/* Allocate a of size 2*pqlen for result */
a = snewn(2 * pqlen, BignumInt);
+ /* Scratch space for multiplies */
+ scratchlen = mul_compute_scratch(pqlen);
+ scratch = snewn(scratchlen, BignumInt);
+
/* Main computation */
- internal_mul(n, o, a, pqlen);
+ internal_mul(n, o, a, pqlen, scratch);
internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
/* Fixup result in case the modulus was shifted */
result[0]--;
/* Free temporary arrays */
- for (i = 0; i < 2 * pqlen; i++)
- a[i] = 0;
+ smemclr(scratch, scratchlen * sizeof(*scratch));
+ sfree(scratch);
+ smemclr(a, 2 * pqlen * sizeof(*a));
sfree(a);
- for (i = 0; i < mlen; i++)
- m[i] = 0;
+ smemclr(m, mlen * sizeof(*m));
sfree(m);
- for (i = 0; i < pqlen; i++)
- n[i] = 0;
+ smemclr(n, pqlen * sizeof(*n));
sfree(n);
- for (i = 0; i < pqlen; i++)
- o[i] = 0;
+ smemclr(o, pqlen * sizeof(*o));
sfree(o);
return result;
int mshift;
int plen, mlen, i, j;
+ /*
+ * 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);
+
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
}
/* Free temporary arrays */
- for (i = 0; i < mlen; i++)
- m[i] = 0;
+ smemclr(m, mlen * sizeof(*m));
sfree(m);
- for (i = 0; i < plen; i++)
- n[i] = 0;
+ smemclr(n, plen * sizeof(*n));
sfree(n);
}
Bignum result;
int w, i;
+ assert(nbytes >= 0 && nbytes < INT_MAX/8);
+
w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */
result = newbn(w);
*/
int bignum_byte(Bignum bn, int i)
{
- if (i >= (int)(BIGNUM_INT_BYTES * bn[0]))
+ if (i < 0 || i >= (int)(BIGNUM_INT_BYTES * bn[0]))
return 0; /* beyond the end */
else
return (bn[i / BIGNUM_INT_BYTES + 1] >>
*/
int bignum_bit(Bignum bn, int i)
{
- if (i >= (int)(BIGNUM_INT_BITS * bn[0]))
+ if (i < 0 || i >= (int)(BIGNUM_INT_BITS * bn[0]))
return 0; /* beyond the end */
else
return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;
*/
void bignum_set_bit(Bignum bn, int bitnum, int value)
{
- if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
+ if (bitnum < 0 || bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
abort(); /* beyond the end */
else {
int v = bitnum / BIGNUM_INT_BITS + 1;
int bignum_cmp(Bignum a, Bignum b)
{
int amax = a[0], bmax = b[0];
- int i = (amax > bmax ? amax : bmax);
+ int i;
+
+ /* Annoyingly we have two representations of zero */
+ if (amax == 1 && a[amax] == 0)
+ amax = 0;
+ if (bmax == 1 && b[bmax] == 0)
+ bmax = 0;
+
+ assert(amax == 0 || a[amax] != 0);
+ assert(bmax == 0 || b[bmax] != 0);
+
+ i = (amax > bmax ? amax : bmax);
while (i) {
BignumInt aval = (i > amax ? 0 : a[i]);
BignumInt bval = (i > bmax ? 0 : b[i]);
int i, shiftw, shiftb, shiftbb, bits;
BignumInt ai, ai1;
+ assert(shift >= 0);
+
bits = bignum_bitcount(a) - shift;
ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
int alen = a[0], blen = b[0];
int mlen = (alen > blen ? alen : blen);
int rlen, i, maxspot;
+ int wslen;
BignumInt *workspace;
Bignum ret;
- /* mlen space for a, mlen space for b, 2*mlen for result */
- workspace = snewn(mlen * 4, BignumInt);
+ /* mlen space for a, mlen space for b, 2*mlen for result,
+ * plus scratch space for multiplication */
+ wslen = mlen * 4 + mul_compute_scratch(mlen);
+ workspace = snewn(wslen, BignumInt);
for (i = 0; i < mlen; i++) {
workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);
workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);
}
internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,
- workspace + 2 * mlen, mlen);
+ workspace + 2 * mlen, mlen, workspace + 4 * mlen);
/* now just copy the result back */
rlen = alen + blen + 1;
}
ret[0] = maxspot;
+ smemclr(workspace, wslen * sizeof(*workspace));
sfree(workspace);
return ret;
}
Bignum x = copybn(One);
int sign = +1;
+ assert(number[number[0]] != 0);
+ assert(modulus[modulus[0]] != 0);
+
while (bignum_cmp(b, One) != 0) {
- Bignum t = newbn(b[0]);
- Bignum q = newbn(a[0]);
+ Bignum t, q;
+
+ if (bignum_cmp(b, Zero) == 0) {
+ /*
+ * Found a common factor between the inputs, so we cannot
+ * return a modular inverse at all.
+ */
+ freebn(b);
+ freebn(a);
+ freebn(xp);
+ freebn(x);
+ return NULL;
+ }
+
+ t = newbn(b[0]);
+ q = newbn(a[0]);
bigdivmod(a, b, t, q);
while (t[0] > 1 && t[t[0]] == 0)
t[0]--;
/*
* Done.
*/
+ smemclr(workspace, x[0] * sizeof(*workspace));
sfree(workspace);
return ret;
}
+
+#ifdef TESTBN
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <ctype.h>
+
+/*
+ * gcc -Wall -g -O0 -DTESTBN -o testbn sshbn.c misc.c conf.c tree234.c unix/uxmisc.c -I. -I unix -I charset
+ *
+ * Then feed to this program's standard input the output of
+ * testdata/bignum.py .
+ */
+
+void modalfatalbox(char *p, ...)
+{
+ va_list ap;
+ fprintf(stderr, "FATAL ERROR: ");
+ va_start(ap, p);
+ vfprintf(stderr, p, ap);
+ va_end(ap);
+ fputc('\n', stderr);
+ exit(1);
+}
+
+#define fromxdigit(c) ( (c)>'9' ? ((c)&0xDF) - 'A' + 10 : (c) - '0' )
+
+int main(int argc, char **argv)
+{
+ char *buf;
+ int line = 0;
+ int passes = 0, fails = 0;
+
+ while ((buf = fgetline(stdin)) != NULL) {
+ int maxlen = strlen(buf);
+ unsigned char *data = snewn(maxlen, unsigned char);
+ unsigned char *ptrs[5], *q;
+ int ptrnum;
+ char *bufp = buf;
+
+ line++;
+
+ q = data;
+ ptrnum = 0;
+
+ while (*bufp && !isspace((unsigned char)*bufp))
+ bufp++;
+ if (bufp)
+ *bufp++ = '\0';
+
+ while (*bufp) {
+ char *start, *end;
+ int i;
+
+ while (*bufp && !isxdigit((unsigned char)*bufp))
+ bufp++;
+ start = bufp;
+
+ if (!*bufp)
+ break;
+
+ while (*bufp && isxdigit((unsigned char)*bufp))
+ bufp++;
+ end = bufp;
+
+ if (ptrnum >= lenof(ptrs))
+ break;
+ ptrs[ptrnum++] = q;
+
+ for (i = -((end - start) & 1); i < end-start; i += 2) {
+ unsigned char val = (i < 0 ? 0 : fromxdigit(start[i]));
+ val = val * 16 + fromxdigit(start[i+1]);
+ *q++ = val;
+ }
+
+ ptrs[ptrnum] = q;
+ }
+
+ if (!strcmp(buf, "mul")) {
+ Bignum a, b, c, p;
+
+ if (ptrnum != 3) {
+ printf("%d: mul with %d parameters, expected 3\n", line, ptrnum);
+ exit(1);
+ }
+ a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
+ b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
+ c = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
+ p = bigmul(a, b);
+
+ if (bignum_cmp(c, p) == 0) {
+ passes++;
+ } else {
+ char *as = bignum_decimal(a);
+ char *bs = bignum_decimal(b);
+ char *cs = bignum_decimal(c);
+ char *ps = bignum_decimal(p);
+
+ printf("%d: fail: %s * %s gave %s expected %s\n",
+ line, as, bs, ps, cs);
+ fails++;
+
+ sfree(as);
+ sfree(bs);
+ sfree(cs);
+ sfree(ps);
+ }
+ freebn(a);
+ freebn(b);
+ freebn(c);
+ freebn(p);
+ } else if (!strcmp(buf, "modmul")) {
+ Bignum a, b, m, c, p;
+
+ if (ptrnum != 4) {
+ printf("%d: modmul with %d parameters, expected 4\n",
+ line, ptrnum);
+ exit(1);
+ }
+ a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
+ b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
+ m = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
+ c = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);
+ p = modmul(a, b, m);
+
+ if (bignum_cmp(c, p) == 0) {
+ passes++;
+ } else {
+ char *as = bignum_decimal(a);
+ char *bs = bignum_decimal(b);
+ char *ms = bignum_decimal(m);
+ char *cs = bignum_decimal(c);
+ char *ps = bignum_decimal(p);
+
+ printf("%d: fail: %s * %s mod %s gave %s expected %s\n",
+ line, as, bs, ms, ps, cs);
+ fails++;
+
+ sfree(as);
+ sfree(bs);
+ sfree(ms);
+ sfree(cs);
+ sfree(ps);
+ }
+ freebn(a);
+ freebn(b);
+ freebn(m);
+ freebn(c);
+ freebn(p);
+ } else if (!strcmp(buf, "pow")) {
+ Bignum base, expt, modulus, expected, answer;
+
+ if (ptrnum != 4) {
+ printf("%d: mul with %d parameters, expected 4\n", line, ptrnum);
+ exit(1);
+ }
+
+ base = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
+ expt = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
+ modulus = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
+ expected = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);
+ answer = modpow(base, expt, modulus);
+
+ if (bignum_cmp(expected, answer) == 0) {
+ passes++;
+ } else {
+ char *as = bignum_decimal(base);
+ char *bs = bignum_decimal(expt);
+ char *cs = bignum_decimal(modulus);
+ char *ds = bignum_decimal(answer);
+ char *ps = bignum_decimal(expected);
+
+ printf("%d: fail: %s ^ %s mod %s gave %s expected %s\n",
+ line, as, bs, cs, ds, ps);
+ fails++;
+
+ sfree(as);
+ sfree(bs);
+ sfree(cs);
+ sfree(ds);
+ sfree(ps);
+ }
+ freebn(base);
+ freebn(expt);
+ freebn(modulus);
+ freebn(expected);
+ freebn(answer);
+ } else {
+ printf("%d: unrecognised test keyword: '%s'\n", line, buf);
+ exit(1);
+ }
+
+ sfree(buf);
+ sfree(data);
+ }
+
+ printf("passed %d failed %d total %d\n", passes, fails, passes+fails);
+ return fails != 0;
+}
+
+#endif
projects / u / mdw / putty / blobdiff