/*
* 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);
}
* 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
/* 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++) {
#endif
/* a_0 b_0 */
- internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen);
+ 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("\n");
#endif
- /*
- * 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);
-
/* 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 */
/*
* 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++) {
* 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
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;
- j--;
+ i--;
}
#ifdef KARA_DEBUG
printf("ab = 0x");
printf("\n");
#endif
- /* Free scratch. */
- for (j = 0; j < 4 * midlen; j++)
- scratch[j] = 0;
- sfree(scratch);
-
} 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;
*/
Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)
{
- BignumInt *a, *b, *n, *m;
+ BignumInt *a, *b, *n, *m, *scratch;
int mshift;
- int mlen, i, j;
+ int mlen, scratchlen, i, j;
Bignum base, result;
/*
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;
/* Main computation */
while (i < (int)exp[0]) {
while (j >= 0) {
- internal_mul(a + mlen, a + mlen, b, mlen);
+ 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);
+ internal_mul(b + mlen, n, a, mlen, scratch);
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
} else {
BignumInt *t;
for (i = 0; i < 2 * mlen; i++)
a[i] = 0;
sfree(a);
+ for (i = 0; i < scratchlen; i++)
+ scratch[i] = 0;
+ sfree(scratch);
for (i = 0; i < 2 * mlen; i++)
b[i] = 0;
sfree(b);
*/
Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
{
- BignumInt *a, *b, *x, *n, *mninv, *tmp;
- int len, i, j;
+ BignumInt *a, *b, *x, *n, *mninv, *scratch;
+ int len, scratchlen, i, j;
Bignum base, base2, r, rn, inv, result;
/*
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 < scratchlen; i++)
+ scratch[i] = 0;
+ sfree(scratch);
for (i = 0; i < 2 * len; i++)
a[i] = 0;
sfree(a);
*/
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;
/* 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 < scratchlen; i++)
+ scratch[i] = 0;
+ sfree(scratch);
for (i = 0; i < 2 * pqlen; i++)
a[i] = 0;
sfree(a);
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;
+ for (i = 0; i < wslen; i++)
+ workspace[i] = 0;
sfree(workspace);
return ret;
}
#include <ctype.h>
/*
- * gcc -g -O0 -DTESTBN -o testbn sshbn.c misc.c -I unix -I charset
+ * 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 .
Bignum a, b, c, p;
if (ptrnum != 3) {
- printf("%d: mul with %d parameters, expected 3\n", line);
+ printf("%d: mul with %d parameters, expected 3\n", line, ptrnum);
exit(1);
}
a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
Bignum base, expt, modulus, expected, answer;
if (ptrnum != 4) {
- printf("%d: mul with %d parameters, expected 3\n", line);
+ printf("%d: mul with %d parameters, expected 4\n", line, ptrnum);
exit(1);
}
projects / u / mdw / putty / blobdiff