/*
* 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);
}
/*
* Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all
- * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried
+ * little-endian arrays of 'len' BignumInts. Returns a BignumInt carried
* off the top.
*/
static BignumInt internal_add(const BignumInt *a, const BignumInt *b,
int i;
BignumDblInt carry = 0;
- for (i = len-1; i >= 0; i--) {
+ for (i = 0; i < len; i++) {
carry += (BignumDblInt)a[i] + b[i];
c[i] = (BignumInt)carry;
carry >>= BIGNUM_INT_BITS;
/*
* Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are
- * all big-endian arrays of 'len' BignumInts. Any borrow from the top
+ * all little-endian arrays of 'len' BignumInts. Any borrow from the top
* is ignored.
*/
static void internal_sub(const BignumInt *a, const BignumInt *b,
int i;
BignumDblInt carry = 1;
- for (i = len-1; i >= 0; i--) {
+ for (i = 0; i < len; i++) {
carry += (BignumDblInt)a[i] + (b[i] ^ BIGNUM_INT_MASK);
c[i] = (BignumInt)carry;
carry >>= BIGNUM_INT_BITS;
* 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
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("%0*x", BIGNUM_INT_BITS/4, a[len - 1 - 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("%0*x", BIGNUM_INT_BITS/4, b[len - 1 - i]);
}
printf("\n");
#endif
/* a_1 b_1 */
- internal_mul(a, b, c, toplen);
+ internal_mul(a + botlen, b + botlen, c + 2*botlen, 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("%0*x", BIGNUM_INT_BITS/4, c[2*len - 1 - i]);
}
printf("\n");
#endif
/* a_0 b_0 */
- internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen);
+ internal_mul(a, b, c, 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("%0*x", BIGNUM_INT_BITS/4, c[2*botlen - 1 - 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'.
+ /* Zero padding. botlen exceeds toplen by at most 1, and we'll set
+ * the extra carry explicitly below, so we only need to zero at most
+ * one of the top words here.
*/
- 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;
+ scratch[midlen - 2] = scratch[2*midlen - 2] = 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[i] = a[i + botlen]; /* a_1 */
+ scratch[midlen + i] = b[i + botlen]; /* b_1 */
}
/* compute a_1 + a_0 */
- scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen);
+ scratch[midlen - 1] = internal_add(scratch, a, scratch, botlen);
#ifdef KARA_DEBUG
printf("a1plusa0 = 0x");
for (i = 0; i < midlen; i++) {
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen - 1 - i]);
}
printf("\n");
#endif
/* compute b_1 + b_0 */
- scratch[midlen] = internal_add(scratch+midlen+1, b+toplen,
- scratch+midlen+1, botlen);
+ scratch[2*midlen - 1] = internal_add(scratch+midlen, b,
+ scratch+midlen, botlen);
#ifdef KARA_DEBUG
printf("b1plusb0 = 0x");
for (i = 0; i < midlen; i++) {
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]);
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen - 1 - 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("%0*x", BIGNUM_INT_BITS/4, scratch[4*midlen - 1 - i]);
}
printf("\n");
#endif
* sum of the outer two coefficients, to subtract from that
* 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];
- scratch[1] = internal_add(scratch+2, c + 2*toplen,
- scratch+2, 2*botlen);
+ scratch[2*botlen - 2] = scratch[2*botlen - 1] = 0;
+ for (i = 0; i < 2*toplen; i++)
+ scratch[i] = c[2*botlen + i];
+ scratch[2*botlen] = internal_add(scratch, c, scratch, 2*botlen);
+ scratch[2*botlen + 1] = 0;
#ifdef KARA_DEBUG
printf("a1b1plusa0b0 = 0x");
for (i = 0; i < 2*midlen; i++) {
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
+ printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen - 1 - i]);
}
printf("\n");
#endif
- internal_sub(scratch + 2*midlen, scratch,
- scratch + 2*midlen, 2*midlen);
+ internal_sub(scratch + 2*midlen, scratch, scratch, 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("%0*x", BIGNUM_INT_BITS/4, scratch[4*midlen - 1 - i]);
}
printf("\n");
#endif
* further up the output, but we can be sure it won't
* propagate right the way off the top.
*/
- 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;
+ carry = internal_add(c + botlen, scratch, c + botlen, 2*midlen);
+ i = botlen + 2*midlen;
while (carry) {
- assert(j >= 0);
- carry += c[j];
- c[j] = (BignumInt)carry;
+ assert(i <= 2*len);
+ carry += c[i];
+ c[i] = (BignumInt)carry;
carry >>= BIGNUM_INT_BITS;
- j--;
+ i++;
}
#ifdef KARA_DEBUG
printf("ab = 0x");
for (i = 0; i < 2*len; i++) {
- printf("%0*x", BIGNUM_INT_BITS/4, c[i]);
+ printf("%0*x", BIGNUM_INT_BITS/4, c[2*len - i]);
}
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, *alim = a + len, *bp, *blim = b + len;
+ 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, ap = a; ap < alim; ap++, cps++) {
+ carry = 0;
+ for (cp = cps, bp = b, i = blim - bp; i--; bp++, cp++) {
+ 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, b, 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 + botlen, b, scratch + toplen, toplen,
+ scratch + 2*len);
/* a_0 b_1 */
- internal_mul_low(a + len - toplen, b, scratch, toplen);
+ internal_mul_low(a, b + botlen, 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[i] = scratch[2*toplen + i];
/* Add the two small coefficients, throwing away the returned carry */
internal_add(scratch, scratch + toplen, scratch, toplen);
/* And add that to the large coefficient, leaving the result in c. */
- internal_add(scratch, scratch + 2*toplen + botlen - toplen,
- c, toplen);
-
- /* Free scratch. */
- for (j = 0; j < len*2; j++)
- scratch[j] = 0;
- sfree(scratch);
+ internal_add(scratch, scratch + 2*toplen + botlen,
+ c + botlen, toplen);
} else {
+ int i;
+ BignumInt carry;
+ BignumDblInt t;
+ const BignumInt *ap, *alim = a + len, *bp;
+ BignumInt *cp, *cps, *clim = c + len;
- 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, ap = a; ap < alim; ap++, cps++) {
+ carry = 0;
+ for (cp = cps, bp = b, i = clim - cp; i--; bp++, cp++) {
+ t = (MUL_WORD(*ap, *bp) + carry) + *cp;
+ *cp = (BignumInt) t;
+ carry = (BignumInt)(t >> BIGNUM_INT_BITS);
}
}
-
}
}
/*
- * Montgomery reduction. Expects x to be a big-endian array of 2*len
+ * Montgomery reduction. Expects x to be a little-endian array of 2*len
* BignumInts whose value satisfies 0 <= x < rn (where r = 2^(len *
* BIGNUM_INT_BITS) is the Montgomery base). Returns in the same array
* a value x' which is congruent to xr^{-1} mod n, and satisfies 0 <=
* x' < n.
*
- * 'n' and 'mninv' should be big-endian arrays of 'len' BignumInts
+ * 'n' and 'mninv' should be little-endian arrays of 'len' BignumInts
* 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, 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;
+ x[i] = x[len + i], x[len + i] = 0;
/*
* Reduce t mod n. This doesn't require a full-on division by n,
* + yielding 0 <= (mn+x)/r < 2n as required.
*/
if (!carry) {
- for (i = 0; i < len; i++)
- if (x[len + i] != n[i])
+ for (i = len; i-- > 0; )
+ if (x[i] != n[i])
break;
}
- if (carry || i >= len || x[len + i] > n[i])
- internal_sub(x+len, n, x+len, len);
+ if (carry || i < 0 || x[i] > n[i])
+ internal_sub(x, n, x, len);
}
static void internal_add_shifted(BignumInt *number,
* Compute a = a % m.
* Input in first alen words of a and first mlen words of m.
* Output in first alen words of a
- * (of which first alen-mlen words will be zero).
+ * (of which last alen-mlen words will be zero).
* The MSW of m MUST have its high bit set.
- * Quotient is accumulated in the `quotient' array, which is a Bignum
- * rather than the internal bigendian format. Quotient parts are shifted
- * left by `qshift' before adding into quot.
+ * Quotient is accumulated in the `quotient' array. Quotient parts
+ * are shifted left by `qshift' before adding into quot.
*/
static void internal_mod(BignumInt *a, int alen,
BignumInt *m, int mlen,
{
BignumInt m0, m1;
unsigned int h;
- int i, k;
+ int i, j, k;
- m0 = m[0];
+ m0 = m[mlen - 1];
if (mlen > 1)
- m1 = m[1];
+ m1 = m[mlen - 2];
else
m1 = 0;
- for (i = 0; i <= alen - mlen; i++) {
+ for (i = alen, h = 0; i-- >= mlen; ) {
BignumDblInt t;
unsigned int q, r, c, ai1;
- if (i == 0) {
- h = 0;
- } else {
- h = a[i - 1];
- a[i - 1] = 0;
- }
-
- if (i == alen - 1)
- ai1 = 0;
- else
- ai1 = a[i + 1];
+ if (i)
+ ai1 = a[i - 1];
+ else
+ ai1 = 0;
/* Find q = h:a[i] / m0 */
if (h >= m0) {
DIVMOD_WORD(q, r, h, tmplo, m0);
/* Refine our estimate of q by looking at
- h:a[i]:a[i+1] / m0:m1 */
+ h:a[i]:a[i-1] / m0:m1 */
t = MUL_WORD(m1, q);
if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
q--;
}
}
+ j = i + 1 - mlen;
+
/* Subtract q * m from a[i...] */
c = 0;
- for (k = mlen - 1; k >= 0; k--) {
+ for (k = 0; k < mlen; k++) {
t = MUL_WORD(q, m[k]);
t += c;
c = (unsigned)(t >> BIGNUM_INT_BITS);
- if ((BignumInt) t > a[i + k])
+ if ((BignumInt) t > a[j + k])
c++;
- a[i + k] -= (BignumInt) t;
+ a[j + k] -= (BignumInt) t;
}
/* Add back m in case of borrow */
if (c != h) {
t = 0;
- for (k = mlen - 1; k >= 0; k--) {
+ for (k = 0; k < mlen; k++) {
t += m[k];
- t += a[i + k];
- a[i + k] = (BignumInt) t;
+ t += a[j + k];
+ a[j + k] = (BignumInt) t;
t = t >> BIGNUM_INT_BITS;
}
q--;
}
+
if (quot)
- internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
+ internal_add_shifted(quot, q,
+ qshift + BIGNUM_INT_BITS * (i + 1 - mlen));
+
+ if (i >= mlen) {
+ h = a[i];
+ a[i] = 0;
+ }
}
}
+static void shift_left(BignumInt *x, int xlen, int shift)
+{
+ int i;
+
+ if (!shift)
+ return;
+ for (i = xlen; --i > 0; )
+ x[i] = (x[i] << shift) | (x[i - 1] >> (BIGNUM_INT_BITS - shift));
+ x[0] = x[0] << shift;
+}
+
+static void shift_right(BignumInt *x, int xlen, int shift)
+{
+ int i;
+
+ if (!shift || !xlen)
+ return;
+ xlen--;
+ for (i = 0; i < xlen; i++)
+ x[i] = (x[i] >> shift) | (x[i + 1] << (BIGNUM_INT_BITS - shift));
+ x[i] = x[i] >> shift;
+}
+
/*
* Compute (base ^ exp) % mod, the pedestrian way.
*/
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;
/*
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];
+ m[j] = mod[j + 1];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
+ if ((m[mlen - 1] << 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;
- }
+ if (mshift)
+ shift_left(m, mlen, 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];
+ for (i = 0; i < (int)base[0]; i++)
+ n[i] = base[i + 1];
+ for (; i < mlen; i++)
+ n[i] = 0;
/* 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[0] = 1;
+ for (i = 1; 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;
/* Main computation */
while (i < (int)exp[0]) {
while (j >= 0) {
- internal_mul(a + mlen, a + mlen, b, mlen);
+ internal_mul(a, a, 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, n, a, mlen, scratch);
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
} else {
BignumInt *t;
/* 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));
+ shift_left(a, mlen + 1, mshift);
+ internal_mod(a, mlen + 1, m, mlen, NULL, 0);
+ shift_right(a, mlen, mshift);
}
/* Copy result to buffer */
result = newbn(mod[0]);
for (i = 0; i < mlen; i++)
- result[result[0] - i] = a[i + mlen];
+ result[i + 1] = a[i];
while (result[0] > 1 && result[result[0]] == 0)
result[0]--;
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;
/*
freebn(r); /* won't need this any more */
/*
- * Set up internal arrays of the right lengths, in big-endian
- * format, containing the base, the modulus, and the modulus's
- * inverse.
+ * Set up internal arrays of the right lengths containing the base,
+ * the modulus, and the modulus's inverse.
*/
n = snewn(len, BignumInt);
for (j = 0; j < len; j++)
- n[len - 1 - j] = mod[j + 1];
+ n[j] = mod[j + 1];
mninv = snewn(len, BignumInt);
for (j = 0; j < len; j++)
- mninv[len - 1 - j] = (j < inv[0] ? inv[j + 1] : 0);
+ mninv[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[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[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, a, 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, 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]);
for (i = 0; i < len; i++)
- result[result[0] - i] = a[i + len];
+ result[i + 1] = a[i];
while (result[0] > 1 && result[result[0]] == 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 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];
+ m[j] = mod[j + 1];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
+ if ((m[mlen - 1] << 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;
- }
+ if (mshift)
+ shift_left(m, mlen, mshift);
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];
- for (j = 0; j < i; j++)
- n[j] = 0;
- for (j = 0; j < (int)p[0]; j++)
- n[i + j] = p[p[0] - j];
+ for (i = 0; i < (int)p[0]; i++)
+ n[i] = p[i + 1];
+ for (; i < pqlen; i++)
+ n[i] = 0;
/* Allocate o of size pqlen, copy q to o */
o = snewn(pqlen, BignumInt);
- i = pqlen - q[0];
- for (j = 0; j < i; j++)
- o[j] = 0;
- for (j = 0; j < (int)q[0]; j++)
- o[i + j] = q[q[0] - j];
+ for (i = 0; i < (int)q[0]; i++)
+ o[i] = q[i + 1];
+ for (; i < pqlen; i++)
+ o[i] = 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 */
if (mshift) {
- for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)
- a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
- a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;
- internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
- for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)
- a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
+ shift_left(a, mlen + 1, mshift);
+ internal_mod(a, mlen + 1, m, mlen, NULL, 0);
+ shift_right(a, mlen, mshift);
}
/* Copy result to buffer */
rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);
result = newbn(rlen);
for (i = 0; i < rlen; i++)
- result[result[0] - i] = a[i + 2 * pqlen - rlen];
+ result[i + 1] = a[i];
while (result[0] > 1 && result[result[0]] == 0)
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 plen, mlen, i, j;
/* 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];
+ m[j] = mod[j + 1];
/* Shift m left to make msb bit set */
for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
+ if ((m[mlen - 1] << 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;
- }
+ if (mshift)
+ shift_left(m, mlen, mshift);
plen = p[0];
/* Ensure plen > mlen */
/* Allocate n of size plen, copy p to n */
n = snewn(plen, BignumInt);
- for (j = 0; j < plen; j++)
- n[j] = 0;
- for (j = 1; j <= (int)p[0]; j++)
- n[plen - j] = p[j];
+ for (i = 0; i < (int)p[0]; i++)
+ n[i] = p[i + 1];
+ for (; i < plen; i++)
+ n[i] = 0;
/* Main computation */
internal_mod(n, plen, m, mlen, quotient, mshift);
/* Fixup result in case the modulus was shifted */
if (mshift) {
- for (i = plen - mlen - 1; i < plen - 1; i++)
- n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));
- n[plen - 1] = n[plen - 1] << mshift;
+ shift_left(n, mlen + 1, mshift);
internal_mod(n, plen, m, mlen, quotient, 0);
- for (i = plen - 1; i >= plen - mlen; i--)
- n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));
+ shift_right(n, mlen, mshift);
}
/* Copy result to buffer */
if (result) {
- for (i = 1; i <= (int)result[0]; i++) {
- int j = plen - i;
- result[i] = j >= 0 ? n[j] : 0;
- }
+ for (i = 0; i < (int)result[0]; i++)
+ result[i + 1] = i < plen ? n[i] : 0;
+ bn_restore_invariant(result);
}
/* Free temporary arrays */
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);
+ workspace[0 * mlen + i] = i < (int)a[0] ? a[i + 1] : 0;
+ workspace[1 * mlen + i] = i < (int)b[0] ? b[i + 1] : 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;
rlen = addend[0] + 1;
ret = newbn(rlen);
maxspot = 0;
- for (i = 1; i <= (int)ret[0]; i++) {
- ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);
- if (ret[i] != 0)
- maxspot = i;
+ for (i = 0; i < (int)ret[0]; i++) {
+ ret[i + 1] = (i < 2 * mlen ? workspace[2 * mlen + i] : 0);
+ if (ret[i + 1] != 0)
+ maxspot = i + 1;
}
ret[0] = maxspot;
}
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