X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/32e51f76a4d1eb739b6ba581bc845880eef13b18..134a1ab5f9b5976073bfb9a5f723b945ca06533a:/sshbn.c diff --git a/sshbn.c b/sshbn.c index c0ae5288..cae1bd9e 100644 --- a/sshbn.c +++ b/sshbn.c @@ -160,31 +160,430 @@ Bignum bn_power_2(int n) } /* + * Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all + * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried + * off the top. + */ +static BignumInt internal_add(const BignumInt *a, const BignumInt *b, + BignumInt *c, int len) +{ + int i; + BignumDblInt carry = 0; + + for (i = len-1; i >= 0; i--) { + carry += (BignumDblInt)a[i] + b[i]; + c[i] = (BignumInt)carry; + carry >>= BIGNUM_INT_BITS; + } + + return (BignumInt)carry; +} + +/* + * Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are + * all big-endian arrays of 'len' BignumInts. Any borrow from the top + * is ignored. + */ +static void internal_sub(const BignumInt *a, const BignumInt *b, + BignumInt *c, int len) +{ + int i; + BignumDblInt carry = 1; + + for (i = len-1; i >= 0; 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. */ -static void internal_mul(BignumInt *a, BignumInt *b, +#define KARATSUBA_THRESHOLD 50 +static void internal_mul(const BignumInt *a, const BignumInt *b, BignumInt *c, int len) { int i, j; BignumDblInt t; - for (j = 0; j < 2 * len; j++) - c[j] = 0; + if (len > KARATSUBA_THRESHOLD) { + + /* + * Karatsuba divide-and-conquer algorithm. Cut each input in + * half, so that it's expressed as two big 'digits' in a giant + * base D: + * + * a = a_1 D + a_0 + * b = b_1 D + b_0 + * + * Then the product is of course + * + * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0 + * + * and we compute the three coefficients by recursively + * calling ourself to do half-length multiplications. + * + * The clever bit that makes this worth doing is that we only + * need _one_ half-length multiplication for the central + * coefficient rather than the two that it obviouly looks + * like, because we can use a single multiplication to compute + * + * (a_1 + a_0) (b_1 + b_0) = a_1 b_1 + a_1 b_0 + a_0 b_1 + a_0 b_0 + * + * and then we subtract the other two coefficients (a_1 b_1 + * and a_0 b_0) which we were computing anyway. + * + * Hence we get to multiply two numbers of length N in about + * three times as much work as it takes to multiply numbers of + * length N/2, which is obviously better than the four times + * as much work it would take if we just did a long + * conventional multiply. + */ + + 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 - 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; - } - c[i] = (BignumInt) t; + /* + * The coefficients a_1 b_1 and a_0 b_0 just avoid overlapping + * in the output array, so we can compute them immediately in + * 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); +#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); +#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 + + /* + * 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 */ + } + + /* 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); +#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 + * 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); +#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 + * back into the output. We may have to propagate a carry + * 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; + while (carry) { + assert(j >= 0); + carry += c[j]; + c[j] = (BignumInt)carry; + carry >>= BIGNUM_INT_BITS; + j--; + } +#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 + + /* Free scratch. */ + for (j = 0; j < 4 * midlen; j++) + scratch[j] = 0; + sfree(scratch); + + } else { + + /* + * Multiply in the ordinary O(N^2) way. + */ + + for (j = 0; j < 2 * len; j++) + c[j] = 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; + } + c[i] = (BignumInt) t; + } } } +/* + * Variant form of internal_mul used for the initial step of + * Montgomery reduction. Only bothers outputting 'len' words + * (everything above that is thrown away). + */ +static void internal_mul_low(const BignumInt *a, const BignumInt *b, + BignumInt *c, int len) +{ + int i, j; + BignumDblInt t; + + if (len > KARATSUBA_THRESHOLD) { + + /* + * Karatsuba-aware version of internal_mul_low. As before, we + * express each input value as a shifted combination of two + * halves: + * + * a = a_1 D + a_0 + * b = b_1 D + b_0 + * + * Then the full product is, as before, + * + * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0 + * + * Provided we choose D on the large side (so that a_0 and b_0 + * are _at least_ as long as a_1 and b_1), we don't need the + * topmost term at all, and we only need half of the middle + * term. So there's no point in doing the proper Karatsuba + * optimisation which computes the middle term using the top + * one, because we'd take as long computing the top one as + * just computing the middle one directly. + * + * So instead, we do a much more obvious thing: we call the + * fully optimised internal_mul to compute a_0 b_0, and we + * recursively call ourself to compute the _bottom halves_ of + * a_1 b_0 and a_0 b_1, each of which we add into the result + * in the obvious way. + * + * In other words, there's no actual Karatsuba _optimisation_ + * in this function; the only benefit in doing it this way is + * that we call internal_mul proper for a large part of the + * work, and _that_ can optimise its operation. + */ + + 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 = snewn(len*2, BignumInt); + + /* a_0 b_0 */ + internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen); + + /* a_1 b_0 */ + internal_mul_low(a, b + len - toplen, scratch + toplen, toplen); + + /* a_0 b_1 */ + internal_mul_low(a + len - toplen, b, scratch, toplen); + + /* Copy the bottom half of the big coefficient into place */ + for (j = 0; j < botlen; j++) + c[toplen + j] = scratch[2*toplen + botlen + j]; + + /* 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); + + } else { + + for (j = 0; j < len; j++) + c[j] = 0; + + 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; + } + } + + } +} + +/* + * Montgomery reduction. Expects x to be a big-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 + * 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. + */ +static void monty_reduce(BignumInt *x, const BignumInt *n, + const BignumInt *mninv, BignumInt *tmp, int len) +{ + int i; + BignumInt carry; + + /* + * Multiply x by (-n)^{-1} mod r. This gives us a value m such + * 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); + + /* + * Compute t = (mn+x)/r in ordinary, non-modular, integer + * arithmetic. By construction this is exact, and is congruent mod + * n to x * r^{-1}, i.e. the answer we want. + * + * The following multiply leaves that answer in the _most_ + * significant half of the 'x' array, so then we must shift it + * down. + */ + internal_mul(tmp, n, tmp+len, len); + carry = internal_add(x, tmp+len, x, 2*len); + for (i = 0; i < len; i++) + x[len + i] = x[i], x[i] = 0; + + /* + * Reduce t mod n. This doesn't require a full-on division by n, + * but merely a test and single optional subtraction, since we can + * show that 0 <= t < 2n. + * + * Proof: + * + we computed m mod r, so 0 <= m < r. + * + so 0 <= mn < rn, obviously + * + hence we only need 0 <= x < rn to guarantee that 0 <= mn+x < 2rn + * + yielding 0 <= (mn+x)/r < 2n as required. + */ + if (!carry) { + for (i = 0; i < len; i++) + if (x[len + i] != n[i]) + break; + } + if (carry || i >= len || x[len + i] > n[i]) + internal_sub(x+len, n, x+len, len); +} + static void internal_add_shifted(BignumInt *number, unsigned n, int shift) { @@ -306,14 +705,14 @@ static void internal_mod(BignumInt *a, int alen, } /* - * Compute (base ^ exp) % mod. + * Compute (base ^ exp) % mod. Uses the Montgomery multiplication + * technique. */ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) { - BignumInt *a, *b, *n, *m; - int mshift; - int mlen, i, j; - Bignum base, result; + BignumInt *a, *b, *x, *n, *mninv, *tmp; + int len, i, j; + Bignum base, base2, r, rn, inv, result; /* * The most significant word of mod needs to be non-zero. It @@ -327,37 +726,64 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) */ 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]; + /* + * mod had better be odd, or we can't do Montgomery multiplication + * using a power of two at all. + */ + assert(mod[1] & 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) - 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; - } + /* + * 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 + * below.) + */ + len = mod[0]; + r = bn_power_2(BIGNUM_INT_BITS * len); + inv = modinv(mod, r); - /* 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]; + /* + * Multiply the base by r mod n, to get it into Montgomery + * representation. + */ + base2 = modmul(base, r, mod); + freebn(base); + base = base2; - /* 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; + rn = bigmod(r, mod); /* r mod n, i.e. Montgomerified 1 */ + + 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. + */ + n = snewn(len, BignumInt); + for (j = 0; j < len; j++) + n[len - 1 - 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); + 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); + for (j = 0; j < len; j++) + x[j] = 0; + internal_sub(x, mninv, mninv, len); + + /* x = snewn(len, BignumInt); */ /* already done above */ + for (j = 0; j < len; j++) + x[len - 1 - j] = (j < 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); + freebn(rn); + + tmp = snewn(3*len, BignumInt); /* Skip leading zero bits of exp. */ i = 0; @@ -373,11 +799,11 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) /* 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); + internal_mul(a + len, a + len, b, len); + monty_reduce(b, n, mninv, tmp, len); if ((exp[exp[0] - i] & (1 << j)) != 0) { - internal_mul(b + mlen, n, a, mlen); - internal_mod(a, mlen * 2, m, mlen, NULL, 0); + internal_mul(b + len, x, a, len); + monty_reduce(a, n, mninv, tmp, len); } else { BignumInt *t; t = a; @@ -390,38 +816,38 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) 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)); - } + /* + * Final monty_reduce to get back from the adjusted Montgomery + * representation. + */ + monty_reduce(a, n, mninv, tmp, len); /* Copy result to buffer */ result = newbn(mod[0]); - for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i + mlen]; + for (i = 0; i < len; i++) + result[result[0] - i] = a[i + len]; while (result[0] > 1 && result[result[0]] == 0) result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2 * mlen; i++) + for (i = 0; i < 3 * len; i++) + tmp[i] = 0; + sfree(tmp); + for (i = 0; i < 2 * len; i++) a[i] = 0; sfree(a); - for (i = 0; i < 2 * mlen; i++) + for (i = 0; i < 2 * len; i++) b[i] = 0; sfree(b); - for (i = 0; i < mlen; i++) - m[i] = 0; - sfree(m); - for (i = 0; i < mlen; i++) + for (i = 0; i < len; i++) + mninv[i] = 0; + sfree(mninv); + for (i = 0; i < len; i++) n[i] = 0; sfree(n); - - freebn(base); + for (i = 0; i < len; i++) + x[i] = 0; + sfree(x); return result; } @@ -840,6 +1266,69 @@ Bignum bigmul(Bignum a, Bignum b) } /* + * Simple addition. + */ +Bignum bigadd(Bignum a, Bignum b) +{ + int alen = a[0], blen = b[0]; + int rlen = (alen > blen ? alen : blen) + 1; + int i, maxspot; + Bignum ret; + BignumDblInt carry; + + ret = newbn(rlen); + + carry = 0; + maxspot = 0; + for (i = 1; i <= rlen; i++) { + carry += (i <= (int)a[0] ? a[i] : 0); + carry += (i <= (int)b[0] ? b[i] : 0); + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0 && i > maxspot) + maxspot = i; + } + ret[0] = maxspot; + + return ret; +} + +/* + * Subtraction. Returns a-b, or NULL if the result would come out + * negative (recall that this entire bignum module only handles + * positive numbers). + */ +Bignum bigsub(Bignum a, Bignum b) +{ + int alen = a[0], blen = b[0]; + int rlen = (alen > blen ? alen : blen); + int i, maxspot; + Bignum ret; + BignumDblInt carry; + + ret = newbn(rlen); + + carry = 1; + maxspot = 0; + for (i = 1; i <= rlen; i++) { + carry += (i <= (int)a[0] ? a[i] : 0); + carry += (i <= (int)b[0] ? b[i] ^ BIGNUM_INT_MASK : BIGNUM_INT_MASK); + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0 && i > maxspot) + maxspot = i; + } + ret[0] = maxspot; + + if (!carry) { + freebn(ret); + return NULL; + } + + return ret; +} + +/* * Create a bignum which is the bitmask covering another one. That * is, the smallest integer which is >= N and is also one less than * a power of two. @@ -1117,3 +1606,110 @@ char *bignum_decimal(Bignum x) sfree(workspace); return ret; } + +#ifdef TESTBN + +#include +#include +#include + +/* + * gcc -g -O0 -DTESTBN -o testbn sshbn.c misc.c -I unix -I charset + */ + +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[4], *q; + int ptrnum; + char *bufp = buf; + + line++; + + q = data; + ptrnum = 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 (ptrnum == 3) { + Bignum a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]); + Bignum b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]); + Bignum c = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]); + Bignum 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); + } + sfree(buf); + sfree(data); + } + + printf("passed %d failed %d total %d\n", passes, fails, passes+fails); + return fails != 0; +} + +#endif