X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/6e522441172d5b1c2a2fa4d0f6bbe905ce6b647a..HEAD:/sshbn.c diff --git a/sshbn.c b/sshbn.c index 693b4ac7..a5e0552f 100644 --- a/sshbn.c +++ b/sshbn.c @@ -3,81 +3,615 @@ */ #include +#include #include #include +#include + +#include "misc.h" + +/* + * Usage notes: + * * Do not call the DIVMOD_WORD macro with expressions such as array + * subscripts, as some implementations object to this (see below). + * * Note that none of the division methods below will cope if the + * quotient won't fit into BIGNUM_INT_BITS. Callers should be careful + * to avoid this case. + * If this condition occurs, in the case of the x86 DIV instruction, + * an overflow exception will occur, which (according to a correspondent) + * will manifest on Windows as something like + * 0xC0000095: Integer overflow + * The C variant won't give the right answer, either. + */ + +#if defined __GNUC__ && defined __i386__ +typedef unsigned long BignumInt; +typedef unsigned long long BignumDblInt; +#define BIGNUM_INT_MASK 0xFFFFFFFFUL +#define BIGNUM_TOP_BIT 0x80000000UL +#define BIGNUM_INT_BITS 32 +#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) +#define DIVMOD_WORD(q, r, hi, lo, w) \ + __asm__("div %2" : \ + "=d" (r), "=a" (q) : \ + "r" (w), "d" (hi), "a" (lo)) +#elif defined _MSC_VER && defined _M_IX86 +typedef unsigned __int32 BignumInt; +typedef unsigned __int64 BignumDblInt; +#define BIGNUM_INT_MASK 0xFFFFFFFFUL +#define BIGNUM_TOP_BIT 0x80000000UL +#define BIGNUM_INT_BITS 32 +#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) +/* Note: MASM interprets array subscripts in the macro arguments as + * assembler syntax, which gives the wrong answer. Don't supply them. + * */ +#define DIVMOD_WORD(q, r, hi, lo, w) do { \ + __asm mov edx, hi \ + __asm mov eax, lo \ + __asm div w \ + __asm mov r, edx \ + __asm mov q, eax \ +} while(0) +#elif defined _LP64 +/* 64-bit architectures can do 32x32->64 chunks at a time */ +typedef unsigned int BignumInt; +typedef unsigned long BignumDblInt; +#define BIGNUM_INT_MASK 0xFFFFFFFFU +#define BIGNUM_TOP_BIT 0x80000000U +#define BIGNUM_INT_BITS 32 +#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) +#define DIVMOD_WORD(q, r, hi, lo, w) do { \ + BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \ + q = n / w; \ + r = n % w; \ +} while (0) +#elif defined _LLP64 +/* 64-bit architectures in which unsigned long is 32 bits, not 64 */ +typedef unsigned long BignumInt; +typedef unsigned long long BignumDblInt; +#define BIGNUM_INT_MASK 0xFFFFFFFFUL +#define BIGNUM_TOP_BIT 0x80000000UL +#define BIGNUM_INT_BITS 32 +#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) +#define DIVMOD_WORD(q, r, hi, lo, w) do { \ + BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \ + q = n / w; \ + r = n % w; \ +} while (0) +#else +/* Fallback for all other cases */ +typedef unsigned short BignumInt; +typedef unsigned long BignumDblInt; +#define BIGNUM_INT_MASK 0xFFFFU +#define BIGNUM_TOP_BIT 0x8000U +#define BIGNUM_INT_BITS 16 +#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2) +#define DIVMOD_WORD(q, r, hi, lo, w) do { \ + BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \ + q = n / w; \ + r = n % w; \ +} while (0) +#endif + +#define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8) + +#define BIGNUM_INTERNAL +typedef BignumInt *Bignum; #include "ssh.h" -unsigned short bnZero[1] = { 0 }; -unsigned short bnOne[2] = { 1, 1 }; +BignumInt bnZero[1] = { 0 }; +BignumInt bnOne[2] = { 1, 1 }; + +/* + * The Bignum format is an array of `BignumInt'. The first + * element of the array counts the remaining elements. The + * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_ + * significant digit first. (So it's trivial to extract the bit + * with value 2^n for any n.) + * + * All Bignums in this module are positive. Negative numbers must + * be dealt with outside it. + * + * INVARIANT: the most significant word of any Bignum must be + * nonzero. + */ Bignum Zero = bnZero, One = bnOne; -Bignum newbn(int length) { - Bignum b = malloc((length+1)*sizeof(unsigned short)); +static Bignum newbn(int length) +{ + 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)); + memset(b, 0, (length + 1) * sizeof(*b)); b[0] = length; return b; } -Bignum copybn(Bignum orig) { - Bignum b = malloc((orig[0]+1)*sizeof(unsigned short)); +void bn_restore_invariant(Bignum b) +{ + while (b[0] > 1 && b[b[0]] == 0) + b[0]--; +} + +Bignum copybn(Bignum orig) +{ + Bignum b = snewn(orig[0] + 1, BignumInt); if (!b) abort(); /* FIXME */ - memcpy(b, orig, (orig[0]+1)*sizeof(*b)); + memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); return b; } -void freebn(Bignum b) { +void freebn(Bignum b) +{ /* * Burn the evidence, just in case. */ - memset(b, 0, sizeof(b[0]) * (b[0] + 1)); - free(b); + smemclr(b, sizeof(b[0]) * (b[0] + 1)); + sfree(b); +} + +Bignum bn_power_2(int n) +{ + Bignum ret; + + assert(n >= 0); + + ret = newbn(n / BIGNUM_INT_BITS + 1); + bignum_set_bit(ret, n, 1); + return ret; +} + +/* + * 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. + * + * '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.) */ -static void internal_mul(unsigned short *a, unsigned short *b, - unsigned short *c, int len) +#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 *scratch) { - int i, j; - unsigned long ai, t; + if (len > KARATSUBA_THRESHOLD) { + int i; - for (j = 0; j < 2*len; j++) - c[j] = 0; + /* + * 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; + BignumDblInt carry; +#ifdef KARA_DEBUG + int i; +#endif + + /* + * 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, 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, 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 - for (i = len - 1; i >= 0; i--) { - ai = a[i]; - t = 0; - for (j = len - 1; j >= 0; j--) { - t += ai * (unsigned long) b[j]; - t += (unsigned long) c[i+j+1]; - c[i+j+1] = (unsigned short)t; - t = t >> 16; - } - c[i] = (unsigned short)t; + /* 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 (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, + 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 + * 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 (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 + * 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); + i = 2*len - botlen - 2*midlen - 1; + while (carry) { + assert(i >= 0); + carry += c[i]; + c[i] = (BignumInt)carry; + carry >>= BIGNUM_INT_BITS; + i--; + } +#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 (i = 0; i < 2 * len; i++) + c[i] = 0; + + 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); + } + *cp = carry; + } + } +} + +/* + * 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, BignumInt *scratch) +{ + if (len > KARATSUBA_THRESHOLD) { + int i; + + /* + * 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 */ + + /* + * 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. + */ + + /* a_0 b_0 */ + 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, + scratch + 2*len); + + /* a_0 b_1 */ + internal_mul_low(a + len - toplen, b, scratch, toplen, + scratch + 2*len); + + /* Copy the bottom half of the big coefficient into place */ + 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); + + /* And add that to the large coefficient, leaving the result in c. */ + internal_add(scratch, scratch + 2*toplen + botlen - toplen, + c, toplen); + + } else { + int i; + BignumInt carry; + BignumDblInt t; + const BignumInt *ap, *bp; + BignumInt *cp, *cps; + + /* + * Multiply in the ordinary O(N^2) way. + */ + + 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); + } + } + } +} + +/* + * 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 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) +{ + 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, tmp + 3*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, 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; + + /* + * 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(unsigned short *number, - unsigned n, int shift) { - int word = 1 + (shift / 16); - int bshift = shift % 16; - unsigned long addend; +static void internal_add_shifted(BignumInt *number, + unsigned n, int shift) +{ + int word = 1 + (shift / BIGNUM_INT_BITS); + int bshift = shift % BIGNUM_INT_BITS; + BignumDblInt addend; - addend = n << bshift; + addend = (BignumDblInt)n << bshift; while (addend) { - addend += number[word]; - number[word] = (unsigned short) addend & 0xFFFF; - addend >>= 16; - word++; + assert(word <= number[0]); + addend += number[word]; + number[word] = (BignumInt) addend & BIGNUM_INT_MASK; + addend >>= BIGNUM_INT_BITS; + word++; } } @@ -91,61 +625,82 @@ static void internal_add_shifted(unsigned short *number, * rather than the internal bigendian format. Quotient parts are shifted * left by `qshift' before adding into quot. */ -static void internal_mod(unsigned short *a, int alen, - unsigned short *m, int mlen, - unsigned short *quot, int qshift) +static void internal_mod(BignumInt *a, int alen, + BignumInt *m, int mlen, + BignumInt *quot, int qshift) { - unsigned short m0, m1; + BignumInt m0, m1; unsigned int h; int i, k; m0 = m[0]; + assert(m0 >> (BIGNUM_INT_BITS-1) == 1); if (mlen > 1) - m1 = m[1]; + m1 = m[1]; else - m1 = 0; + m1 = 0; - for (i = 0; i <= alen-mlen; i++) { - unsigned long t; + for (i = 0; i <= alen - mlen; i++) { + BignumDblInt t; unsigned int q, r, c, ai1; if (i == 0) { h = 0; } else { - h = a[i-1]; - a[i-1] = 0; + h = a[i - 1]; + a[i - 1] = 0; } - if (i == alen-1) - ai1 = 0; - else - ai1 = a[i+1]; + if (i == alen - 1) + ai1 = 0; + else + ai1 = a[i + 1]; /* Find q = h:a[i] / m0 */ - t = ((unsigned long) h << 16) + a[i]; - q = t / m0; - r = t % m0; - - /* Refine our estimate of q by looking at - h:a[i]:a[i+1] / m0:m1 */ - t = (long) m1 * (long) q; - if (t > ((unsigned long) r << 16) + ai1) { - q--; - t -= m1; - r = (r + m0) & 0xffff; /* overflow? */ - if (r >= (unsigned long)m0 && - t > ((unsigned long) r << 16) + ai1) + if (h >= m0) { + /* + * Special case. + * + * To illustrate it, suppose a BignumInt is 8 bits, and + * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then + * our initial division will be 0xA123 / 0xA1, which + * will give a quotient of 0x100 and a divide overflow. + * However, the invariants in this division algorithm + * are not violated, since the full number A1:23:... is + * _less_ than the quotient prefix A1:B2:... and so the + * following correction loop would have sorted it out. + * + * In this situation we set q to be the largest + * quotient we _can_ stomach (0xFF, of course). + */ + q = BIGNUM_INT_MASK; + } else { + /* Macro doesn't want an array subscript expression passed + * into it (see definition), so use a temporary. */ + BignumInt tmplo = a[i]; + DIVMOD_WORD(q, r, h, tmplo, m0); + + /* Refine our estimate of q by looking at + h:a[i]:a[i+1] / m0:m1 */ + t = MUL_WORD(m1, q); + if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { q--; + t -= m1; + r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */ + if (r >= (BignumDblInt) m0 && + t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--; + } } /* Subtract q * m from a[i...] */ c = 0; for (k = mlen - 1; k >= 0; k--) { - t = (long) q * (long) m[k]; + t = MUL_WORD(q, m[k]); t += c; - c = t >> 16; - if ((unsigned short) t > a[i+k]) c++; - a[i+k] -= (unsigned short) t; + c = (unsigned)(t >> BIGNUM_INT_BITS); + if ((BignumInt) t > a[i + k]) + c++; + a[i + k] -= (BignumInt) t; } /* Add back m in case of borrow */ @@ -153,99 +708,284 @@ static void internal_mod(unsigned short *a, int alen, t = 0; for (k = mlen - 1; k >= 0; k--) { t += m[k]; - t += a[i+k]; - a[i+k] = (unsigned short)t; - t = t >> 16; + t += a[i + k]; + a[i + k] = (BignumInt) t; + t = t >> BIGNUM_INT_BITS; } - q--; + q--; } - if (quot) - internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i)); + if (quot) + internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); } } /* - * Compute (base ^ exp) % mod. - * The base MUST be smaller than the modulus. - * The most significant word of mod MUST be non-zero. - * We assume that the result array is the same size as the mod array. + * Compute (base ^ exp) % mod, the pedestrian way. */ -void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) +Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) { - unsigned short *a, *b, *n, *m; + BignumInt *a, *b, *n, *m, *scratch; int mshift; - int mlen, i, j; + int mlen, scratchlen, 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 = malloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + 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 < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + 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] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + 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 = malloc(mlen * sizeof(unsigned short)); + n = snewn(mlen, BignumInt); i = mlen - base[0]; - for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < base[0]; j++) n[i+j] = base[base[0] - j]; + 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 = malloc(2 * mlen * sizeof(unsigned short)); - b = malloc(2 * mlen * sizeof(unsigned short)); - for (i = 0; i < 2*mlen; i++) a[i] = 0; - a[2*mlen-1] = 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 = 15; - while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { + 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 = 15; } + if (j < 0) { + i++; + j = BIGNUM_INT_BITS-1; + } } /* Main computation */ - while (i < exp[0]) { + 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 + 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_mod(a, mlen*2, m, mlen, NULL, 0); + internal_mul(b + mlen, n, a, mlen, scratch); + internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { - unsigned short *t; - t = a; a = b; b = t; + BignumInt *t; + t = a; + a = b; + b = t; } j--; } - i++; j = 15; + 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] >> (16-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] << (16-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]; + 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; free(a); - for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b); - for (i = 0; i < mlen; i++) m[i] = 0; free(m); - for (i = 0; i < mlen; i++) n[i] = 0; free(n); + 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. + */ + 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 + * 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); + 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 + * representation. + */ + base2 = modmul(base, r, mod); + freebn(base); + base = base2; + + 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 < (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); + 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 < (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 < (int)rn[0] ? rn[j + 1] : 0); + freebn(rn); + + /* Scratch space for multiplies */ + scratchlen = 3*len + mul_compute_scratch(len); + 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 + 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, scratch); + monty_reduce(a, n, mninv, scratch, len); + } else { + BignumInt *t; + t = a; + a = b; + b = t; + } + j--; + } + i++; + j = BIGNUM_INT_BITS-1; + } + + /* + * Final monty_reduce to get back from the adjusted Montgomery + * representation. + */ + 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]; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; + + /* Free temporary arrays */ + smemclr(scratch, scratchlen * sizeof(*scratch)); + sfree(scratch); + smemclr(a, 2 * len * sizeof(*a)); + sfree(a); + smemclr(b, 2 * len * sizeof(*b)); + sfree(b); + smemclr(mninv, len * sizeof(*mninv)); + sfree(mninv); + smemclr(n, len * sizeof(*n)); + sfree(n); + smemclr(x, len * sizeof(*x)); + sfree(x); + + return result; } /* @@ -253,104 +993,152 @@ void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) * The most significant word of mod MUST be non-zero. * We assume that the result array is the same size as the mod array. */ -void modmul(Bignum p, Bignum q, Bignum mod, Bignum result) +Bignum modmul(Bignum p, Bignum q, Bignum mod) { - unsigned short *a, *n, *m, *o; - int mshift; - int pqlen, mlen, i, j; + 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]; - m = malloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + 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 < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + 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] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); + m[mlen - 1] = m[mlen - 1] << 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 = malloc(pqlen * sizeof(unsigned short)); + n = snewn(pqlen, BignumInt); i = pqlen - p[0]; - for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < p[0]; j++) n[i+j] = p[p[0] - j]; + for (j = 0; j < i; j++) + n[j] = 0; + for (j = 0; j < (int)p[0]; j++) + n[i + j] = p[p[0] - j]; /* Allocate o of size pqlen, copy q to o */ - o = malloc(pqlen * sizeof(unsigned short)); + o = snewn(pqlen, BignumInt); i = pqlen - q[0]; - for (j = 0; j < i; j++) o[j] = 0; - for (j = 0; j < q[0]; j++) o[i+j] = q[q[0] - j]; + for (j = 0; j < i; j++) + o[j] = 0; + for (j = 0; j < (int)q[0]; j++) + o[i + j] = q[q[0] - j]; /* Allocate a of size 2*pqlen for result */ - a = malloc(2 * pqlen * sizeof(unsigned short)); + 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_mod(a, pqlen*2, m, mlen, NULL, 0); + 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] >> (16-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] << (16-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)); } /* Copy result to buffer */ - for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i+2*pqlen-mlen]; + 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]; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2*pqlen; i++) a[i] = 0; free(a); - for (i = 0; i < mlen; i++) m[i] = 0; free(m); - for (i = 0; i < pqlen; i++) n[i] = 0; free(n); - for (i = 0; i < pqlen; i++) o[i] = 0; free(o); + smemclr(scratch, scratchlen * sizeof(*scratch)); + sfree(scratch); + smemclr(a, 2 * pqlen * sizeof(*a)); + sfree(a); + smemclr(m, mlen * sizeof(*m)); + sfree(m); + smemclr(n, pqlen * sizeof(*n)); + sfree(n); + smemclr(o, pqlen * sizeof(*o)); + sfree(o); + + return result; } /* * Compute p % mod. * The most significant word of mod MUST be non-zero. * We assume that the result array is the same size as the mod array. - * We optionally write out a quotient. + * We optionally write out a quotient if `quotient' is non-NULL. + * We can avoid writing out the result if `result' is NULL. */ -void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) +static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) { - unsigned short *n, *m; + BignumInt *n, *m; 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]; - m = malloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + 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 < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + 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] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } plen = p[0]; /* Ensure plen > mlen */ - if (plen <= mlen) plen = mlen+1; + if (plen <= mlen) + plen = mlen + 1; /* Allocate n of size plen, copy p to n */ - n = malloc(plen * sizeof(unsigned short)); - for (j = 0; j < plen; j++) n[j] = 0; - for (j = 1; j <= p[0]; j++) n[plen-j] = p[j]; + 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]; /* Main computation */ internal_mod(n, plen, m, mlen, quotient, mshift); @@ -358,156 +1146,201 @@ void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* 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] >> (16-mshift)); - n[plen-1] = n[plen-1] << mshift; + n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); + n[plen - 1] = n[plen - 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] << (16-mshift)); + n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ - for (i = 1; i <= result[0]; i++) { - int j = plen-i; - result[i] = j>=0 ? n[j] : 0; + if (result) { + for (i = 1; i <= (int)result[0]; i++) { + int j = plen - i; + result[i] = j >= 0 ? n[j] : 0; + } } /* Free temporary arrays */ - for (i = 0; i < mlen; i++) m[i] = 0; free(m); - for (i = 0; i < plen; i++) n[i] = 0; free(n); + smemclr(m, mlen * sizeof(*m)); + sfree(m); + smemclr(n, plen * sizeof(*n)); + sfree(n); } /* * Decrement a number. */ -void decbn(Bignum bn) { +void decbn(Bignum bn) +{ int i = 1; - while (i < bn[0] && bn[i] == 0) - bn[i++] = 0xFFFF; + while (i < (int)bn[0] && bn[i] == 0) + bn[i++] = BIGNUM_INT_MASK; bn[i]--; } +Bignum bignum_from_bytes(const unsigned char *data, int nbytes) +{ + 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); + for (i = 1; i <= w; i++) + result[i] = 0; + for (i = nbytes; i--;) { + unsigned char byte = *data++; + result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS); + } + + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; + return result; +} + /* - * Read an ssh1-format bignum from a data buffer. Return the number - * of bytes consumed. + * Read an SSH-1-format bignum from a data buffer. Return the number + * of bytes consumed, or -1 if there wasn't enough data. */ -int ssh1_read_bignum(unsigned char *data, Bignum *result) { - unsigned char *p = data; - Bignum bn; +int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result) +{ + const unsigned char *p = data; int i; int w, b; - w = 0; - for (i=0; i<2; i++) - w = (w << 8) + *p++; - - b = (w+7)/8; /* bits -> bytes */ - w = (w+15)/16; /* bits -> words */ + if (len < 2) + return -1; - if (!result) /* just return length */ - return b + 2; + w = 0; + for (i = 0; i < 2; i++) + w = (w << 8) + *p++; + b = (w + 7) / 8; /* bits -> bytes */ - bn = newbn(w); + if (len < b+2) + return -1; - for (i=1; i<=w; i++) - bn[i] = 0; - for (i=b; i-- ;) { - unsigned char byte = *p++; - if (i & 1) - bn[1+i/2] |= byte<<8; - else - bn[1+i/2] |= byte; - } + if (!result) /* just return length */ + return b + 2; - *result = bn; + *result = bignum_from_bytes(p, b); - return p - data; + return p + b - data; } /* - * Return the bit count of a bignum, for ssh1 encoding. + * Return the bit count of a bignum, for SSH-1 encoding. */ -int ssh1_bignum_bitcount(Bignum bn) { - int bitcount = bn[0] * 16 - 1; - - while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) - bitcount--; +int bignum_bitcount(Bignum bn) +{ + int bitcount = bn[0] * BIGNUM_INT_BITS - 1; + while (bitcount >= 0 + && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; return bitcount + 1; } /* - * Return the byte length of a bignum when ssh1 encoded. + * Return the byte length of a bignum when SSH-1 encoded. */ -int ssh1_bignum_length(Bignum bn) { - return 2 + (ssh1_bignum_bitcount(bn)+7)/8; +int ssh1_bignum_length(Bignum bn) +{ + return 2 + (bignum_bitcount(bn) + 7) / 8; +} + +/* + * Return the byte length of a bignum when SSH-2 encoded. + */ +int ssh2_bignum_length(Bignum bn) +{ + return 4 + (bignum_bitcount(bn) + 8) / 8; } /* * Return a byte from a bignum; 0 is least significant, etc. */ -int bignum_byte(Bignum bn, int i) { - if (i >= 2*bn[0]) - return 0; /* beyond the end */ - else if (i & 1) - return (bn[i/2+1] >> 8) & 0xFF; +int bignum_byte(Bignum bn, int i) +{ + if (i < 0 || i >= (int)(BIGNUM_INT_BYTES * bn[0])) + return 0; /* beyond the end */ else - return (bn[i/2+1] ) & 0xFF; + return (bn[i / BIGNUM_INT_BYTES + 1] >> + ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; } /* * Return a bit from a bignum; 0 is least significant, etc. */ -int bignum_bit(Bignum bn, int i) { - if (i >= 16*bn[0]) - return 0; /* beyond the end */ +int bignum_bit(Bignum bn, int i) +{ + if (i < 0 || i >= (int)(BIGNUM_INT_BITS * bn[0])) + return 0; /* beyond the end */ else - return (bn[i/16+1] >> (i%16)) & 1; + return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; } /* * Set a bit in a bignum; 0 is least significant, etc. */ -void bignum_set_bit(Bignum bn, int bitnum, int value) { - if (bitnum >= 16*bn[0]) - abort(); /* beyond the end */ +void bignum_set_bit(Bignum bn, int bitnum, int value) +{ + if (bitnum < 0 || bitnum >= (int)(BIGNUM_INT_BITS * bn[0])) + abort(); /* beyond the end */ else { - int v = bitnum/16+1; - int mask = 1 << (bitnum%16); - if (value) - bn[v] |= mask; - else - bn[v] &= ~mask; + int v = bitnum / BIGNUM_INT_BITS + 1; + int mask = 1 << (bitnum % BIGNUM_INT_BITS); + if (value) + bn[v] |= mask; + else + bn[v] &= ~mask; } } /* - * Write a ssh1-format bignum into a buffer. It is assumed the + * Write a SSH-1-format bignum into a buffer. It is assumed the * buffer is big enough. Returns the number of bytes used. */ -int ssh1_write_bignum(void *data, Bignum bn) { +int ssh1_write_bignum(void *data, Bignum bn) +{ unsigned char *p = data; int len = ssh1_bignum_length(bn); int i; - int bitc = ssh1_bignum_bitcount(bn); + int bitc = bignum_bitcount(bn); *p++ = (bitc >> 8) & 0xFF; - *p++ = (bitc ) & 0xFF; - for (i = len-2; i-- ;) - *p++ = bignum_byte(bn, i); + *p++ = (bitc) & 0xFF; + for (i = len - 2; i--;) + *p++ = bignum_byte(bn, i); return len; } /* * Compare two bignums. Returns like strcmp. */ -int bignum_cmp(Bignum a, Bignum b) { +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) { - unsigned short aval = (i > amax ? 0 : a[i]); - unsigned short bval = (i > bmax ? 0 : b[i]); - if (aval < bval) return -1; - if (aval > bval) return +1; - i--; + BignumInt aval = (i > amax ? 0 : a[i]); + BignumInt bval = (i > bmax ? 0 : b[i]); + if (aval < bval) + return -1; + if (aval > bval) + return +1; + i--; } return 0; } @@ -515,25 +1348,28 @@ int bignum_cmp(Bignum a, Bignum b) { /* * Right-shift one bignum to form another. */ -Bignum bignum_rshift(Bignum a, int shift) { +Bignum bignum_rshift(Bignum a, int shift) +{ Bignum ret; int i, shiftw, shiftb, shiftbb, bits; - unsigned short ai, ai1; + BignumInt ai, ai1; + + assert(shift >= 0); - bits = ssh1_bignum_bitcount(a) - shift; - ret = newbn((bits+15)/16); + bits = bignum_bitcount(a) - shift; + ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); if (ret) { - shiftw = shift / 16; - shiftb = shift % 16; - shiftbb = 16 - shiftb; - - ai1 = a[shiftw+1]; - for (i = 1; i <= ret[0]; i++) { - ai = ai1; - ai1 = (i+shiftw+1 <= a[0] ? a[i+shiftw+1] : 0); - ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF; - } + shiftw = shift / BIGNUM_INT_BITS; + shiftb = shift % BIGNUM_INT_BITS; + shiftbb = BIGNUM_INT_BITS - shiftb; + + ai1 = a[shiftw + 1]; + for (i = 1; i <= (int)ret[0]; i++) { + ai = ai1; + ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0); + ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; + } } return ret; @@ -542,88 +1378,188 @@ Bignum bignum_rshift(Bignum a, int shift) { /* * Non-modular multiplication and addition. */ -Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { +Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) +{ int alen = a[0], blen = b[0]; int mlen = (alen > blen ? alen : blen); int rlen, i, maxspot; - unsigned short *workspace; + int wslen; + BignumInt *workspace; Bignum ret; - /* mlen space for a, mlen space for b, 2*mlen for result */ - workspace = malloc(mlen * 4 * sizeof(unsigned short)); + /* 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 <= a[0] ? a[mlen-i] : 0); - workspace[1*mlen + i] = (mlen-i <= b[0] ? b[mlen-i] : 0); + 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); + internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, + workspace + 2 * mlen, mlen, workspace + 4 * mlen); /* now just copy the result back */ rlen = alen + blen + 1; - if (addend && rlen <= addend[0]) - rlen = addend[0] + 1; + if (addend && rlen <= (int)addend[0]) + rlen = addend[0] + 1; ret = newbn(rlen); maxspot = 0; - for (i = 1; i <= ret[0]; i++) { - ret[i] = (i <= 2*mlen ? workspace[4*mlen - i] : 0); - if (ret[i] != 0) - maxspot = i; + for (i = 1; i <= (int)ret[0]; i++) { + ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); + if (ret[i] != 0) + maxspot = i; } ret[0] = maxspot; /* now add in the addend, if any */ if (addend) { - unsigned long carry = 0; - for (i = 1; i <= rlen; i++) { - carry += (i <= ret[0] ? ret[i] : 0); - carry += (i <= addend[0] ? addend[i] : 0); - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; - if (ret[i] != 0 && i > maxspot) - maxspot = i; - } + BignumDblInt carry = 0; + for (i = 1; i <= rlen; i++) { + carry += (i <= (int)ret[0] ? ret[i] : 0); + carry += (i <= (int)addend[0] ? addend[i] : 0); + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0 && i > maxspot) + maxspot = i; + } } ret[0] = maxspot; + smemclr(workspace, wslen * sizeof(*workspace)); + sfree(workspace); return ret; } /* * Non-modular multiplication. */ -Bignum bigmul(Bignum a, Bignum b) { +Bignum bigmul(Bignum a, Bignum b) +{ return bigmuladd(a, b, NULL); } /* - * Convert a (max 16-bit) short into a bignum. + * Simple addition. */ -Bignum bignum_from_short(unsigned short n) { +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; - ret = newbn(2); - ret[1] = n & 0xFFFF; - ret[2] = (n >> 16) & 0xFFFF; - ret[0] = (ret[2] ? 2 : 1); - return ret; + 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. + */ +Bignum bignum_bitmask(Bignum n) +{ + Bignum ret = copybn(n); + int i; + BignumInt j; + + i = ret[0]; + while (n[i] == 0 && i > 0) + i--; + if (i <= 0) + return ret; /* input was zero */ + j = 1; + while (j < n[i]) + j = 2 * j + 1; + ret[i] = j; + while (--i > 0) + ret[i] = BIGNUM_INT_MASK; + return ret; +} + +/* + * Convert a (max 32-bit) long into a bignum. + */ +Bignum bignum_from_long(unsigned long nn) +{ + Bignum ret; + BignumDblInt n = nn; + + ret = newbn(3); + ret[1] = (BignumInt)(n & BIGNUM_INT_MASK); + ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK); + ret[3] = 0; + ret[0] = (ret[2] ? 2 : 1); + return ret; } /* * Add a long to a bignum. */ -Bignum bignum_add_long(Bignum number, unsigned long addend) { - Bignum ret = newbn(number[0]+1); +Bignum bignum_add_long(Bignum number, unsigned long addendx) +{ + Bignum ret = newbn(number[0] + 1); int i, maxspot = 0; - unsigned long carry = 0; - - for (i = 1; i <= ret[0]; i++) { - carry += addend & 0xFFFF; - carry += (i <= number[0] ? number[i] : 0); - addend >>= 16; - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; - if (ret[i] != 0) - maxspot = i; + BignumDblInt carry = 0, addend = addendx; + + for (i = 1; i <= (int)ret[0]; i++) { + carry += addend & BIGNUM_INT_MASK; + carry += (i <= (int)number[0] ? number[i] : 0); + addend >>= BIGNUM_INT_BITS; + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0) + maxspot = i; } ret[0] = maxspot; return ret; @@ -632,49 +1568,77 @@ Bignum bignum_add_long(Bignum number, unsigned long addend) { /* * Compute the residue of a bignum, modulo a (max 16-bit) short. */ -unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { - unsigned long mod, r; +unsigned short bignum_mod_short(Bignum number, unsigned short modulus) +{ + BignumDblInt mod, r; int i; r = 0; mod = modulus; for (i = number[0]; i > 0; i--) - r = (r * 65536 + number[i]) % mod; + r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; return (unsigned short) r; } -static void diagbn(char *prefix, Bignum md) { +#ifdef DEBUG +void diagbn(char *prefix, Bignum md) +{ int i, nibbles, morenibbles; static const char hex[] = "0123456789ABCDEF"; - printf("%s0x", prefix ? prefix : ""); + debug(("%s0x", prefix ? prefix : "")); + + nibbles = (3 + bignum_bitcount(md)) / 4; + if (nibbles < 1) + nibbles = 1; + morenibbles = 4 * md[0] - nibbles; + for (i = 0; i < morenibbles; i++) + debug(("-")); + for (i = nibbles; i--;) + debug(("%c", + hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF])); - nibbles = (3 + ssh1_bignum_bitcount(md))/4; if (nibbles<1) nibbles=1; - morenibbles = 4*md[0] - nibbles; - for (i=0; i> (4*(i%2))) & 0xF]); + if (prefix) + debug(("\n")); +} +#endif - if (prefix) putchar('\n'); +/* + * Simple division. + */ +Bignum bigdiv(Bignum a, Bignum b) +{ + Bignum q = newbn(a[0]); + bigdivmod(a, b, NULL, q); + return q; +} + +/* + * Simple remainder. + */ +Bignum bigmod(Bignum a, Bignum b) +{ + Bignum r = newbn(b[0]); + bigdivmod(a, b, r, NULL); + return r; } /* * Greatest common divisor. */ -Bignum biggcd(Bignum av, Bignum bv) { +Bignum biggcd(Bignum av, Bignum bv) +{ Bignum a = copybn(av); Bignum b = copybn(bv); - diagbn("a = ", a); - diagbn("b = ", b); while (bignum_cmp(b, Zero) != 0) { - Bignum t = newbn(b[0]); - bigmod(a, b, t, NULL); - diagbn("t = ", t); - while (t[0] > 1 && t[t[0]] == 0) t[0]--; - freebn(a); - a = b; - b = t; + Bignum t = newbn(b[0]); + bigdivmod(a, b, t, NULL); + while (t[0] > 1 && t[t[0]] == 0) + t[0]--; + freebn(a); + a = b; + b = t; } freebn(b); @@ -684,26 +1648,46 @@ Bignum biggcd(Bignum av, Bignum bv) { /* * Modular inverse, using Euclid's extended algorithm. */ -Bignum modinv(Bignum number, Bignum modulus) { +Bignum modinv(Bignum number, Bignum modulus) +{ Bignum a = copybn(modulus); Bignum b = copybn(number); Bignum xp = copybn(Zero); 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]); - bigmod(a, b, t, q); - while (t[0] > 1 && t[t[0]] == 0) t[0]--; - freebn(a); - a = b; - b = t; - t = xp; - xp = x; - x = bigmuladd(q, xp, t); - sign = -sign; - freebn(t); + 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]--; + freebn(a); + a = b; + b = t; + t = xp; + xp = x; + x = bigmuladd(q, xp, t); + sign = -sign; + freebn(t); + freebn(q); } freebn(b); @@ -712,24 +1696,24 @@ Bignum modinv(Bignum number, Bignum modulus) { /* now we know that sign * x == 1, and that x < modulus */ if (sign < 0) { - /* set a new x to be modulus - x */ - Bignum newx = newbn(modulus[0]); - unsigned short carry = 0; - int maxspot = 1; - int i; - - for (i = 1; i <= newx[0]; i++) { - unsigned short aword = (i <= modulus[0] ? modulus[i] : 0); - unsigned short bword = (i <= x[0] ? x[i] : 0); - newx[i] = aword - bword - carry; - bword = ~bword; - carry = carry ? (newx[i] >= bword) : (newx[i] > bword); - if (newx[i] != 0) - maxspot = i; - } - newx[0] = maxspot; - freebn(x); - x = newx; + /* set a new x to be modulus - x */ + Bignum newx = newbn(modulus[0]); + BignumInt carry = 0; + int maxspot = 1; + int i; + + for (i = 1; i <= (int)newx[0]; i++) { + BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0); + BignumInt bword = (i <= (int)x[0] ? x[i] : 0); + newx[i] = aword - bword - carry; + bword = ~bword; + carry = carry ? (newx[i] >= bword) : (newx[i] > bword); + if (newx[i] != 0) + maxspot = i; + } + newx[0] = maxspot; + freebn(x); + x = newx; } /* and return. */ @@ -740,12 +1724,13 @@ Bignum modinv(Bignum number, Bignum modulus) { * Render a bignum into decimal. Return a malloced string holding * the decimal representation. */ -char *bignum_decimal(Bignum x) { +char *bignum_decimal(Bignum x) +{ int ndigits, ndigit; int i, iszero; - unsigned long carry; + BignumDblInt carry; char *ret; - unsigned short *workspace; + BignumInt *workspace; /* * First, estimate the number of digits. Since log(10)/log(2) @@ -759,39 +1744,44 @@ char *bignum_decimal(Bignum x) { * round up (rounding down might make it less than x again). * Therefore if we multiply the bit count by 28/93, rounding * up, we will have enough digits. + * + * i=0 (i.e., x=0) is an irritating special case. */ - i = ssh1_bignum_bitcount(x); - ndigits = (28*i + 92)/93; /* multiply by 28/93 and round up */ - ndigits++; /* allow for trailing \0 */ - ret = malloc(ndigits); + i = bignum_bitcount(x); + if (!i) + ndigits = 1; /* x = 0 */ + else + ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ + ndigits++; /* allow for trailing \0 */ + ret = snewn(ndigits, char); /* * Now allocate some workspace to hold the binary form as we * repeatedly divide it by ten. Initialise this to the * big-endian form of the number. */ - workspace = malloc(sizeof(unsigned short) * x[0]); - for (i = 0; i < x[0]; i++) - workspace[i] = x[x[0] - i]; + workspace = snewn(x[0], BignumInt); + for (i = 0; i < (int)x[0]; i++) + workspace[i] = x[x[0] - i]; /* * Next, write the decimal number starting with the last digit. * We use ordinary short division, dividing 10 into the * workspace. */ - ndigit = ndigits-1; + ndigit = ndigits - 1; ret[ndigit] = '\0'; do { - iszero = 1; - carry = 0; - for (i = 0; i < x[0]; i++) { - carry = (carry << 16) + workspace[i]; - workspace[i] = (unsigned short) (carry / 10); - if (workspace[i]) - iszero = 0; - carry %= 10; - } - ret[--ndigit] = (char)(carry + '0'); + iszero = 1; + carry = 0; + for (i = 0; i < (int)x[0]; i++) { + carry = (carry << BIGNUM_INT_BITS) + workspace[i]; + workspace[i] = (BignumInt) (carry / 10); + if (workspace[i]) + iszero = 0; + carry %= 10; + } + ret[--ndigit] = (char) (carry + '0'); } while (!iszero); /* @@ -799,10 +1789,213 @@ char *bignum_decimal(Bignum x) { * string. Correct if so. */ if (ndigit > 0) - memmove(ret, ret+ndigit, ndigits-ndigit); + memmove(ret, ret + ndigit, ndigits - ndigit); /* * Done. */ + smemclr(workspace, x[0] * sizeof(*workspace)); + sfree(workspace); return ret; } + +#ifdef TESTBN + +#include +#include +#include + +/* + * 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