X-Git-Url: http://git.osdn.net/view?a=blobdiff_plain;f=putty%2FSSHBN.C;fp=putty%2FSSHBN.C;h=0000000000000000000000000000000000000000;hb=9899fe5c3103887bb167b820e8863e67b3ea372c;hp=51cecdf2b0247725803e92e5c2e8affcc08876ec;hpb=eb4bba58018c0bb08e8564600c2c66257c3a3077;p=ffftp%2Fffftp.git diff --git a/putty/SSHBN.C b/putty/SSHBN.C deleted file mode 100644 index 51cecdf..0000000 --- a/putty/SSHBN.C +++ /dev/null @@ -1,1918 +0,0 @@ -/* - * Bignum routines for RSA and DH and stuff. - */ - -#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" - -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; - -static Bignum newbn(int length) -{ - Bignum b = snewn(length + 1, BignumInt); - if (!b) - abort(); /* FIXME */ - memset(b, 0, (length + 1) * sizeof(*b)); - b[0] = length; - return b; -} - -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)); - return b; -} - -void freebn(Bignum b) -{ - /* - * Burn the evidence, just in case. - */ - memset(b, 0, sizeof(b[0]) * (b[0] + 1)); - sfree(b); -} - -Bignum bn_power_2(int n) -{ - Bignum 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.) - */ -#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) -{ - if (len > KARATSUBA_THRESHOLD) { - int i; - - /* - * 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 - - /* 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(BignumInt *number, - unsigned n, int shift) -{ - int word = 1 + (shift / BIGNUM_INT_BITS); - int bshift = shift % BIGNUM_INT_BITS; - BignumDblInt addend; - - addend = (BignumDblInt)n << bshift; - - while (addend) { - addend += number[word]; - number[word] = (BignumInt) addend & BIGNUM_INT_MASK; - addend >>= BIGNUM_INT_BITS; - word++; - } -} - -/* - * 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). - * 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. - */ -static void internal_mod(BignumInt *a, int alen, - BignumInt *m, int mlen, - BignumInt *quot, int qshift) -{ - BignumInt m0, m1; - unsigned int h; - int i, k; - - m0 = m[0]; - if (mlen > 1) - m1 = m[1]; - else - m1 = 0; - - 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; - } - - if (i == alen - 1) - ai1 = 0; - else - ai1 = a[i + 1]; - - /* Find q = h:a[i] / m0 */ - 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 = MUL_WORD(q, m[k]); - t += c; - 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 */ - if (c != h) { - t = 0; - for (k = mlen - 1; k >= 0; k--) { - t += m[k]; - t += a[i + k]; - a[i + k] = (BignumInt) t; - t = t >> BIGNUM_INT_BITS; - } - q--; - } - if (quot) - internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); - } -} - -/* - * Compute (base ^ exp) % mod, the pedestrian way. - */ -Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) -{ - BignumInt *a, *b, *n, *m, *scratch; - int mshift; - int mlen, scratchlen, i, j; - Bignum base, result; - - /* - * The most significant word of mod needs to be non-zero. It - * 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 = snewn(mlen, BignumInt); - for (j = 0; j < mlen; j++) - m[j] = mod[mod[0] - j]; - - /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) - if ((m[0] << mshift) & BIGNUM_TOP_BIT) - break; - if (mshift) { - for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); - m[mlen - 1] = m[mlen - 1] << mshift; - } - - /* Allocate n of size mlen, copy base to n */ - n = snewn(mlen, BignumInt); - i = mlen - base[0]; - for (j = 0; j < i; j++) - n[j] = 0; - for (j = 0; j < (int)base[0]; j++) - n[i + j] = base[base[0] - j]; - - /* Allocate a and b of size 2*mlen. Set a = 1 */ - a = snewn(2 * mlen, BignumInt); - b = snewn(2 * mlen, BignumInt); - for (i = 0; i < 2 * mlen; i++) - a[i] = 0; - a[2 * mlen - 1] = 1; - - /* Scratch space for multiplies */ - scratchlen = mul_compute_scratch(mlen); - scratch = snewn(scratchlen, BignumInt); - - /* Skip leading zero bits of exp. */ - i = 0; - j = BIGNUM_INT_BITS-1; - while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { - j--; - if (j < 0) { - i++; - j = BIGNUM_INT_BITS-1; - } - } - - /* Main computation */ - while (i < (int)exp[0]) { - while (j >= 0) { - internal_mul(a + mlen, a + mlen, b, mlen, scratch); - internal_mod(b, mlen * 2, m, mlen, NULL, 0); - if ((exp[exp[0] - i] & (1 << j)) != 0) { - internal_mul(b + mlen, n, a, mlen, scratch); - internal_mod(a, mlen * 2, m, mlen, NULL, 0); - } else { - BignumInt *t; - t = a; - a = b; - b = t; - } - j--; - } - i++; - j = BIGNUM_INT_BITS-1; - } - - /* Fixup result in case the modulus was shifted */ - if (mshift) { - for (i = mlen - 1; i < 2 * mlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); - a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; - internal_mod(a, mlen * 2, m, mlen, NULL, 0); - for (i = 2 * mlen - 1; i >= mlen; i--) - a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); - } - - /* Copy result to buffer */ - result = newbn(mod[0]); - for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i + mlen]; - while (result[0] > 1 && result[result[0]] == 0) - result[0]--; - - /* Free temporary arrays */ - 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); - for (i = 0; i < mlen; i++) - m[i] = 0; - sfree(m); - for (i = 0; i < mlen; i++) - n[i] = 0; - 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); - - /* - * 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 */ - for (i = 0; i < scratchlen; i++) - scratch[i] = 0; - sfree(scratch); - for (i = 0; i < 2 * len; i++) - a[i] = 0; - sfree(a); - for (i = 0; i < 2 * len; i++) - b[i] = 0; - sfree(b); - for (i = 0; i < len; i++) - mninv[i] = 0; - sfree(mninv); - for (i = 0; i < len; i++) - n[i] = 0; - sfree(n); - for (i = 0; i < len; i++) - x[i] = 0; - sfree(x); - - return result; -} - -/* - * Compute (p * q) % 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. - */ -Bignum modmul(Bignum p, Bignum q, Bignum mod) -{ - 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]; - - /* 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; - } - - pqlen = (p[0] > q[0] ? p[0] : q[0]); - - /* 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]; - - /* 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]; - - /* 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, 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)); - } - - /* 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]; - 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); - for (i = 0; i < mlen; i++) - m[i] = 0; - sfree(m); - for (i = 0; i < pqlen; i++) - n[i] = 0; - sfree(n); - for (i = 0; i < pqlen; i++) - o[i] = 0; - 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 if `quotient' is non-NULL. - * We can avoid writing out the result if `result' is NULL. - */ -static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) -{ - BignumInt *n, *m; - int mshift; - 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]; - - /* 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; - } - - plen = p[0]; - /* Ensure plen > mlen */ - if (plen <= mlen) - plen = mlen + 1; - - /* 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]; - - /* 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; - 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)); - } - - /* 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; - } - } - - /* Free temporary arrays */ - for (i = 0; i < mlen; i++) - m[i] = 0; - sfree(m); - for (i = 0; i < plen; i++) - n[i] = 0; - sfree(n); -} - -/* - * Decrement a number. - */ -void decbn(Bignum bn) -{ - int i = 1; - 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; - - 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 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(const unsigned char *data, int len, Bignum * result) -{ - const unsigned char *p = data; - int i; - int w, b; - - if (len < 2) - return -1; - - w = 0; - for (i = 0; i < 2; i++) - w = (w << 8) + *p++; - b = (w + 7) / 8; /* bits -> bytes */ - - if (len < b+2) - return -1; - - if (!result) /* just return length */ - return b + 2; - - *result = bignum_from_bytes(p, b); - - return p + b - data; -} - -/* - * Return the bit count of a bignum, for SSH-1 encoding. - */ -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 SSH-1 encoded. - */ -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 >= (int)(BIGNUM_INT_BYTES * bn[0])) - return 0; /* beyond the end */ - else - 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 >= (int)(BIGNUM_INT_BITS * bn[0])) - return 0; /* beyond the end */ - else - 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 >= (int)(BIGNUM_INT_BITS * bn[0])) - abort(); /* beyond the end */ - else { - 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 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) -{ - unsigned char *p = data; - int len = ssh1_bignum_length(bn); - int i; - int bitc = bignum_bitcount(bn); - - *p++ = (bitc >> 8) & 0xFF; - *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 amax = a[0], bmax = b[0]; - int i = (amax > bmax ? amax : bmax); - while (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; -} - -/* - * Right-shift one bignum to form another. - */ -Bignum bignum_rshift(Bignum a, int shift) -{ - Bignum ret; - int i, shiftw, shiftb, shiftbb, bits; - BignumInt ai, ai1; - - bits = bignum_bitcount(a) - shift; - ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); - - if (ret) { - 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; -} - -/* - * Non-modular multiplication and addition. - */ -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; - int wslen; - BignumInt *workspace; - Bignum ret; - - /* mlen space for a, mlen space for b, 2*mlen for result, - * plus scratch space for multiplication */ - wslen = mlen * 4 + mul_compute_scratch(mlen); - workspace = snewn(wslen, BignumInt); - for (i = 0; i < mlen; i++) { - workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0); - workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0); - } - - internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, - workspace + 2 * mlen, mlen, workspace + 4 * mlen); - - /* now just copy the result back */ - rlen = alen + blen + 1; - if (addend && rlen <= (int)addend[0]) - 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; - } - ret[0] = maxspot; - - /* now add in the addend, if any */ - if (addend) { - 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; - - for (i = 0; i < wslen; i++) - workspace[i] = 0; - sfree(workspace); - return ret; -} - -/* - * Non-modular multiplication. - */ -Bignum bigmul(Bignum a, Bignum b) -{ - return bigmuladd(a, b, NULL); -} - -/* - * 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. - */ -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 addendx) -{ - Bignum ret = newbn(number[0] + 1); - int i, maxspot = 0; - 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; -} - -/* - * Compute the residue of a bignum, modulo a (max 16-bit) short. - */ -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 * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; - return (unsigned short) r; -} - -#ifdef DEBUG -void diagbn(char *prefix, Bignum md) -{ - int i, nibbles, morenibbles; - static const char hex[] = "0123456789ABCDEF"; - - 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])); - - if (prefix) - debug(("\n")); -} -#endif - -/* - * 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 a = copybn(av); - Bignum b = copybn(bv); - - while (bignum_cmp(b, Zero) != 0) { - 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); - return a; -} - -/* - * Modular inverse, using Euclid's extended algorithm. - */ -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; - - while (bignum_cmp(b, One) != 0) { - Bignum t = newbn(b[0]); - Bignum 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); - freebn(a); - freebn(xp); - - /* 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]); - 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. */ - return x; -} - -/* - * Render a bignum into decimal. Return a malloced string holding - * the decimal representation. - */ -char *bignum_decimal(Bignum x) -{ - int ndigits, ndigit; - int i, iszero; - BignumDblInt carry; - char *ret; - BignumInt *workspace; - - /* - * First, estimate the number of digits. Since log(10)/log(2) - * is just greater than 93/28 (the joys of continued fraction - * approximations...) we know that for every 93 bits, we need - * at most 28 digits. This will tell us how much to malloc. - * - * Formally: if x has i bits, that means x is strictly less - * than 2^i. Since 2 is less than 10^(28/93), this is less than - * 10^(28i/93). We need an integer power of ten, so we must - * 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 = 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 = 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; - ret[ndigit] = '\0'; - do { - 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); - - /* - * There's a chance we've fallen short of the start of the - * string. Correct if so. - */ - if (ndigit > 0) - memmove(ret, ret + ndigit, ndigits - ndigit); - - /* - * Done. - */ - sfree(workspace); - return ret; -} - -#ifdef TESTBN - -#include -#include -#include - -/* - * gcc -g -O0 -DTESTBN -o testbn sshbn.c misc.c -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); - 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, "pow")) { - Bignum base, expt, modulus, expected, answer; - - if (ptrnum != 4) { - printf("%d: mul with %d parameters, expected 3\n", line); - 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