/* * 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