+++ /dev/null
-/*\r
- * Bignum routines for RSA and DH and stuff.\r
- */\r
-\r
-#include <stdio.h>\r
-#include <assert.h>\r
-#include <stdlib.h>\r
-#include <string.h>\r
-\r
-#include "misc.h"\r
-\r
-/*\r
- * Usage notes:\r
- * * Do not call the DIVMOD_WORD macro with expressions such as array\r
- * subscripts, as some implementations object to this (see below).\r
- * * Note that none of the division methods below will cope if the\r
- * quotient won't fit into BIGNUM_INT_BITS. Callers should be careful\r
- * to avoid this case.\r
- * If this condition occurs, in the case of the x86 DIV instruction,\r
- * an overflow exception will occur, which (according to a correspondent)\r
- * will manifest on Windows as something like\r
- * 0xC0000095: Integer overflow\r
- * The C variant won't give the right answer, either.\r
- */\r
-\r
-#if defined __GNUC__ && defined __i386__\r
-typedef unsigned long BignumInt;\r
-typedef unsigned long long BignumDblInt;\r
-#define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
-#define BIGNUM_TOP_BIT 0x80000000UL\r
-#define BIGNUM_INT_BITS 32\r
-#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
-#define DIVMOD_WORD(q, r, hi, lo, w) \\r
- __asm__("div %2" : \\r
- "=d" (r), "=a" (q) : \\r
- "r" (w), "d" (hi), "a" (lo))\r
-#elif defined _MSC_VER && defined _M_IX86\r
-typedef unsigned __int32 BignumInt;\r
-typedef unsigned __int64 BignumDblInt;\r
-#define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
-#define BIGNUM_TOP_BIT 0x80000000UL\r
-#define BIGNUM_INT_BITS 32\r
-#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
-/* Note: MASM interprets array subscripts in the macro arguments as\r
- * assembler syntax, which gives the wrong answer. Don't supply them.\r
- * <http://msdn2.microsoft.com/en-us/library/bf1dw62z.aspx> */\r
-#define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
- __asm mov edx, hi \\r
- __asm mov eax, lo \\r
- __asm div w \\r
- __asm mov r, edx \\r
- __asm mov q, eax \\r
-} while(0)\r
-#elif defined _LP64\r
-/* 64-bit architectures can do 32x32->64 chunks at a time */\r
-typedef unsigned int BignumInt;\r
-typedef unsigned long BignumDblInt;\r
-#define BIGNUM_INT_MASK 0xFFFFFFFFU\r
-#define BIGNUM_TOP_BIT 0x80000000U\r
-#define BIGNUM_INT_BITS 32\r
-#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
-#define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
- BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
- q = n / w; \\r
- r = n % w; \\r
-} while (0)\r
-#elif defined _LLP64\r
-/* 64-bit architectures in which unsigned long is 32 bits, not 64 */\r
-typedef unsigned long BignumInt;\r
-typedef unsigned long long BignumDblInt;\r
-#define BIGNUM_INT_MASK 0xFFFFFFFFUL\r
-#define BIGNUM_TOP_BIT 0x80000000UL\r
-#define BIGNUM_INT_BITS 32\r
-#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
-#define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
- BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
- q = n / w; \\r
- r = n % w; \\r
-} while (0)\r
-#else\r
-/* Fallback for all other cases */\r
-typedef unsigned short BignumInt;\r
-typedef unsigned long BignumDblInt;\r
-#define BIGNUM_INT_MASK 0xFFFFU\r
-#define BIGNUM_TOP_BIT 0x8000U\r
-#define BIGNUM_INT_BITS 16\r
-#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)\r
-#define DIVMOD_WORD(q, r, hi, lo, w) do { \\r
- BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \\r
- q = n / w; \\r
- r = n % w; \\r
-} while (0)\r
-#endif\r
-\r
-#define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8)\r
-\r
-#define BIGNUM_INTERNAL\r
-typedef BignumInt *Bignum;\r
-\r
-#include "ssh.h"\r
-\r
-BignumInt bnZero[1] = { 0 };\r
-BignumInt bnOne[2] = { 1, 1 };\r
-\r
-/*\r
- * The Bignum format is an array of `BignumInt'. The first\r
- * element of the array counts the remaining elements. The\r
- * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_\r
- * significant digit first. (So it's trivial to extract the bit\r
- * with value 2^n for any n.)\r
- *\r
- * All Bignums in this module are positive. Negative numbers must\r
- * be dealt with outside it.\r
- *\r
- * INVARIANT: the most significant word of any Bignum must be\r
- * nonzero.\r
- */\r
-\r
-Bignum Zero = bnZero, One = bnOne;\r
-\r
-static Bignum newbn(int length)\r
-{\r
- Bignum b = snewn(length + 1, BignumInt);\r
- if (!b)\r
- abort(); /* FIXME */\r
- memset(b, 0, (length + 1) * sizeof(*b));\r
- b[0] = length;\r
- return b;\r
-}\r
-\r
-void bn_restore_invariant(Bignum b)\r
-{\r
- while (b[0] > 1 && b[b[0]] == 0)\r
- b[0]--;\r
-}\r
-\r
-Bignum copybn(Bignum orig)\r
-{\r
- Bignum b = snewn(orig[0] + 1, BignumInt);\r
- if (!b)\r
- abort(); /* FIXME */\r
- memcpy(b, orig, (orig[0] + 1) * sizeof(*b));\r
- return b;\r
-}\r
-\r
-void freebn(Bignum b)\r
-{\r
- /*\r
- * Burn the evidence, just in case.\r
- */\r
- memset(b, 0, sizeof(b[0]) * (b[0] + 1));\r
- sfree(b);\r
-}\r
-\r
-Bignum bn_power_2(int n)\r
-{\r
- Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);\r
- bignum_set_bit(ret, n, 1);\r
- return ret;\r
-}\r
-\r
-/*\r
- * Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all\r
- * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried\r
- * off the top.\r
- */\r
-static BignumInt internal_add(const BignumInt *a, const BignumInt *b,\r
- BignumInt *c, int len)\r
-{\r
- int i;\r
- BignumDblInt carry = 0;\r
-\r
- for (i = len-1; i >= 0; i--) {\r
- carry += (BignumDblInt)a[i] + b[i];\r
- c[i] = (BignumInt)carry;\r
- carry >>= BIGNUM_INT_BITS;\r
- }\r
-\r
- return (BignumInt)carry;\r
-}\r
-\r
-/*\r
- * Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are\r
- * all big-endian arrays of 'len' BignumInts. Any borrow from the top\r
- * is ignored.\r
- */\r
-static void internal_sub(const BignumInt *a, const BignumInt *b,\r
- BignumInt *c, int len)\r
-{\r
- int i;\r
- BignumDblInt carry = 1;\r
-\r
- for (i = len-1; i >= 0; i--) {\r
- carry += (BignumDblInt)a[i] + (b[i] ^ BIGNUM_INT_MASK);\r
- c[i] = (BignumInt)carry;\r
- carry >>= BIGNUM_INT_BITS;\r
- }\r
-}\r
-\r
-/*\r
- * Compute c = a * b.\r
- * Input is in the first len words of a and b.\r
- * Result is returned in the first 2*len words of c.\r
- *\r
- * 'scratch' must point to an array of BignumInt of size at least\r
- * mul_compute_scratch(len). (This covers the needs of internal_mul\r
- * and all its recursive calls to itself.)\r
- */\r
-#define KARATSUBA_THRESHOLD 50\r
-static int mul_compute_scratch(int len)\r
-{\r
- int ret = 0;\r
- while (len > KARATSUBA_THRESHOLD) {\r
- int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
- int midlen = botlen + 1;\r
- ret += 4*midlen;\r
- len = midlen;\r
- }\r
- return ret;\r
-}\r
-static void internal_mul(const BignumInt *a, const BignumInt *b,\r
- BignumInt *c, int len, BignumInt *scratch)\r
-{\r
- if (len > KARATSUBA_THRESHOLD) {\r
- int i;\r
-\r
- /*\r
- * Karatsuba divide-and-conquer algorithm. Cut each input in\r
- * half, so that it's expressed as two big 'digits' in a giant\r
- * base D:\r
- *\r
- * a = a_1 D + a_0\r
- * b = b_1 D + b_0\r
- *\r
- * Then the product is of course\r
- *\r
- * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0\r
- *\r
- * and we compute the three coefficients by recursively\r
- * calling ourself to do half-length multiplications.\r
- *\r
- * The clever bit that makes this worth doing is that we only\r
- * need _one_ half-length multiplication for the central\r
- * coefficient rather than the two that it obviouly looks\r
- * like, because we can use a single multiplication to compute\r
- *\r
- * (a_1 + a_0) (b_1 + b_0) = a_1 b_1 + a_1 b_0 + a_0 b_1 + a_0 b_0\r
- *\r
- * and then we subtract the other two coefficients (a_1 b_1\r
- * and a_0 b_0) which we were computing anyway.\r
- *\r
- * Hence we get to multiply two numbers of length N in about\r
- * three times as much work as it takes to multiply numbers of\r
- * length N/2, which is obviously better than the four times\r
- * as much work it would take if we just did a long\r
- * conventional multiply.\r
- */\r
-\r
- int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
- int midlen = botlen + 1;\r
- BignumDblInt carry;\r
-#ifdef KARA_DEBUG\r
- int i;\r
-#endif\r
-\r
- /*\r
- * The coefficients a_1 b_1 and a_0 b_0 just avoid overlapping\r
- * in the output array, so we can compute them immediately in\r
- * place.\r
- */\r
-\r
-#ifdef KARA_DEBUG\r
- printf("a1,a0 = 0x");\r
- for (i = 0; i < len; i++) {\r
- if (i == toplen) printf(", 0x");\r
- printf("%0*x", BIGNUM_INT_BITS/4, a[i]);\r
- }\r
- printf("\n");\r
- printf("b1,b0 = 0x");\r
- for (i = 0; i < len; i++) {\r
- if (i == toplen) printf(", 0x");\r
- printf("%0*x", BIGNUM_INT_BITS/4, b[i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /* a_1 b_1 */\r
- internal_mul(a, b, c, toplen, scratch);\r
-#ifdef KARA_DEBUG\r
- printf("a1b1 = 0x");\r
- for (i = 0; i < 2*toplen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, c[i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /* a_0 b_0 */\r
- internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch);\r
-#ifdef KARA_DEBUG\r
- printf("a0b0 = 0x");\r
- for (i = 0; i < 2*botlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, c[2*toplen+i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /* Zero padding. midlen exceeds toplen by at most 2, so just\r
- * zero the first two words of each input and the rest will be\r
- * copied over. */\r
- scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0;\r
-\r
- for (i = 0; i < toplen; i++) {\r
- scratch[midlen - toplen + i] = a[i]; /* a_1 */\r
- scratch[2*midlen - toplen + i] = b[i]; /* b_1 */\r
- }\r
-\r
- /* compute a_1 + a_0 */\r
- scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen);\r
-#ifdef KARA_DEBUG\r
- printf("a1plusa0 = 0x");\r
- for (i = 0; i < midlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);\r
- }\r
- printf("\n");\r
-#endif\r
- /* compute b_1 + b_0 */\r
- scratch[midlen] = internal_add(scratch+midlen+1, b+toplen,\r
- scratch+midlen+1, botlen);\r
-#ifdef KARA_DEBUG\r
- printf("b1plusb0 = 0x");\r
- for (i = 0; i < midlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /*\r
- * Now we can do the third multiplication.\r
- */\r
- internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen,\r
- scratch + 4*midlen);\r
-#ifdef KARA_DEBUG\r
- printf("a1plusa0timesb1plusb0 = 0x");\r
- for (i = 0; i < 2*midlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /*\r
- * Now we can reuse the first half of 'scratch' to compute the\r
- * sum of the outer two coefficients, to subtract from that\r
- * product to obtain the middle one.\r
- */\r
- scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0;\r
- for (i = 0; i < 2*toplen; i++)\r
- scratch[2*midlen - 2*toplen + i] = c[i];\r
- scratch[1] = internal_add(scratch+2, c + 2*toplen,\r
- scratch+2, 2*botlen);\r
-#ifdef KARA_DEBUG\r
- printf("a1b1plusa0b0 = 0x");\r
- for (i = 0; i < 2*midlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- internal_sub(scratch + 2*midlen, scratch,\r
- scratch + 2*midlen, 2*midlen);\r
-#ifdef KARA_DEBUG\r
- printf("a1b0plusa0b1 = 0x");\r
- for (i = 0; i < 2*midlen; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- /*\r
- * And now all we need to do is to add that middle coefficient\r
- * back into the output. We may have to propagate a carry\r
- * further up the output, but we can be sure it won't\r
- * propagate right the way off the top.\r
- */\r
- carry = internal_add(c + 2*len - botlen - 2*midlen,\r
- scratch + 2*midlen,\r
- c + 2*len - botlen - 2*midlen, 2*midlen);\r
- i = 2*len - botlen - 2*midlen - 1;\r
- while (carry) {\r
- assert(i >= 0);\r
- carry += c[i];\r
- c[i] = (BignumInt)carry;\r
- carry >>= BIGNUM_INT_BITS;\r
- i--;\r
- }\r
-#ifdef KARA_DEBUG\r
- printf("ab = 0x");\r
- for (i = 0; i < 2*len; i++) {\r
- printf("%0*x", BIGNUM_INT_BITS/4, c[i]);\r
- }\r
- printf("\n");\r
-#endif\r
-\r
- } else {\r
- int i;\r
- BignumInt carry;\r
- BignumDblInt t;\r
- const BignumInt *ap, *bp;\r
- BignumInt *cp, *cps;\r
-\r
- /*\r
- * Multiply in the ordinary O(N^2) way.\r
- */\r
-\r
- for (i = 0; i < 2 * len; i++)\r
- c[i] = 0;\r
-\r
- for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) {\r
- carry = 0;\r
- for (cp = cps, bp = b + len; cp--, bp-- > b ;) {\r
- t = (MUL_WORD(*ap, *bp) + carry) + *cp;\r
- *cp = (BignumInt) t;\r
- carry = (BignumInt)(t >> BIGNUM_INT_BITS);\r
- }\r
- *cp = carry;\r
- }\r
- }\r
-}\r
-\r
-/*\r
- * Variant form of internal_mul used for the initial step of\r
- * Montgomery reduction. Only bothers outputting 'len' words\r
- * (everything above that is thrown away).\r
- */\r
-static void internal_mul_low(const BignumInt *a, const BignumInt *b,\r
- BignumInt *c, int len, BignumInt *scratch)\r
-{\r
- if (len > KARATSUBA_THRESHOLD) {\r
- int i;\r
-\r
- /*\r
- * Karatsuba-aware version of internal_mul_low. As before, we\r
- * express each input value as a shifted combination of two\r
- * halves:\r
- *\r
- * a = a_1 D + a_0\r
- * b = b_1 D + b_0\r
- *\r
- * Then the full product is, as before,\r
- *\r
- * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0\r
- *\r
- * Provided we choose D on the large side (so that a_0 and b_0\r
- * are _at least_ as long as a_1 and b_1), we don't need the\r
- * topmost term at all, and we only need half of the middle\r
- * term. So there's no point in doing the proper Karatsuba\r
- * optimisation which computes the middle term using the top\r
- * one, because we'd take as long computing the top one as\r
- * just computing the middle one directly.\r
- *\r
- * So instead, we do a much more obvious thing: we call the\r
- * fully optimised internal_mul to compute a_0 b_0, and we\r
- * recursively call ourself to compute the _bottom halves_ of\r
- * a_1 b_0 and a_0 b_1, each of which we add into the result\r
- * in the obvious way.\r
- *\r
- * In other words, there's no actual Karatsuba _optimisation_\r
- * in this function; the only benefit in doing it this way is\r
- * that we call internal_mul proper for a large part of the\r
- * work, and _that_ can optimise its operation.\r
- */\r
-\r
- int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */\r
-\r
- /*\r
- * Scratch space for the various bits and pieces we're going\r
- * to be adding together: we need botlen*2 words for a_0 b_0\r
- * (though we may end up throwing away its topmost word), and\r
- * toplen words for each of a_1 b_0 and a_0 b_1. That adds up\r
- * to exactly 2*len.\r
- */\r
-\r
- /* a_0 b_0 */\r
- internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen,\r
- scratch + 2*len);\r
-\r
- /* a_1 b_0 */\r
- internal_mul_low(a, b + len - toplen, scratch + toplen, toplen,\r
- scratch + 2*len);\r
-\r
- /* a_0 b_1 */\r
- internal_mul_low(a + len - toplen, b, scratch, toplen,\r
- scratch + 2*len);\r
-\r
- /* Copy the bottom half of the big coefficient into place */\r
- for (i = 0; i < botlen; i++)\r
- c[toplen + i] = scratch[2*toplen + botlen + i];\r
-\r
- /* Add the two small coefficients, throwing away the returned carry */\r
- internal_add(scratch, scratch + toplen, scratch, toplen);\r
-\r
- /* And add that to the large coefficient, leaving the result in c. */\r
- internal_add(scratch, scratch + 2*toplen + botlen - toplen,\r
- c, toplen);\r
-\r
- } else {\r
- int i;\r
- BignumInt carry;\r
- BignumDblInt t;\r
- const BignumInt *ap, *bp;\r
- BignumInt *cp, *cps;\r
-\r
- /*\r
- * Multiply in the ordinary O(N^2) way.\r
- */\r
-\r
- for (i = 0; i < len; i++)\r
- c[i] = 0;\r
-\r
- for (cps = c + len, ap = a + len; ap-- > a; cps--) {\r
- carry = 0;\r
- for (cp = cps, bp = b + len; bp--, cp-- > c ;) {\r
- t = (MUL_WORD(*ap, *bp) + carry) + *cp;\r
- *cp = (BignumInt) t;\r
- carry = (BignumInt)(t >> BIGNUM_INT_BITS);\r
- }\r
- }\r
- }\r
-}\r
-\r
-/*\r
- * Montgomery reduction. Expects x to be a big-endian array of 2*len\r
- * BignumInts whose value satisfies 0 <= x < rn (where r = 2^(len *\r
- * BIGNUM_INT_BITS) is the Montgomery base). Returns in the same array\r
- * a value x' which is congruent to xr^{-1} mod n, and satisfies 0 <=\r
- * x' < n.\r
- *\r
- * 'n' and 'mninv' should be big-endian arrays of 'len' BignumInts\r
- * each, containing respectively n and the multiplicative inverse of\r
- * -n mod r.\r
- *\r
- * 'tmp' is an array of BignumInt used as scratch space, of length at\r
- * least 3*len + mul_compute_scratch(len).\r
- */\r
-static void monty_reduce(BignumInt *x, const BignumInt *n,\r
- const BignumInt *mninv, BignumInt *tmp, int len)\r
-{\r
- int i;\r
- BignumInt carry;\r
-\r
- /*\r
- * Multiply x by (-n)^{-1} mod r. This gives us a value m such\r
- * that mn is congruent to -x mod r. Hence, mn+x is an exact\r
- * multiple of r, and is also (obviously) congruent to x mod n.\r
- */\r
- internal_mul_low(x + len, mninv, tmp, len, tmp + 3*len);\r
-\r
- /*\r
- * Compute t = (mn+x)/r in ordinary, non-modular, integer\r
- * arithmetic. By construction this is exact, and is congruent mod\r
- * n to x * r^{-1}, i.e. the answer we want.\r
- *\r
- * The following multiply leaves that answer in the _most_\r
- * significant half of the 'x' array, so then we must shift it\r
- * down.\r
- */\r
- internal_mul(tmp, n, tmp+len, len, tmp + 3*len);\r
- carry = internal_add(x, tmp+len, x, 2*len);\r
- for (i = 0; i < len; i++)\r
- x[len + i] = x[i], x[i] = 0;\r
-\r
- /*\r
- * Reduce t mod n. This doesn't require a full-on division by n,\r
- * but merely a test and single optional subtraction, since we can\r
- * show that 0 <= t < 2n.\r
- *\r
- * Proof:\r
- * + we computed m mod r, so 0 <= m < r.\r
- * + so 0 <= mn < rn, obviously\r
- * + hence we only need 0 <= x < rn to guarantee that 0 <= mn+x < 2rn\r
- * + yielding 0 <= (mn+x)/r < 2n as required.\r
- */\r
- if (!carry) {\r
- for (i = 0; i < len; i++)\r
- if (x[len + i] != n[i])\r
- break;\r
- }\r
- if (carry || i >= len || x[len + i] > n[i])\r
- internal_sub(x+len, n, x+len, len);\r
-}\r
-\r
-static void internal_add_shifted(BignumInt *number,\r
- unsigned n, int shift)\r
-{\r
- int word = 1 + (shift / BIGNUM_INT_BITS);\r
- int bshift = shift % BIGNUM_INT_BITS;\r
- BignumDblInt addend;\r
-\r
- addend = (BignumDblInt)n << bshift;\r
-\r
- while (addend) {\r
- addend += number[word];\r
- number[word] = (BignumInt) addend & BIGNUM_INT_MASK;\r
- addend >>= BIGNUM_INT_BITS;\r
- word++;\r
- }\r
-}\r
-\r
-/*\r
- * Compute a = a % m.\r
- * Input in first alen words of a and first mlen words of m.\r
- * Output in first alen words of a\r
- * (of which first alen-mlen words will be zero).\r
- * The MSW of m MUST have its high bit set.\r
- * Quotient is accumulated in the `quotient' array, which is a Bignum\r
- * rather than the internal bigendian format. Quotient parts are shifted\r
- * left by `qshift' before adding into quot.\r
- */\r
-static void internal_mod(BignumInt *a, int alen,\r
- BignumInt *m, int mlen,\r
- BignumInt *quot, int qshift)\r
-{\r
- BignumInt m0, m1;\r
- unsigned int h;\r
- int i, k;\r
-\r
- m0 = m[0];\r
- if (mlen > 1)\r
- m1 = m[1];\r
- else\r
- m1 = 0;\r
-\r
- for (i = 0; i <= alen - mlen; i++) {\r
- BignumDblInt t;\r
- unsigned int q, r, c, ai1;\r
-\r
- if (i == 0) {\r
- h = 0;\r
- } else {\r
- h = a[i - 1];\r
- a[i - 1] = 0;\r
- }\r
-\r
- if (i == alen - 1)\r
- ai1 = 0;\r
- else\r
- ai1 = a[i + 1];\r
-\r
- /* Find q = h:a[i] / m0 */\r
- if (h >= m0) {\r
- /*\r
- * Special case.\r
- * \r
- * To illustrate it, suppose a BignumInt is 8 bits, and\r
- * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then\r
- * our initial division will be 0xA123 / 0xA1, which\r
- * will give a quotient of 0x100 and a divide overflow.\r
- * However, the invariants in this division algorithm\r
- * are not violated, since the full number A1:23:... is\r
- * _less_ than the quotient prefix A1:B2:... and so the\r
- * following correction loop would have sorted it out.\r
- * \r
- * In this situation we set q to be the largest\r
- * quotient we _can_ stomach (0xFF, of course).\r
- */\r
- q = BIGNUM_INT_MASK;\r
- } else {\r
- /* Macro doesn't want an array subscript expression passed\r
- * into it (see definition), so use a temporary. */\r
- BignumInt tmplo = a[i];\r
- DIVMOD_WORD(q, r, h, tmplo, m0);\r
-\r
- /* Refine our estimate of q by looking at\r
- h:a[i]:a[i+1] / m0:m1 */\r
- t = MUL_WORD(m1, q);\r
- if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {\r
- q--;\r
- t -= m1;\r
- r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */\r
- if (r >= (BignumDblInt) m0 &&\r
- t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;\r
- }\r
- }\r
-\r
- /* Subtract q * m from a[i...] */\r
- c = 0;\r
- for (k = mlen - 1; k >= 0; k--) {\r
- t = MUL_WORD(q, m[k]);\r
- t += c;\r
- c = (unsigned)(t >> BIGNUM_INT_BITS);\r
- if ((BignumInt) t > a[i + k])\r
- c++;\r
- a[i + k] -= (BignumInt) t;\r
- }\r
-\r
- /* Add back m in case of borrow */\r
- if (c != h) {\r
- t = 0;\r
- for (k = mlen - 1; k >= 0; k--) {\r
- t += m[k];\r
- t += a[i + k];\r
- a[i + k] = (BignumInt) t;\r
- t = t >> BIGNUM_INT_BITS;\r
- }\r
- q--;\r
- }\r
- if (quot)\r
- internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));\r
- }\r
-}\r
-\r
-/*\r
- * Compute (base ^ exp) % mod, the pedestrian way.\r
- */\r
-Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)\r
-{\r
- BignumInt *a, *b, *n, *m, *scratch;\r
- int mshift;\r
- int mlen, scratchlen, i, j;\r
- Bignum base, result;\r
-\r
- /*\r
- * The most significant word of mod needs to be non-zero. It\r
- * should already be, but let's make sure.\r
- */\r
- assert(mod[mod[0]] != 0);\r
-\r
- /*\r
- * Make sure the base is smaller than the modulus, by reducing\r
- * it modulo the modulus if not.\r
- */\r
- base = bigmod(base_in, mod);\r
-\r
- /* Allocate m of size mlen, copy mod to m */\r
- /* We use big endian internally */\r
- mlen = mod[0];\r
- m = snewn(mlen, BignumInt);\r
- for (j = 0; j < mlen; j++)\r
- m[j] = mod[mod[0] - j];\r
-\r
- /* Shift m left to make msb bit set */\r
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
- break;\r
- if (mshift) {\r
- for (i = 0; i < mlen - 1; i++)\r
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- m[mlen - 1] = m[mlen - 1] << mshift;\r
- }\r
-\r
- /* Allocate n of size mlen, copy base to n */\r
- n = snewn(mlen, BignumInt);\r
- i = mlen - base[0];\r
- for (j = 0; j < i; j++)\r
- n[j] = 0;\r
- for (j = 0; j < (int)base[0]; j++)\r
- n[i + j] = base[base[0] - j];\r
-\r
- /* Allocate a and b of size 2*mlen. Set a = 1 */\r
- a = snewn(2 * mlen, BignumInt);\r
- b = snewn(2 * mlen, BignumInt);\r
- for (i = 0; i < 2 * mlen; i++)\r
- a[i] = 0;\r
- a[2 * mlen - 1] = 1;\r
-\r
- /* Scratch space for multiplies */\r
- scratchlen = mul_compute_scratch(mlen);\r
- scratch = snewn(scratchlen, BignumInt);\r
-\r
- /* Skip leading zero bits of exp. */\r
- i = 0;\r
- j = BIGNUM_INT_BITS-1;\r
- while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {\r
- j--;\r
- if (j < 0) {\r
- i++;\r
- j = BIGNUM_INT_BITS-1;\r
- }\r
- }\r
-\r
- /* Main computation */\r
- while (i < (int)exp[0]) {\r
- while (j >= 0) {\r
- internal_mul(a + mlen, a + mlen, b, mlen, scratch);\r
- internal_mod(b, mlen * 2, m, mlen, NULL, 0);\r
- if ((exp[exp[0] - i] & (1 << j)) != 0) {\r
- internal_mul(b + mlen, n, a, mlen, scratch);\r
- internal_mod(a, mlen * 2, m, mlen, NULL, 0);\r
- } else {\r
- BignumInt *t;\r
- t = a;\r
- a = b;\r
- b = t;\r
- }\r
- j--;\r
- }\r
- i++;\r
- j = BIGNUM_INT_BITS-1;\r
- }\r
-\r
- /* Fixup result in case the modulus was shifted */\r
- if (mshift) {\r
- for (i = mlen - 1; i < 2 * mlen - 1; i++)\r
- a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;\r
- internal_mod(a, mlen * 2, m, mlen, NULL, 0);\r
- for (i = 2 * mlen - 1; i >= mlen; i--)\r
- a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));\r
- }\r
-\r
- /* Copy result to buffer */\r
- result = newbn(mod[0]);\r
- for (i = 0; i < mlen; i++)\r
- result[result[0] - i] = a[i + mlen];\r
- while (result[0] > 1 && result[result[0]] == 0)\r
- result[0]--;\r
-\r
- /* Free temporary arrays */\r
- for (i = 0; i < 2 * mlen; i++)\r
- a[i] = 0;\r
- sfree(a);\r
- for (i = 0; i < scratchlen; i++)\r
- scratch[i] = 0;\r
- sfree(scratch);\r
- for (i = 0; i < 2 * mlen; i++)\r
- b[i] = 0;\r
- sfree(b);\r
- for (i = 0; i < mlen; i++)\r
- m[i] = 0;\r
- sfree(m);\r
- for (i = 0; i < mlen; i++)\r
- n[i] = 0;\r
- sfree(n);\r
-\r
- freebn(base);\r
-\r
- return result;\r
-}\r
-\r
-/*\r
- * Compute (base ^ exp) % mod. Uses the Montgomery multiplication\r
- * technique where possible, falling back to modpow_simple otherwise.\r
- */\r
-Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)\r
-{\r
- BignumInt *a, *b, *x, *n, *mninv, *scratch;\r
- int len, scratchlen, i, j;\r
- Bignum base, base2, r, rn, inv, result;\r
-\r
- /*\r
- * The most significant word of mod needs to be non-zero. It\r
- * should already be, but let's make sure.\r
- */\r
- assert(mod[mod[0]] != 0);\r
-\r
- /*\r
- * mod had better be odd, or we can't do Montgomery multiplication\r
- * using a power of two at all.\r
- */\r
- if (!(mod[1] & 1))\r
- return modpow_simple(base_in, exp, mod);\r
-\r
- /*\r
- * Make sure the base is smaller than the modulus, by reducing\r
- * it modulo the modulus if not.\r
- */\r
- base = bigmod(base_in, mod);\r
-\r
- /*\r
- * Compute the inverse of n mod r, for monty_reduce. (In fact we\r
- * want the inverse of _minus_ n mod r, but we'll sort that out\r
- * below.)\r
- */\r
- len = mod[0];\r
- r = bn_power_2(BIGNUM_INT_BITS * len);\r
- inv = modinv(mod, r);\r
-\r
- /*\r
- * Multiply the base by r mod n, to get it into Montgomery\r
- * representation.\r
- */\r
- base2 = modmul(base, r, mod);\r
- freebn(base);\r
- base = base2;\r
-\r
- rn = bigmod(r, mod); /* r mod n, i.e. Montgomerified 1 */\r
-\r
- freebn(r); /* won't need this any more */\r
-\r
- /*\r
- * Set up internal arrays of the right lengths, in big-endian\r
- * format, containing the base, the modulus, and the modulus's\r
- * inverse.\r
- */\r
- n = snewn(len, BignumInt);\r
- for (j = 0; j < len; j++)\r
- n[len - 1 - j] = mod[j + 1];\r
-\r
- mninv = snewn(len, BignumInt);\r
- for (j = 0; j < len; j++)\r
- mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0);\r
- freebn(inv); /* we don't need this copy of it any more */\r
- /* Now negate mninv mod r, so it's the inverse of -n rather than +n. */\r
- x = snewn(len, BignumInt);\r
- for (j = 0; j < len; j++)\r
- x[j] = 0;\r
- internal_sub(x, mninv, mninv, len);\r
-\r
- /* x = snewn(len, BignumInt); */ /* already done above */\r
- for (j = 0; j < len; j++)\r
- x[len - 1 - j] = (j < (int)base[0] ? base[j + 1] : 0);\r
- freebn(base); /* we don't need this copy of it any more */\r
-\r
- a = snewn(2*len, BignumInt);\r
- b = snewn(2*len, BignumInt);\r
- for (j = 0; j < len; j++)\r
- a[2*len - 1 - j] = (j < (int)rn[0] ? rn[j + 1] : 0);\r
- freebn(rn);\r
-\r
- /* Scratch space for multiplies */\r
- scratchlen = 3*len + mul_compute_scratch(len);\r
- scratch = snewn(scratchlen, BignumInt);\r
-\r
- /* Skip leading zero bits of exp. */\r
- i = 0;\r
- j = BIGNUM_INT_BITS-1;\r
- while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {\r
- j--;\r
- if (j < 0) {\r
- i++;\r
- j = BIGNUM_INT_BITS-1;\r
- }\r
- }\r
-\r
- /* Main computation */\r
- while (i < (int)exp[0]) {\r
- while (j >= 0) {\r
- internal_mul(a + len, a + len, b, len, scratch);\r
- monty_reduce(b, n, mninv, scratch, len);\r
- if ((exp[exp[0] - i] & (1 << j)) != 0) {\r
- internal_mul(b + len, x, a, len, scratch);\r
- monty_reduce(a, n, mninv, scratch, len);\r
- } else {\r
- BignumInt *t;\r
- t = a;\r
- a = b;\r
- b = t;\r
- }\r
- j--;\r
- }\r
- i++;\r
- j = BIGNUM_INT_BITS-1;\r
- }\r
-\r
- /*\r
- * Final monty_reduce to get back from the adjusted Montgomery\r
- * representation.\r
- */\r
- monty_reduce(a, n, mninv, scratch, len);\r
-\r
- /* Copy result to buffer */\r
- result = newbn(mod[0]);\r
- for (i = 0; i < len; i++)\r
- result[result[0] - i] = a[i + len];\r
- while (result[0] > 1 && result[result[0]] == 0)\r
- result[0]--;\r
-\r
- /* Free temporary arrays */\r
- for (i = 0; i < scratchlen; i++)\r
- scratch[i] = 0;\r
- sfree(scratch);\r
- for (i = 0; i < 2 * len; i++)\r
- a[i] = 0;\r
- sfree(a);\r
- for (i = 0; i < 2 * len; i++)\r
- b[i] = 0;\r
- sfree(b);\r
- for (i = 0; i < len; i++)\r
- mninv[i] = 0;\r
- sfree(mninv);\r
- for (i = 0; i < len; i++)\r
- n[i] = 0;\r
- sfree(n);\r
- for (i = 0; i < len; i++)\r
- x[i] = 0;\r
- sfree(x);\r
-\r
- return result;\r
-}\r
-\r
-/*\r
- * Compute (p * q) % mod.\r
- * The most significant word of mod MUST be non-zero.\r
- * We assume that the result array is the same size as the mod array.\r
- */\r
-Bignum modmul(Bignum p, Bignum q, Bignum mod)\r
-{\r
- BignumInt *a, *n, *m, *o, *scratch;\r
- int mshift, scratchlen;\r
- int pqlen, mlen, rlen, i, j;\r
- Bignum result;\r
-\r
- /* Allocate m of size mlen, copy mod to m */\r
- /* We use big endian internally */\r
- mlen = mod[0];\r
- m = snewn(mlen, BignumInt);\r
- for (j = 0; j < mlen; j++)\r
- m[j] = mod[mod[0] - j];\r
-\r
- /* Shift m left to make msb bit set */\r
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
- break;\r
- if (mshift) {\r
- for (i = 0; i < mlen - 1; i++)\r
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- m[mlen - 1] = m[mlen - 1] << mshift;\r
- }\r
-\r
- pqlen = (p[0] > q[0] ? p[0] : q[0]);\r
-\r
- /* Allocate n of size pqlen, copy p to n */\r
- n = snewn(pqlen, BignumInt);\r
- i = pqlen - p[0];\r
- for (j = 0; j < i; j++)\r
- n[j] = 0;\r
- for (j = 0; j < (int)p[0]; j++)\r
- n[i + j] = p[p[0] - j];\r
-\r
- /* Allocate o of size pqlen, copy q to o */\r
- o = snewn(pqlen, BignumInt);\r
- i = pqlen - q[0];\r
- for (j = 0; j < i; j++)\r
- o[j] = 0;\r
- for (j = 0; j < (int)q[0]; j++)\r
- o[i + j] = q[q[0] - j];\r
-\r
- /* Allocate a of size 2*pqlen for result */\r
- a = snewn(2 * pqlen, BignumInt);\r
-\r
- /* Scratch space for multiplies */\r
- scratchlen = mul_compute_scratch(pqlen);\r
- scratch = snewn(scratchlen, BignumInt);\r
-\r
- /* Main computation */\r
- internal_mul(n, o, a, pqlen, scratch);\r
- internal_mod(a, pqlen * 2, m, mlen, NULL, 0);\r
-\r
- /* Fixup result in case the modulus was shifted */\r
- if (mshift) {\r
- for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)\r
- a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;\r
- internal_mod(a, pqlen * 2, m, mlen, NULL, 0);\r
- for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)\r
- a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));\r
- }\r
-\r
- /* Copy result to buffer */\r
- rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);\r
- result = newbn(rlen);\r
- for (i = 0; i < rlen; i++)\r
- result[result[0] - i] = a[i + 2 * pqlen - rlen];\r
- while (result[0] > 1 && result[result[0]] == 0)\r
- result[0]--;\r
-\r
- /* Free temporary arrays */\r
- for (i = 0; i < scratchlen; i++)\r
- scratch[i] = 0;\r
- sfree(scratch);\r
- for (i = 0; i < 2 * pqlen; i++)\r
- a[i] = 0;\r
- sfree(a);\r
- for (i = 0; i < mlen; i++)\r
- m[i] = 0;\r
- sfree(m);\r
- for (i = 0; i < pqlen; i++)\r
- n[i] = 0;\r
- sfree(n);\r
- for (i = 0; i < pqlen; i++)\r
- o[i] = 0;\r
- sfree(o);\r
-\r
- return result;\r
-}\r
-\r
-/*\r
- * Compute p % mod.\r
- * The most significant word of mod MUST be non-zero.\r
- * We assume that the result array is the same size as the mod array.\r
- * We optionally write out a quotient if `quotient' is non-NULL.\r
- * We can avoid writing out the result if `result' is NULL.\r
- */\r
-static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)\r
-{\r
- BignumInt *n, *m;\r
- int mshift;\r
- int plen, mlen, i, j;\r
-\r
- /* Allocate m of size mlen, copy mod to m */\r
- /* We use big endian internally */\r
- mlen = mod[0];\r
- m = snewn(mlen, BignumInt);\r
- for (j = 0; j < mlen; j++)\r
- m[j] = mod[mod[0] - j];\r
-\r
- /* Shift m left to make msb bit set */\r
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)\r
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)\r
- break;\r
- if (mshift) {\r
- for (i = 0; i < mlen - 1; i++)\r
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- m[mlen - 1] = m[mlen - 1] << mshift;\r
- }\r
-\r
- plen = p[0];\r
- /* Ensure plen > mlen */\r
- if (plen <= mlen)\r
- plen = mlen + 1;\r
-\r
- /* Allocate n of size plen, copy p to n */\r
- n = snewn(plen, BignumInt);\r
- for (j = 0; j < plen; j++)\r
- n[j] = 0;\r
- for (j = 1; j <= (int)p[0]; j++)\r
- n[plen - j] = p[j];\r
-\r
- /* Main computation */\r
- internal_mod(n, plen, m, mlen, quotient, mshift);\r
-\r
- /* Fixup result in case the modulus was shifted */\r
- if (mshift) {\r
- for (i = plen - mlen - 1; i < plen - 1; i++)\r
- n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));\r
- n[plen - 1] = n[plen - 1] << mshift;\r
- internal_mod(n, plen, m, mlen, quotient, 0);\r
- for (i = plen - 1; i >= plen - mlen; i--)\r
- n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));\r
- }\r
-\r
- /* Copy result to buffer */\r
- if (result) {\r
- for (i = 1; i <= (int)result[0]; i++) {\r
- int j = plen - i;\r
- result[i] = j >= 0 ? n[j] : 0;\r
- }\r
- }\r
-\r
- /* Free temporary arrays */\r
- for (i = 0; i < mlen; i++)\r
- m[i] = 0;\r
- sfree(m);\r
- for (i = 0; i < plen; i++)\r
- n[i] = 0;\r
- sfree(n);\r
-}\r
-\r
-/*\r
- * Decrement a number.\r
- */\r
-void decbn(Bignum bn)\r
-{\r
- int i = 1;\r
- while (i < (int)bn[0] && bn[i] == 0)\r
- bn[i++] = BIGNUM_INT_MASK;\r
- bn[i]--;\r
-}\r
-\r
-Bignum bignum_from_bytes(const unsigned char *data, int nbytes)\r
-{\r
- Bignum result;\r
- int w, i;\r
-\r
- w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */\r
-\r
- result = newbn(w);\r
- for (i = 1; i <= w; i++)\r
- result[i] = 0;\r
- for (i = nbytes; i--;) {\r
- unsigned char byte = *data++;\r
- result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);\r
- }\r
-\r
- while (result[0] > 1 && result[result[0]] == 0)\r
- result[0]--;\r
- return result;\r
-}\r
-\r
-/*\r
- * Read an SSH-1-format bignum from a data buffer. Return the number\r
- * of bytes consumed, or -1 if there wasn't enough data.\r
- */\r
-int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)\r
-{\r
- const unsigned char *p = data;\r
- int i;\r
- int w, b;\r
-\r
- if (len < 2)\r
- return -1;\r
-\r
- w = 0;\r
- for (i = 0; i < 2; i++)\r
- w = (w << 8) + *p++;\r
- b = (w + 7) / 8; /* bits -> bytes */\r
-\r
- if (len < b+2)\r
- return -1;\r
-\r
- if (!result) /* just return length */\r
- return b + 2;\r
-\r
- *result = bignum_from_bytes(p, b);\r
-\r
- return p + b - data;\r
-}\r
-\r
-/*\r
- * Return the bit count of a bignum, for SSH-1 encoding.\r
- */\r
-int bignum_bitcount(Bignum bn)\r
-{\r
- int bitcount = bn[0] * BIGNUM_INT_BITS - 1;\r
- while (bitcount >= 0\r
- && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;\r
- return bitcount + 1;\r
-}\r
-\r
-/*\r
- * Return the byte length of a bignum when SSH-1 encoded.\r
- */\r
-int ssh1_bignum_length(Bignum bn)\r
-{\r
- return 2 + (bignum_bitcount(bn) + 7) / 8;\r
-}\r
-\r
-/*\r
- * Return the byte length of a bignum when SSH-2 encoded.\r
- */\r
-int ssh2_bignum_length(Bignum bn)\r
-{\r
- return 4 + (bignum_bitcount(bn) + 8) / 8;\r
-}\r
-\r
-/*\r
- * Return a byte from a bignum; 0 is least significant, etc.\r
- */\r
-int bignum_byte(Bignum bn, int i)\r
-{\r
- if (i >= (int)(BIGNUM_INT_BYTES * bn[0]))\r
- return 0; /* beyond the end */\r
- else\r
- return (bn[i / BIGNUM_INT_BYTES + 1] >>\r
- ((i % BIGNUM_INT_BYTES)*8)) & 0xFF;\r
-}\r
-\r
-/*\r
- * Return a bit from a bignum; 0 is least significant, etc.\r
- */\r
-int bignum_bit(Bignum bn, int i)\r
-{\r
- if (i >= (int)(BIGNUM_INT_BITS * bn[0]))\r
- return 0; /* beyond the end */\r
- else\r
- return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;\r
-}\r
-\r
-/*\r
- * Set a bit in a bignum; 0 is least significant, etc.\r
- */\r
-void bignum_set_bit(Bignum bn, int bitnum, int value)\r
-{\r
- if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))\r
- abort(); /* beyond the end */\r
- else {\r
- int v = bitnum / BIGNUM_INT_BITS + 1;\r
- int mask = 1 << (bitnum % BIGNUM_INT_BITS);\r
- if (value)\r
- bn[v] |= mask;\r
- else\r
- bn[v] &= ~mask;\r
- }\r
-}\r
-\r
-/*\r
- * Write a SSH-1-format bignum into a buffer. It is assumed the\r
- * buffer is big enough. Returns the number of bytes used.\r
- */\r
-int ssh1_write_bignum(void *data, Bignum bn)\r
-{\r
- unsigned char *p = data;\r
- int len = ssh1_bignum_length(bn);\r
- int i;\r
- int bitc = bignum_bitcount(bn);\r
-\r
- *p++ = (bitc >> 8) & 0xFF;\r
- *p++ = (bitc) & 0xFF;\r
- for (i = len - 2; i--;)\r
- *p++ = bignum_byte(bn, i);\r
- return len;\r
-}\r
-\r
-/*\r
- * Compare two bignums. Returns like strcmp.\r
- */\r
-int bignum_cmp(Bignum a, Bignum b)\r
-{\r
- int amax = a[0], bmax = b[0];\r
- int i = (amax > bmax ? amax : bmax);\r
- while (i) {\r
- BignumInt aval = (i > amax ? 0 : a[i]);\r
- BignumInt bval = (i > bmax ? 0 : b[i]);\r
- if (aval < bval)\r
- return -1;\r
- if (aval > bval)\r
- return +1;\r
- i--;\r
- }\r
- return 0;\r
-}\r
-\r
-/*\r
- * Right-shift one bignum to form another.\r
- */\r
-Bignum bignum_rshift(Bignum a, int shift)\r
-{\r
- Bignum ret;\r
- int i, shiftw, shiftb, shiftbb, bits;\r
- BignumInt ai, ai1;\r
-\r
- bits = bignum_bitcount(a) - shift;\r
- ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);\r
-\r
- if (ret) {\r
- shiftw = shift / BIGNUM_INT_BITS;\r
- shiftb = shift % BIGNUM_INT_BITS;\r
- shiftbb = BIGNUM_INT_BITS - shiftb;\r
-\r
- ai1 = a[shiftw + 1];\r
- for (i = 1; i <= (int)ret[0]; i++) {\r
- ai = ai1;\r
- ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0);\r
- ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK;\r
- }\r
- }\r
-\r
- return ret;\r
-}\r
-\r
-/*\r
- * Non-modular multiplication and addition.\r
- */\r
-Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)\r
-{\r
- int alen = a[0], blen = b[0];\r
- int mlen = (alen > blen ? alen : blen);\r
- int rlen, i, maxspot;\r
- int wslen;\r
- BignumInt *workspace;\r
- Bignum ret;\r
-\r
- /* mlen space for a, mlen space for b, 2*mlen for result,\r
- * plus scratch space for multiplication */\r
- wslen = mlen * 4 + mul_compute_scratch(mlen);\r
- workspace = snewn(wslen, BignumInt);\r
- for (i = 0; i < mlen; i++) {\r
- workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);\r
- workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);\r
- }\r
-\r
- internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,\r
- workspace + 2 * mlen, mlen, workspace + 4 * mlen);\r
-\r
- /* now just copy the result back */\r
- rlen = alen + blen + 1;\r
- if (addend && rlen <= (int)addend[0])\r
- rlen = addend[0] + 1;\r
- ret = newbn(rlen);\r
- maxspot = 0;\r
- for (i = 1; i <= (int)ret[0]; i++) {\r
- ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);\r
- if (ret[i] != 0)\r
- maxspot = i;\r
- }\r
- ret[0] = maxspot;\r
-\r
- /* now add in the addend, if any */\r
- if (addend) {\r
- BignumDblInt carry = 0;\r
- for (i = 1; i <= rlen; i++) {\r
- carry += (i <= (int)ret[0] ? ret[i] : 0);\r
- carry += (i <= (int)addend[0] ? addend[i] : 0);\r
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
- carry >>= BIGNUM_INT_BITS;\r
- if (ret[i] != 0 && i > maxspot)\r
- maxspot = i;\r
- }\r
- }\r
- ret[0] = maxspot;\r
-\r
- for (i = 0; i < wslen; i++)\r
- workspace[i] = 0;\r
- sfree(workspace);\r
- return ret;\r
-}\r
-\r
-/*\r
- * Non-modular multiplication.\r
- */\r
-Bignum bigmul(Bignum a, Bignum b)\r
-{\r
- return bigmuladd(a, b, NULL);\r
-}\r
-\r
-/*\r
- * Simple addition.\r
- */\r
-Bignum bigadd(Bignum a, Bignum b)\r
-{\r
- int alen = a[0], blen = b[0];\r
- int rlen = (alen > blen ? alen : blen) + 1;\r
- int i, maxspot;\r
- Bignum ret;\r
- BignumDblInt carry;\r
-\r
- ret = newbn(rlen);\r
-\r
- carry = 0;\r
- maxspot = 0;\r
- for (i = 1; i <= rlen; i++) {\r
- carry += (i <= (int)a[0] ? a[i] : 0);\r
- carry += (i <= (int)b[0] ? b[i] : 0);\r
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
- carry >>= BIGNUM_INT_BITS;\r
- if (ret[i] != 0 && i > maxspot)\r
- maxspot = i;\r
- }\r
- ret[0] = maxspot;\r
-\r
- return ret;\r
-}\r
-\r
-/*\r
- * Subtraction. Returns a-b, or NULL if the result would come out\r
- * negative (recall that this entire bignum module only handles\r
- * positive numbers).\r
- */\r
-Bignum bigsub(Bignum a, Bignum b)\r
-{\r
- int alen = a[0], blen = b[0];\r
- int rlen = (alen > blen ? alen : blen);\r
- int i, maxspot;\r
- Bignum ret;\r
- BignumDblInt carry;\r
-\r
- ret = newbn(rlen);\r
-\r
- carry = 1;\r
- maxspot = 0;\r
- for (i = 1; i <= rlen; i++) {\r
- carry += (i <= (int)a[0] ? a[i] : 0);\r
- carry += (i <= (int)b[0] ? b[i] ^ BIGNUM_INT_MASK : BIGNUM_INT_MASK);\r
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
- carry >>= BIGNUM_INT_BITS;\r
- if (ret[i] != 0 && i > maxspot)\r
- maxspot = i;\r
- }\r
- ret[0] = maxspot;\r
-\r
- if (!carry) {\r
- freebn(ret);\r
- return NULL;\r
- }\r
-\r
- return ret;\r
-}\r
-\r
-/*\r
- * Create a bignum which is the bitmask covering another one. That\r
- * is, the smallest integer which is >= N and is also one less than\r
- * a power of two.\r
- */\r
-Bignum bignum_bitmask(Bignum n)\r
-{\r
- Bignum ret = copybn(n);\r
- int i;\r
- BignumInt j;\r
-\r
- i = ret[0];\r
- while (n[i] == 0 && i > 0)\r
- i--;\r
- if (i <= 0)\r
- return ret; /* input was zero */\r
- j = 1;\r
- while (j < n[i])\r
- j = 2 * j + 1;\r
- ret[i] = j;\r
- while (--i > 0)\r
- ret[i] = BIGNUM_INT_MASK;\r
- return ret;\r
-}\r
-\r
-/*\r
- * Convert a (max 32-bit) long into a bignum.\r
- */\r
-Bignum bignum_from_long(unsigned long nn)\r
-{\r
- Bignum ret;\r
- BignumDblInt n = nn;\r
-\r
- ret = newbn(3);\r
- ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);\r
- ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);\r
- ret[3] = 0;\r
- ret[0] = (ret[2] ? 2 : 1);\r
- return ret;\r
-}\r
-\r
-/*\r
- * Add a long to a bignum.\r
- */\r
-Bignum bignum_add_long(Bignum number, unsigned long addendx)\r
-{\r
- Bignum ret = newbn(number[0] + 1);\r
- int i, maxspot = 0;\r
- BignumDblInt carry = 0, addend = addendx;\r
-\r
- for (i = 1; i <= (int)ret[0]; i++) {\r
- carry += addend & BIGNUM_INT_MASK;\r
- carry += (i <= (int)number[0] ? number[i] : 0);\r
- addend >>= BIGNUM_INT_BITS;\r
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;\r
- carry >>= BIGNUM_INT_BITS;\r
- if (ret[i] != 0)\r
- maxspot = i;\r
- }\r
- ret[0] = maxspot;\r
- return ret;\r
-}\r
-\r
-/*\r
- * Compute the residue of a bignum, modulo a (max 16-bit) short.\r
- */\r
-unsigned short bignum_mod_short(Bignum number, unsigned short modulus)\r
-{\r
- BignumDblInt mod, r;\r
- int i;\r
-\r
- r = 0;\r
- mod = modulus;\r
- for (i = number[0]; i > 0; i--)\r
- r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;\r
- return (unsigned short) r;\r
-}\r
-\r
-#ifdef DEBUG\r
-void diagbn(char *prefix, Bignum md)\r
-{\r
- int i, nibbles, morenibbles;\r
- static const char hex[] = "0123456789ABCDEF";\r
-\r
- debug(("%s0x", prefix ? prefix : ""));\r
-\r
- nibbles = (3 + bignum_bitcount(md)) / 4;\r
- if (nibbles < 1)\r
- nibbles = 1;\r
- morenibbles = 4 * md[0] - nibbles;\r
- for (i = 0; i < morenibbles; i++)\r
- debug(("-"));\r
- for (i = nibbles; i--;)\r
- debug(("%c",\r
- hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));\r
-\r
- if (prefix)\r
- debug(("\n"));\r
-}\r
-#endif\r
-\r
-/*\r
- * Simple division.\r
- */\r
-Bignum bigdiv(Bignum a, Bignum b)\r
-{\r
- Bignum q = newbn(a[0]);\r
- bigdivmod(a, b, NULL, q);\r
- return q;\r
-}\r
-\r
-/*\r
- * Simple remainder.\r
- */\r
-Bignum bigmod(Bignum a, Bignum b)\r
-{\r
- Bignum r = newbn(b[0]);\r
- bigdivmod(a, b, r, NULL);\r
- return r;\r
-}\r
-\r
-/*\r
- * Greatest common divisor.\r
- */\r
-Bignum biggcd(Bignum av, Bignum bv)\r
-{\r
- Bignum a = copybn(av);\r
- Bignum b = copybn(bv);\r
-\r
- while (bignum_cmp(b, Zero) != 0) {\r
- Bignum t = newbn(b[0]);\r
- bigdivmod(a, b, t, NULL);\r
- while (t[0] > 1 && t[t[0]] == 0)\r
- t[0]--;\r
- freebn(a);\r
- a = b;\r
- b = t;\r
- }\r
-\r
- freebn(b);\r
- return a;\r
-}\r
-\r
-/*\r
- * Modular inverse, using Euclid's extended algorithm.\r
- */\r
-Bignum modinv(Bignum number, Bignum modulus)\r
-{\r
- Bignum a = copybn(modulus);\r
- Bignum b = copybn(number);\r
- Bignum xp = copybn(Zero);\r
- Bignum x = copybn(One);\r
- int sign = +1;\r
-\r
- while (bignum_cmp(b, One) != 0) {\r
- Bignum t = newbn(b[0]);\r
- Bignum q = newbn(a[0]);\r
- bigdivmod(a, b, t, q);\r
- while (t[0] > 1 && t[t[0]] == 0)\r
- t[0]--;\r
- freebn(a);\r
- a = b;\r
- b = t;\r
- t = xp;\r
- xp = x;\r
- x = bigmuladd(q, xp, t);\r
- sign = -sign;\r
- freebn(t);\r
- freebn(q);\r
- }\r
-\r
- freebn(b);\r
- freebn(a);\r
- freebn(xp);\r
-\r
- /* now we know that sign * x == 1, and that x < modulus */\r
- if (sign < 0) {\r
- /* set a new x to be modulus - x */\r
- Bignum newx = newbn(modulus[0]);\r
- BignumInt carry = 0;\r
- int maxspot = 1;\r
- int i;\r
-\r
- for (i = 1; i <= (int)newx[0]; i++) {\r
- BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);\r
- BignumInt bword = (i <= (int)x[0] ? x[i] : 0);\r
- newx[i] = aword - bword - carry;\r
- bword = ~bword;\r
- carry = carry ? (newx[i] >= bword) : (newx[i] > bword);\r
- if (newx[i] != 0)\r
- maxspot = i;\r
- }\r
- newx[0] = maxspot;\r
- freebn(x);\r
- x = newx;\r
- }\r
-\r
- /* and return. */\r
- return x;\r
-}\r
-\r
-/*\r
- * Render a bignum into decimal. Return a malloced string holding\r
- * the decimal representation.\r
- */\r
-char *bignum_decimal(Bignum x)\r
-{\r
- int ndigits, ndigit;\r
- int i, iszero;\r
- BignumDblInt carry;\r
- char *ret;\r
- BignumInt *workspace;\r
-\r
- /*\r
- * First, estimate the number of digits. Since log(10)/log(2)\r
- * is just greater than 93/28 (the joys of continued fraction\r
- * approximations...) we know that for every 93 bits, we need\r
- * at most 28 digits. This will tell us how much to malloc.\r
- *\r
- * Formally: if x has i bits, that means x is strictly less\r
- * than 2^i. Since 2 is less than 10^(28/93), this is less than\r
- * 10^(28i/93). We need an integer power of ten, so we must\r
- * round up (rounding down might make it less than x again).\r
- * Therefore if we multiply the bit count by 28/93, rounding\r
- * up, we will have enough digits.\r
- *\r
- * i=0 (i.e., x=0) is an irritating special case.\r
- */\r
- i = bignum_bitcount(x);\r
- if (!i)\r
- ndigits = 1; /* x = 0 */\r
- else\r
- ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */\r
- ndigits++; /* allow for trailing \0 */\r
- ret = snewn(ndigits, char);\r
-\r
- /*\r
- * Now allocate some workspace to hold the binary form as we\r
- * repeatedly divide it by ten. Initialise this to the\r
- * big-endian form of the number.\r
- */\r
- workspace = snewn(x[0], BignumInt);\r
- for (i = 0; i < (int)x[0]; i++)\r
- workspace[i] = x[x[0] - i];\r
-\r
- /*\r
- * Next, write the decimal number starting with the last digit.\r
- * We use ordinary short division, dividing 10 into the\r
- * workspace.\r
- */\r
- ndigit = ndigits - 1;\r
- ret[ndigit] = '\0';\r
- do {\r
- iszero = 1;\r
- carry = 0;\r
- for (i = 0; i < (int)x[0]; i++) {\r
- carry = (carry << BIGNUM_INT_BITS) + workspace[i];\r
- workspace[i] = (BignumInt) (carry / 10);\r
- if (workspace[i])\r
- iszero = 0;\r
- carry %= 10;\r
- }\r
- ret[--ndigit] = (char) (carry + '0');\r
- } while (!iszero);\r
-\r
- /*\r
- * There's a chance we've fallen short of the start of the\r
- * string. Correct if so.\r
- */\r
- if (ndigit > 0)\r
- memmove(ret, ret + ndigit, ndigits - ndigit);\r
-\r
- /*\r
- * Done.\r
- */\r
- sfree(workspace);\r
- return ret;\r
-}\r
-\r
-#ifdef TESTBN\r
-\r
-#include <stdio.h>\r
-#include <stdlib.h>\r
-#include <ctype.h>\r
-\r
-/*\r
- * gcc -g -O0 -DTESTBN -o testbn sshbn.c misc.c -I unix -I charset\r
- *\r
- * Then feed to this program's standard input the output of\r
- * testdata/bignum.py .\r
- */\r
-\r
-void modalfatalbox(char *p, ...)\r
-{\r
- va_list ap;\r
- fprintf(stderr, "FATAL ERROR: ");\r
- va_start(ap, p);\r
- vfprintf(stderr, p, ap);\r
- va_end(ap);\r
- fputc('\n', stderr);\r
- exit(1);\r
-}\r
-\r
-#define fromxdigit(c) ( (c)>'9' ? ((c)&0xDF) - 'A' + 10 : (c) - '0' )\r
-\r
-int main(int argc, char **argv)\r
-{\r
- char *buf;\r
- int line = 0;\r
- int passes = 0, fails = 0;\r
-\r
- while ((buf = fgetline(stdin)) != NULL) {\r
- int maxlen = strlen(buf);\r
- unsigned char *data = snewn(maxlen, unsigned char);\r
- unsigned char *ptrs[5], *q;\r
- int ptrnum;\r
- char *bufp = buf;\r
-\r
- line++;\r
-\r
- q = data;\r
- ptrnum = 0;\r
-\r
- while (*bufp && !isspace((unsigned char)*bufp))\r
- bufp++;\r
- if (bufp)\r
- *bufp++ = '\0';\r
-\r
- while (*bufp) {\r
- char *start, *end;\r
- int i;\r
-\r
- while (*bufp && !isxdigit((unsigned char)*bufp))\r
- bufp++;\r
- start = bufp;\r
-\r
- if (!*bufp)\r
- break;\r
-\r
- while (*bufp && isxdigit((unsigned char)*bufp))\r
- bufp++;\r
- end = bufp;\r
-\r
- if (ptrnum >= lenof(ptrs))\r
- break;\r
- ptrs[ptrnum++] = q;\r
- \r
- for (i = -((end - start) & 1); i < end-start; i += 2) {\r
- unsigned char val = (i < 0 ? 0 : fromxdigit(start[i]));\r
- val = val * 16 + fromxdigit(start[i+1]);\r
- *q++ = val;\r
- }\r
-\r
- ptrs[ptrnum] = q;\r
- }\r
-\r
- if (!strcmp(buf, "mul")) {\r
- Bignum a, b, c, p;\r
-\r
- if (ptrnum != 3) {\r
- printf("%d: mul with %d parameters, expected 3\n", line);\r
- exit(1);\r
- }\r
- a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);\r
- b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);\r
- c = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);\r
- p = bigmul(a, b);\r
-\r
- if (bignum_cmp(c, p) == 0) {\r
- passes++;\r
- } else {\r
- char *as = bignum_decimal(a);\r
- char *bs = bignum_decimal(b);\r
- char *cs = bignum_decimal(c);\r
- char *ps = bignum_decimal(p);\r
- \r
- printf("%d: fail: %s * %s gave %s expected %s\n",\r
- line, as, bs, ps, cs);\r
- fails++;\r
-\r
- sfree(as);\r
- sfree(bs);\r
- sfree(cs);\r
- sfree(ps);\r
- }\r
- freebn(a);\r
- freebn(b);\r
- freebn(c);\r
- freebn(p);\r
- } else if (!strcmp(buf, "pow")) {\r
- Bignum base, expt, modulus, expected, answer;\r
-\r
- if (ptrnum != 4) {\r
- printf("%d: mul with %d parameters, expected 3\n", line);\r
- exit(1);\r
- }\r
-\r
- base = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);\r
- expt = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);\r
- modulus = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);\r
- expected = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);\r
- answer = modpow(base, expt, modulus);\r
-\r
- if (bignum_cmp(expected, answer) == 0) {\r
- passes++;\r
- } else {\r
- char *as = bignum_decimal(base);\r
- char *bs = bignum_decimal(expt);\r
- char *cs = bignum_decimal(modulus);\r
- char *ds = bignum_decimal(answer);\r
- char *ps = bignum_decimal(expected);\r
- \r
- printf("%d: fail: %s ^ %s mod %s gave %s expected %s\n",\r
- line, as, bs, cs, ds, ps);\r
- fails++;\r
-\r
- sfree(as);\r
- sfree(bs);\r
- sfree(cs);\r
- sfree(ds);\r
- sfree(ps);\r
- }\r
- freebn(base);\r
- freebn(expt);\r
- freebn(modulus);\r
- freebn(expected);\r
- freebn(answer);\r
- } else {\r
- printf("%d: unrecognised test keyword: '%s'\n", line, buf);\r
- exit(1);\r
- }\r
-\r
- sfree(buf);\r
- sfree(data);\r
- }\r
-\r
- printf("passed %d failed %d total %d\n", passes, fails, passes+fails);\r
- return fails != 0;\r
-}\r
-\r
-#endif\r
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