X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/f28753ab5739c73d3488df61c4c52da3f904d857..62ddb51e0424dd4bd1098b024f2427959aefc729:/sshbn.c diff --git a/sshbn.c b/sshbn.c index 22ed5dcd..ba3d5b63 100644 --- a/sshbn.c +++ b/sshbn.c @@ -3,23 +3,82 @@ */ #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) +#else +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 unsigned short *Bignum; +typedef BignumInt *Bignum; #include "ssh.h" -unsigned short bnZero[1] = { 0 }; -unsigned short bnOne[2] = { 1, 1 }; +BignumInt bnZero[1] = { 0 }; +BignumInt bnOne[2] = { 1, 1 }; /* - * The Bignum format is an array of `unsigned short'. The first + * 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 2^16, _least_ + * 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.) * @@ -34,7 +93,7 @@ Bignum Zero = bnZero, One = bnOne; static Bignum newbn(int length) { - Bignum b = smalloc((length + 1) * sizeof(unsigned short)); + Bignum b = snewn(length + 1, BignumInt); if (!b) abort(); /* FIXME */ memset(b, 0, (length + 1) * sizeof(*b)); @@ -50,7 +109,7 @@ void bn_restore_invariant(Bignum b) Bignum copybn(Bignum orig) { - Bignum b = smalloc((orig[0] + 1) * sizeof(unsigned short)); + Bignum b = snewn(orig[0] + 1, BignumInt); if (!b) abort(); /* FIXME */ memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); @@ -68,7 +127,7 @@ void freebn(Bignum b) Bignum bn_power_2(int n) { - Bignum ret = newbn(n / 16 + 1); + Bignum ret = newbn(n / BIGNUM_INT_BITS + 1); bignum_set_bit(ret, n, 1); return ret; } @@ -78,41 +137,40 @@ Bignum bn_power_2(int n) * Input is in the first len words of a and b. * Result is returned in the first 2*len words of c. */ -static void internal_mul(unsigned short *a, unsigned short *b, - unsigned short *c, int len) +static void internal_mul(BignumInt *a, BignumInt *b, + BignumInt *c, int len) { int i, j; - unsigned long ai, t; + BignumDblInt t; for (j = 0; j < 2 * len; j++) c[j] = 0; for (i = len - 1; i >= 0; i--) { - ai = a[i]; t = 0; for (j = len - 1; j >= 0; j--) { - t += ai * (unsigned long) b[j]; - t += (unsigned long) c[i + j + 1]; - c[i + j + 1] = (unsigned short) t; - t = t >> 16; + t += MUL_WORD(a[i], (BignumDblInt) b[j]); + t += (BignumDblInt) c[i + j + 1]; + c[i + j + 1] = (BignumInt) t; + t = t >> BIGNUM_INT_BITS; } - c[i] = (unsigned short) t; + c[i] = (BignumInt) t; } } -static void internal_add_shifted(unsigned short *number, +static void internal_add_shifted(BignumInt *number, unsigned n, int shift) { - int word = 1 + (shift / 16); - int bshift = shift % 16; - unsigned long addend; + int word = 1 + (shift / BIGNUM_INT_BITS); + int bshift = shift % BIGNUM_INT_BITS; + BignumDblInt addend; - addend = n << bshift; + addend = (BignumDblInt)n << bshift; while (addend) { addend += number[word]; - number[word] = (unsigned short) addend & 0xFFFF; - addend >>= 16; + number[word] = (BignumInt) addend & BIGNUM_INT_MASK; + addend >>= BIGNUM_INT_BITS; word++; } } @@ -127,11 +185,11 @@ static void internal_add_shifted(unsigned short *number, * rather than the internal bigendian format. Quotient parts are shifted * left by `qshift' before adding into quot. */ -static void internal_mod(unsigned short *a, int alen, - unsigned short *m, int mlen, - unsigned short *quot, int qshift) +static void internal_mod(BignumInt *a, int alen, + BignumInt *m, int mlen, + BignumInt *quot, int qshift) { - unsigned short m0, m1; + BignumInt m0, m1; unsigned int h; int i, k; @@ -142,7 +200,7 @@ static void internal_mod(unsigned short *a, int alen, m1 = 0; for (i = 0; i <= alen - mlen; i++) { - unsigned long t; + BignumDblInt t; unsigned int q, r, c, ai1; if (i == 0) { @@ -158,30 +216,50 @@ static void internal_mod(unsigned short *a, int alen, ai1 = a[i + 1]; /* Find q = h:a[i] / m0 */ - t = ((unsigned long) h << 16) + a[i]; - q = t / m0; - r = t % m0; - - /* Refine our estimate of q by looking at - h:a[i]:a[i+1] / m0:m1 */ - t = (long) m1 *(long) q; - if (t > ((unsigned long) r << 16) + ai1) { - q--; - t -= m1; - r = (r + m0) & 0xffff; /* overflow? */ - if (r >= (unsigned long) m0 && - t > ((unsigned long) r << 16) + ai1) q--; + if (h >= m0) { + /* + * Special case. + * + * To illustrate it, suppose a BignumInt is 8 bits, and + * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then + * our initial division will be 0xA123 / 0xA1, which + * will give a quotient of 0x100 and a divide overflow. + * However, the invariants in this division algorithm + * are not violated, since the full number A1:23:... is + * _less_ than the quotient prefix A1:B2:... and so the + * following correction loop would have sorted it out. + * + * In this situation we set q to be the largest + * quotient we _can_ stomach (0xFF, of course). + */ + q = BIGNUM_INT_MASK; + } else { + /* Macro doesn't want an array subscript expression passed + * into it (see definition), so use a temporary. */ + BignumInt tmplo = a[i]; + DIVMOD_WORD(q, r, h, tmplo, m0); + + /* Refine our estimate of q by looking at + h:a[i]:a[i+1] / m0:m1 */ + t = MUL_WORD(m1, q); + if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { + q--; + t -= m1; + r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */ + if (r >= (BignumDblInt) m0 && + t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--; + } } /* Subtract q * m from a[i...] */ c = 0; for (k = mlen - 1; k >= 0; k--) { - t = (long) q *(long) m[k]; + t = MUL_WORD(q, m[k]); t += c; - c = t >> 16; - if ((unsigned short) t > a[i + k]) + c = (unsigned)(t >> BIGNUM_INT_BITS); + if ((BignumInt) t > a[i + k]) c++; - a[i + k] -= (unsigned short) t; + a[i + k] -= (BignumInt) t; } /* Add back m in case of borrow */ @@ -190,74 +268,83 @@ static void internal_mod(unsigned short *a, int alen, for (k = mlen - 1; k >= 0; k--) { t += m[k]; t += a[i + k]; - a[i + k] = (unsigned short) t; - t = t >> 16; + a[i + k] = (BignumInt) t; + t = t >> BIGNUM_INT_BITS; } q--; } if (quot) - internal_add_shifted(quot, q, qshift + 16 * (alen - mlen - i)); + internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); } } /* * Compute (base ^ exp) % mod. - * The base MUST be smaller than the modulus. - * The most significant word of mod MUST be non-zero. - * We assume that the result array is the same size as the mod array. */ -Bignum modpow(Bignum base, Bignum exp, Bignum mod) +Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) { - unsigned short *a, *b, *n, *m; + BignumInt *a, *b, *n, *m; int mshift; int mlen, i, j; - Bignum result; + 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 = smalloc(mlen * sizeof(unsigned short)); + m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[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 = smalloc(mlen * sizeof(unsigned short)); + n = snewn(mlen, BignumInt); i = mlen - base[0]; for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < base[0]; j++) + 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 = smalloc(2 * mlen * sizeof(unsigned short)); - b = smalloc(2 * mlen * sizeof(unsigned short)); + 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; /* Skip leading zero bits of exp. */ i = 0; - j = 15; - while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { + j = BIGNUM_INT_BITS-1; + while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { j--; if (j < 0) { i++; - j = 15; + j = BIGNUM_INT_BITS-1; } } /* Main computation */ - while (i < exp[0]) { + while (i < (int)exp[0]) { while (j >= 0) { internal_mul(a + mlen, a + mlen, b, mlen); internal_mod(b, mlen * 2, m, mlen, NULL, 0); @@ -265,7 +352,7 @@ Bignum modpow(Bignum base, Bignum exp, Bignum mod) internal_mul(b + mlen, n, a, mlen); internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { - unsigned short *t; + BignumInt *t; t = a; a = b; b = t; @@ -273,17 +360,17 @@ Bignum modpow(Bignum base, Bignum exp, Bignum mod) j--; } i++; - j = 15; + j = BIGNUM_INT_BITS-1; } /* Fixup result in case the modulus was shifted */ if (mshift) { for (i = mlen - 1; i < 2 * mlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i + 1] >> (16 - mshift)); + a[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] << (16 - mshift)); + a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ @@ -307,6 +394,8 @@ Bignum modpow(Bignum base, Bignum exp, Bignum mod) n[i] = 0; sfree(n); + freebn(base); + return result; } @@ -317,7 +406,7 @@ Bignum modpow(Bignum base, Bignum exp, Bignum mod) */ Bignum modmul(Bignum p, Bignum q, Bignum mod) { - unsigned short *a, *n, *m, *o; + BignumInt *a, *n, *m, *o; int mshift; int pqlen, mlen, rlen, i, j; Bignum result; @@ -325,40 +414,40 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Allocate m of size mlen, copy mod to m */ /* We use big endian internally */ mlen = mod[0]; - m = smalloc(mlen * sizeof(unsigned short)); + m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[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 = smalloc(pqlen * sizeof(unsigned short)); + n = snewn(pqlen, BignumInt); i = pqlen - p[0]; for (j = 0; j < i; j++) n[j] = 0; - for (j = 0; j < p[0]; j++) + 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 = smalloc(pqlen * sizeof(unsigned short)); + o = snewn(pqlen, BignumInt); i = pqlen - q[0]; for (j = 0; j < i; j++) o[j] = 0; - for (j = 0; j < q[0]; j++) + for (j = 0; j < (int)q[0]; j++) o[i + j] = q[q[0] - j]; /* Allocate a of size 2*pqlen for result */ - a = smalloc(2 * pqlen * sizeof(unsigned short)); + a = snewn(2 * pqlen, BignumInt); /* Main computation */ internal_mul(n, o, a, pqlen); @@ -367,11 +456,11 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Fixup result in case the modulus was shifted */ if (mshift) { for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i + 1] >> (16 - mshift)); + a[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] << (16 - mshift)); + a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ @@ -408,24 +497,24 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) */ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) { - unsigned short *n, *m; + BignumInt *n, *m; int mshift; int plen, mlen, i, j; /* Allocate m of size mlen, copy mod to m */ /* We use big endian internally */ mlen = mod[0]; - m = smalloc(mlen * sizeof(unsigned short)); + m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i + 1] >> (16 - mshift)); + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); m[mlen - 1] = m[mlen - 1] << mshift; } @@ -435,10 +524,10 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) plen = mlen + 1; /* Allocate n of size plen, copy p to n */ - n = smalloc(plen * sizeof(unsigned short)); + n = snewn(plen, BignumInt); for (j = 0; j < plen; j++) n[j] = 0; - for (j = 1; j <= p[0]; j++) + for (j = 1; j <= (int)p[0]; j++) n[plen - j] = p[j]; /* Main computation */ @@ -447,16 +536,16 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* Fixup result in case the modulus was shifted */ if (mshift) { for (i = plen - mlen - 1; i < plen - 1; i++) - n[i] = (n[i] << mshift) | (n[i + 1] >> (16 - mshift)); + n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); n[plen - 1] = n[plen - 1] << mshift; internal_mod(n, plen, m, mlen, quotient, 0); for (i = plen - 1; i >= plen - mlen; i--) - n[i] = (n[i] >> mshift) | (n[i - 1] << (16 - mshift)); + n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ if (result) { - for (i = 1; i <= result[0]; i++) { + for (i = 1; i <= (int)result[0]; i++) { int j = plen - i; result[i] = j >= 0 ? n[j] : 0; } @@ -477,8 +566,8 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) void decbn(Bignum bn) { int i = 1; - while (i < bn[0] && bn[i] == 0) - bn[i++] = 0xFFFF; + while (i < (int)bn[0] && bn[i] == 0) + bn[i++] = BIGNUM_INT_MASK; bn[i]--; } @@ -487,17 +576,14 @@ Bignum bignum_from_bytes(const unsigned char *data, int nbytes) Bignum result; int w, i; - w = (nbytes + 1) / 2; /* bytes -> words */ + 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++; - if (i & 1) - result[1 + i / 2] |= byte << 8; - else - result[1 + i / 2] |= byte; + result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS); } while (result[0] > 1 && result[result[0]] == 0) @@ -506,20 +592,26 @@ Bignum bignum_from_bytes(const unsigned char *data, int nbytes) } /* - * Read an ssh1-format bignum from a data buffer. Return the number - * of bytes consumed. + * Read an SSH-1-format bignum from a data buffer. Return the number + * of bytes consumed, or -1 if there wasn't enough data. */ -int ssh1_read_bignum(const unsigned char *data, Bignum * result) +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; @@ -529,18 +621,18 @@ int ssh1_read_bignum(const unsigned char *data, Bignum * result) } /* - * Return the bit count of a bignum, for ssh1 encoding. + * Return the bit count of a bignum, for SSH-1 encoding. */ int bignum_bitcount(Bignum bn) { - int bitcount = bn[0] * 16 - 1; + int bitcount = bn[0] * BIGNUM_INT_BITS - 1; while (bitcount >= 0 - && (bn[bitcount / 16 + 1] >> (bitcount % 16)) == 0) bitcount--; + && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; return bitcount + 1; } /* - * Return the byte length of a bignum when ssh1 encoded. + * Return the byte length of a bignum when SSH-1 encoded. */ int ssh1_bignum_length(Bignum bn) { @@ -548,7 +640,7 @@ int ssh1_bignum_length(Bignum bn) } /* - * Return the byte length of a bignum when ssh2 encoded. + * Return the byte length of a bignum when SSH-2 encoded. */ int ssh2_bignum_length(Bignum bn) { @@ -560,12 +652,11 @@ int ssh2_bignum_length(Bignum bn) */ int bignum_byte(Bignum bn, int i) { - if (i >= 2 * bn[0]) + if (i >= (int)(BIGNUM_INT_BYTES * bn[0])) return 0; /* beyond the end */ - else if (i & 1) - return (bn[i / 2 + 1] >> 8) & 0xFF; else - return (bn[i / 2 + 1]) & 0xFF; + return (bn[i / BIGNUM_INT_BYTES + 1] >> + ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; } /* @@ -573,10 +664,10 @@ int bignum_byte(Bignum bn, int i) */ int bignum_bit(Bignum bn, int i) { - if (i >= 16 * bn[0]) + if (i >= (int)(BIGNUM_INT_BITS * bn[0])) return 0; /* beyond the end */ else - return (bn[i / 16 + 1] >> (i % 16)) & 1; + return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; } /* @@ -584,11 +675,11 @@ int bignum_bit(Bignum bn, int i) */ void bignum_set_bit(Bignum bn, int bitnum, int value) { - if (bitnum >= 16 * bn[0]) + if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0])) abort(); /* beyond the end */ else { - int v = bitnum / 16 + 1; - int mask = 1 << (bitnum % 16); + int v = bitnum / BIGNUM_INT_BITS + 1; + int mask = 1 << (bitnum % BIGNUM_INT_BITS); if (value) bn[v] |= mask; else @@ -597,7 +688,7 @@ void bignum_set_bit(Bignum bn, int bitnum, int value) } /* - * Write a ssh1-format bignum into a buffer. It is assumed the + * Write a SSH-1-format bignum into a buffer. It is assumed the * buffer is big enough. Returns the number of bytes used. */ int ssh1_write_bignum(void *data, Bignum bn) @@ -622,8 +713,8 @@ int bignum_cmp(Bignum a, Bignum b) int amax = a[0], bmax = b[0]; int i = (amax > bmax ? amax : bmax); while (i) { - unsigned short aval = (i > amax ? 0 : a[i]); - unsigned short bval = (i > bmax ? 0 : b[i]); + BignumInt aval = (i > amax ? 0 : a[i]); + BignumInt bval = (i > bmax ? 0 : b[i]); if (aval < bval) return -1; if (aval > bval) @@ -640,21 +731,21 @@ Bignum bignum_rshift(Bignum a, int shift) { Bignum ret; int i, shiftw, shiftb, shiftbb, bits; - unsigned short ai, ai1; + BignumInt ai, ai1; bits = bignum_bitcount(a) - shift; - ret = newbn((bits + 15) / 16); + ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS); if (ret) { - shiftw = shift / 16; - shiftb = shift % 16; - shiftbb = 16 - shiftb; + shiftw = shift / BIGNUM_INT_BITS; + shiftb = shift % BIGNUM_INT_BITS; + shiftbb = BIGNUM_INT_BITS - shiftb; ai1 = a[shiftw + 1]; - for (i = 1; i <= ret[0]; i++) { + for (i = 1; i <= (int)ret[0]; i++) { ai = ai1; - ai1 = (i + shiftw + 1 <= a[0] ? a[i + shiftw + 1] : 0); - ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF; + ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0); + ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; } } @@ -669,14 +760,14 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) int alen = a[0], blen = b[0]; int mlen = (alen > blen ? alen : blen); int rlen, i, maxspot; - unsigned short *workspace; + BignumInt *workspace; Bignum ret; /* mlen space for a, mlen space for b, 2*mlen for result */ - workspace = smalloc(mlen * 4 * sizeof(unsigned short)); + workspace = snewn(mlen * 4, BignumInt); for (i = 0; i < mlen; i++) { - workspace[0 * mlen + i] = (mlen - i <= a[0] ? a[mlen - i] : 0); - workspace[1 * mlen + i] = (mlen - i <= b[0] ? b[mlen - i] : 0); + workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0); + workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0); } internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, @@ -684,11 +775,11 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) /* now just copy the result back */ rlen = alen + blen + 1; - if (addend && rlen <= addend[0]) + if (addend && rlen <= (int)addend[0]) rlen = addend[0] + 1; ret = newbn(rlen); maxspot = 0; - for (i = 1; i <= ret[0]; i++) { + for (i = 1; i <= (int)ret[0]; i++) { ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); if (ret[i] != 0) maxspot = i; @@ -697,18 +788,19 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) /* now add in the addend, if any */ if (addend) { - unsigned long carry = 0; + BignumDblInt carry = 0; for (i = 1; i <= rlen; i++) { - carry += (i <= ret[0] ? ret[i] : 0); - carry += (i <= addend[0] ? addend[i] : 0); - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; + 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; + sfree(workspace); return ret; } @@ -729,7 +821,7 @@ Bignum bignum_bitmask(Bignum n) { Bignum ret = copybn(n); int i; - unsigned short j; + BignumInt j; i = ret[0]; while (n[i] == 0 && i > 0) @@ -741,20 +833,21 @@ Bignum bignum_bitmask(Bignum n) j = 2 * j + 1; ret[i] = j; while (--i > 0) - ret[i] = 0xFFFF; + ret[i] = BIGNUM_INT_MASK; return ret; } /* * Convert a (max 32-bit) long into a bignum. */ -Bignum bignum_from_long(unsigned long n) +Bignum bignum_from_long(unsigned long nn) { Bignum ret; + BignumDblInt n = nn; ret = newbn(3); - ret[1] = (unsigned short)(n & 0xFFFF); - ret[2] = (unsigned short)((n >> 16) & 0xFFFF); + 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; @@ -763,18 +856,18 @@ Bignum bignum_from_long(unsigned long n) /* * Add a long to a bignum. */ -Bignum bignum_add_long(Bignum number, unsigned long addend) +Bignum bignum_add_long(Bignum number, unsigned long addendx) { Bignum ret = newbn(number[0] + 1); int i, maxspot = 0; - unsigned long carry = 0; - - for (i = 1; i <= ret[0]; i++) { - carry += addend & 0xFFFF; - carry += (i <= number[0] ? number[i] : 0); - addend >>= 16; - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; + 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; } @@ -787,20 +880,19 @@ Bignum bignum_add_long(Bignum number, unsigned long addend) */ unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { - unsigned long mod, r; + BignumDblInt mod, r; int i; r = 0; mod = modulus; for (i = number[0]; i > 0; i--) - r = (r * 65536 + number[i]) % mod; + r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; return (unsigned short) r; } -#if 0 +#ifdef DEBUG void diagbn(char *prefix, Bignum md) { -#ifdef DEBUG int i, nibbles, morenibbles; static const char hex[] = "0123456789ABCDEF"; @@ -818,7 +910,6 @@ void diagbn(char *prefix, Bignum md) if (prefix) debug(("\n")); -#endif } #endif @@ -889,6 +980,7 @@ Bignum modinv(Bignum number, Bignum modulus) x = bigmuladd(q, xp, t); sign = -sign; freebn(t); + freebn(q); } freebn(b); @@ -899,13 +991,13 @@ Bignum modinv(Bignum number, Bignum modulus) if (sign < 0) { /* set a new x to be modulus - x */ Bignum newx = newbn(modulus[0]); - unsigned short carry = 0; + BignumInt carry = 0; int maxspot = 1; int i; - for (i = 1; i <= newx[0]; i++) { - unsigned short aword = (i <= modulus[0] ? modulus[i] : 0); - unsigned short bword = (i <= x[0] ? x[i] : 0); + 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); @@ -929,9 +1021,9 @@ char *bignum_decimal(Bignum x) { int ndigits, ndigit; int i, iszero; - unsigned long carry; + BignumDblInt carry; char *ret; - unsigned short *workspace; + BignumInt *workspace; /* * First, estimate the number of digits. Since log(10)/log(2) @@ -945,19 +1037,24 @@ char *bignum_decimal(Bignum x) * round up (rounding down might make it less than x again). * Therefore if we multiply the bit count by 28/93, rounding * up, we will have enough digits. + * + * i=0 (i.e., x=0) is an irritating special case. */ i = bignum_bitcount(x); - ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */ + 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 = smalloc(ndigits); + 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 = smalloc(sizeof(unsigned short) * x[0]); - for (i = 0; i < x[0]; i++) + workspace = snewn(x[0], BignumInt); + for (i = 0; i < (int)x[0]; i++) workspace[i] = x[x[0] - i]; /* @@ -970,9 +1067,9 @@ char *bignum_decimal(Bignum x) do { iszero = 1; carry = 0; - for (i = 0; i < x[0]; i++) { - carry = (carry << 16) + workspace[i]; - workspace[i] = (unsigned short) (carry / 10); + 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; @@ -990,5 +1087,6 @@ char *bignum_decimal(Bignum x) /* * Done. */ + sfree(workspace); return ret; }