X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/ddecd643be56256929ae1c45bebb8e39ae032225..62ddb51e0424dd4bd1098b024f2427959aefc729:/sshbn.c diff --git a/sshbn.c b/sshbn.c index 2fd98f91..ba3d5b63 100644 --- a/sshbn.c +++ b/sshbn.c @@ -3,29 +3,82 @@ */ #include +#include #include #include -#if 0 // use PuTTY main debugging for diagbn() -#include -#include "putty.h" -#define debugprint debug +#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 -#define debugprint(x) printf x +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.) * @@ -38,28 +91,33 @@ unsigned short bnOne[2] = { 1, 1 }; Bignum Zero = bnZero, One = bnOne; -static Bignum newbn(int length) { - Bignum b = smalloc((length+1)*sizeof(unsigned short)); +static Bignum newbn(int length) +{ + Bignum b = snewn(length + 1, BignumInt); if (!b) abort(); /* FIXME */ - memset(b, 0, (length+1)*sizeof(*b)); + memset(b, 0, (length + 1) * sizeof(*b)); b[0] = length; return b; } -void bn_restore_invariant(Bignum b) { - while (b[0] > 1 && b[b[0]] == 0) b[0]--; +void bn_restore_invariant(Bignum b) +{ + while (b[0] > 1 && b[b[0]] == 0) + b[0]--; } -Bignum copybn(Bignum orig) { - Bignum b = smalloc((orig[0]+1)*sizeof(unsigned short)); +Bignum copybn(Bignum orig) +{ + Bignum b = snewn(orig[0] + 1, BignumInt); if (!b) abort(); /* FIXME */ - memcpy(b, orig, (orig[0]+1)*sizeof(*b)); + memcpy(b, orig, (orig[0] + 1) * sizeof(*b)); return b; } -void freebn(Bignum b) { +void freebn(Bignum b) +{ /* * Burn the evidence, just in case. */ @@ -67,8 +125,9 @@ void freebn(Bignum b) { sfree(b); } -Bignum bn_power_2(int n) { - Bignum ret = newbn(n/16+1); +Bignum bn_power_2(int n) +{ + Bignum ret = newbn(n / BIGNUM_INT_BITS + 1); bignum_set_bit(ret, n, 1); return ret; } @@ -78,41 +137,41 @@ 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++) + 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, - unsigned n, int shift) { - int word = 1 + (shift / 16); - int bshift = shift % 16; - unsigned long addend; +static void internal_add_shifted(BignumInt *number, + unsigned n, int shift) +{ + int word = 1 + (shift / BIGNUM_INT_BITS); + int bshift = shift % BIGNUM_INT_BITS; + BignumDblInt addend; - addend = n << bshift; + addend = (BignumDblInt)n << bshift; while (addend) { - addend += number[word]; - number[word] = (unsigned short) addend & 0xFFFF; - addend >>= 16; - word++; + addend += number[word]; + number[word] = (BignumInt) addend & BIGNUM_INT_MASK; + addend >>= BIGNUM_INT_BITS; + word++; } } @@ -126,61 +185,81 @@ static void internal_add_shifted(unsigned short *number, * rather than the internal bigendian format. Quotient parts are shifted * left by `qshift' before adding into quot. */ -static void internal_mod(unsigned short *a, int alen, - unsigned short *m, int mlen, - unsigned short *quot, int qshift) +static void internal_mod(BignumInt *a, int alen, + BignumInt *m, int mlen, + BignumInt *quot, int qshift) { - unsigned short m0, m1; + BignumInt m0, m1; unsigned int h; int i, k; m0 = m[0]; if (mlen > 1) - m1 = m[1]; + m1 = m[1]; else - m1 = 0; + m1 = 0; - for (i = 0; i <= alen-mlen; i++) { - unsigned long t; + for (i = 0; i <= alen - mlen; i++) { + BignumDblInt t; unsigned int q, r, c, ai1; if (i == 0) { h = 0; } else { - h = a[i-1]; - a[i-1] = 0; + h = a[i - 1]; + a[i - 1] = 0; } - if (i == alen-1) - ai1 = 0; - else - ai1 = a[i+1]; + if (i == alen - 1) + ai1 = 0; + else + ai1 = a[i + 1]; /* Find q = h:a[i] / m0 */ - t = ((unsigned long) h << 16) + a[i]; - q = t / m0; - r = t % m0; - - /* Refine our estimate of q by looking at - h:a[i]:a[i+1] / m0:m1 */ - t = (long) m1 * (long) q; - if (t > ((unsigned long) r << 16) + ai1) { - q--; - t -= m1; - r = (r + m0) & 0xffff; /* overflow? */ - if (r >= (unsigned long)m0 && - t > ((unsigned long) r << 16) + ai1) + if (h >= m0) { + /* + * Special case. + * + * To illustrate it, suppose a BignumInt is 8 bits, and + * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then + * our initial division will be 0xA123 / 0xA1, which + * will give a quotient of 0x100 and a divide overflow. + * However, the invariants in this division algorithm + * are not violated, since the full number A1:23:... is + * _less_ than the quotient prefix A1:B2:... and so the + * following correction loop would have sorted it out. + * + * In this situation we set q to be the largest + * quotient we _can_ stomach (0xFF, of course). + */ + q = BIGNUM_INT_MASK; + } else { + /* Macro doesn't want an array subscript expression passed + * into it (see definition), so use a temporary. */ + BignumInt tmplo = a[i]; + DIVMOD_WORD(q, r, h, tmplo, m0); + + /* Refine our estimate of q by looking at + h:a[i]:a[i+1] / m0:m1 */ + t = MUL_WORD(m1, q); + if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { q--; + t -= m1; + r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */ + if (r >= (BignumDblInt) m0 && + t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--; + } } /* Subtract q * m from a[i...] */ c = 0; for (k = mlen - 1; k >= 0; k--) { - t = (long) q * (long) m[k]; + t = MUL_WORD(q, m[k]); t += c; - c = t >> 16; - if ((unsigned short) t > a[i+k]) c++; - a[i+k] -= (unsigned short) t; + c = (unsigned)(t >> BIGNUM_INT_BITS); + if ((BignumInt) t > a[i + k]) + c++; + a[i + k] -= (BignumInt) t; } /* Add back m in case of borrow */ @@ -188,102 +267,134 @@ static void internal_mod(unsigned short *a, int alen, t = 0; for (k = mlen - 1; k >= 0; k--) { t += m[k]; - t += a[i+k]; - a[i+k] = (unsigned short)t; - t = t >> 16; + t += a[i + k]; + a[i + k] = (BignumInt) t; + t = t >> BIGNUM_INT_BITS; } - q--; + q--; } - if (quot) - internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i)); + if (quot) + internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); } } /* * Compute (base ^ exp) % mod. - * The base MUST be smaller than the modulus. - * The most significant word of mod MUST be non-zero. - * We assume that the result array is the same size as the mod array. */ -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)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + m = snewn(mlen, BignumInt); + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } /* Allocate n of size mlen, copy base to n */ - n = 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++) n[i+j] = base[base[0] - j]; + for (j = 0; j < i; j++) + n[j] = 0; + for (j = 0; j < (int)base[0]; j++) + n[i + j] = base[base[0] - j]; /* Allocate a and b of size 2*mlen. Set a = 1 */ - a = smalloc(2 * mlen * sizeof(unsigned short)); - b = smalloc(2 * mlen * sizeof(unsigned short)); - for (i = 0; i < 2*mlen; i++) a[i] = 0; - a[2*mlen-1] = 1; + a = snewn(2 * mlen, BignumInt); + b = snewn(2 * mlen, BignumInt); + for (i = 0; i < 2 * mlen; i++) + a[i] = 0; + a[2 * mlen - 1] = 1; /* Skip leading zero bits of exp. */ - i = 0; j = 15; - while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { + i = 0; + j = BIGNUM_INT_BITS-1; + while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) { j--; - if (j < 0) { i++; j = 15; } + if (j < 0) { + i++; + j = BIGNUM_INT_BITS-1; + } } /* Main computation */ - while (i < exp[0]) { + while (i < (int)exp[0]) { while (j >= 0) { internal_mul(a + mlen, a + mlen, b, mlen); - internal_mod(b, mlen*2, m, mlen, NULL, 0); + internal_mod(b, mlen * 2, m, mlen, NULL, 0); if ((exp[exp[0] - i] & (1 << j)) != 0) { internal_mul(b + mlen, n, a, mlen); - internal_mod(a, mlen*2, m, mlen, NULL, 0); + internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { - unsigned short *t; - t = a; a = b; b = t; + BignumInt *t; + t = a; + a = b; + b = t; } j--; } - i++; j = 15; + i++; + j = BIGNUM_INT_BITS-1; } /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = mlen - 1; i < 2*mlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); - a[2*mlen-1] = a[2*mlen-1] << mshift; - internal_mod(a, mlen*2, m, mlen, NULL, 0); - for (i = 2*mlen - 1; i >= mlen; i--) - a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); + for (i = mlen - 1; i < 2 * mlen - 1; i++) + a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); + a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; + internal_mod(a, mlen * 2, m, mlen, NULL, 0); + for (i = 2 * mlen - 1; i >= mlen; i--) + a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ result = newbn(mod[0]); for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i+mlen]; - while (result[0] > 1 && result[result[0]] == 0) result[0]--; + 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 < 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); + for (i = 0; i < 2 * mlen; i++) + a[i] = 0; + sfree(a); + 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; } @@ -295,7 +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; @@ -303,61 +414,76 @@ 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)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + m = snewn(mlen, BignumInt); + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } pqlen = (p[0] > q[0] ? p[0] : q[0]); /* 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++) n[i+j] = p[p[0] - j]; + for (j = 0; j < i; j++) + n[j] = 0; + for (j = 0; j < (int)p[0]; j++) + n[i + j] = p[p[0] - j]; /* Allocate o of size pqlen, copy q to o */ - o = 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++) o[i+j] = q[q[0] - j]; + for (j = 0; j < i; j++) + o[j] = 0; + for (j = 0; j < (int)q[0]; j++) + o[i + j] = q[q[0] - j]; /* Allocate a of size 2*pqlen for result */ - a = smalloc(2 * pqlen * sizeof(unsigned short)); + a = snewn(2 * pqlen, BignumInt); /* Main computation */ internal_mul(n, o, a, pqlen); - internal_mod(a, pqlen*2, m, mlen, NULL, 0); + internal_mod(a, pqlen * 2, m, mlen, NULL, 0); /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = 2*pqlen - mlen - 1; i < 2*pqlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i+1] >> (16-mshift)); - a[2*pqlen-1] = a[2*pqlen-1] << mshift; - internal_mod(a, pqlen*2, m, mlen, NULL, 0); - for (i = 2*pqlen - 1; i >= 2*pqlen - mlen; i--) - a[i] = (a[i] >> mshift) | (a[i-1] << (16-mshift)); + for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) + a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); + a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift; + internal_mod(a, pqlen * 2, m, mlen, NULL, 0); + for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--) + a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ - rlen = (mlen < pqlen*2 ? mlen : pqlen*2); + 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]--; + result[result[0] - i] = a[i + 2 * pqlen - rlen]; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2*pqlen; i++) a[i] = 0; 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); + 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; } @@ -366,37 +492,43 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) * Compute p % mod. * The most significant word of mod MUST be non-zero. * We assume that the result array is the same size as the mod array. - * We optionally write out a quotient. + * We optionally write out a quotient if `quotient' is non-NULL. + * We can avoid writing out the result if `result' is NULL. */ -void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) +static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) { - unsigned short *n, *m; + BignumInt *n, *m; int mshift; int plen, mlen, i, j; /* Allocate m of size mlen, copy mod to m */ /* We use big endian internally */ mlen = mod[0]; - m = smalloc(mlen * sizeof(unsigned short)); - for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j]; + m = snewn(mlen, BignumInt); + for (j = 0; j < mlen; j++) + m[j] = mod[mod[0] - j]; /* Shift m left to make msb bit set */ - for (mshift = 0; mshift < 15; mshift++) - if ((m[0] << mshift) & 0x8000) break; + for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) + if ((m[0] << mshift) & BIGNUM_TOP_BIT) + break; if (mshift) { for (i = 0; i < mlen - 1; i++) - m[i] = (m[i] << mshift) | (m[i+1] >> (16-mshift)); - m[mlen-1] = m[mlen-1] << mshift; + m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift)); + m[mlen - 1] = m[mlen - 1] << mshift; } plen = p[0]; /* Ensure plen > mlen */ - if (plen <= mlen) plen = mlen+1; + if (plen <= mlen) + plen = mlen + 1; /* Allocate n of size plen, copy p to n */ - n = smalloc(plen * sizeof(unsigned short)); - for (j = 0; j < plen; j++) n[j] = 0; - for (j = 1; j <= p[0]; j++) n[plen-j] = p[j]; + n = snewn(plen, BignumInt); + for (j = 0; j < plen; j++) + n[j] = 0; + for (j = 1; j <= (int)p[0]; j++) + n[plen - j] = p[j]; /* Main computation */ internal_mod(n, plen, m, mlen, quotient, mshift); @@ -404,71 +536,84 @@ void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* Fixup result in case the modulus was shifted */ if (mshift) { for (i = plen - mlen - 1; i < plen - 1; i++) - n[i] = (n[i] << mshift) | (n[i+1] >> (16-mshift)); - n[plen-1] = n[plen-1] << mshift; + n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift)); + n[plen - 1] = n[plen - 1] << mshift; internal_mod(n, plen, m, mlen, quotient, 0); for (i = plen - 1; i >= plen - mlen; i--) - n[i] = (n[i] >> mshift) | (n[i-1] << (16-mshift)); + n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift)); } /* Copy result to buffer */ - for (i = 1; i <= result[0]; i++) { - int j = plen-i; - result[i] = j>=0 ? n[j] : 0; + if (result) { + for (i = 1; i <= (int)result[0]; i++) { + int j = plen - i; + result[i] = j >= 0 ? n[j] : 0; + } } /* Free temporary arrays */ - for (i = 0; i < mlen; i++) m[i] = 0; sfree(m); - for (i = 0; i < plen; i++) n[i] = 0; sfree(n); + 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) { +void decbn(Bignum bn) +{ int i = 1; - while (i < bn[0] && bn[i] == 0) - bn[i++] = 0xFFFF; + while (i < (int)bn[0] && bn[i] == 0) + bn[i++] = BIGNUM_INT_MASK; bn[i]--; } -Bignum bignum_from_bytes(unsigned char *data, int nbytes) { +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; + 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]--; + while (result[0] > 1 && result[result[0]] == 0) + result[0]--; return result; } /* - * Read an ssh1-format bignum from a data buffer. Return the number - * of bytes consumed. + * Read an SSH-1-format bignum from a data buffer. Return the number + * of bytes consumed, or -1 if there wasn't enough data. */ -int ssh1_read_bignum(unsigned char *data, Bignum *result) { - unsigned char *p = data; +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 */ + 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; + if (!result) /* just return length */ + return b + 2; *result = bignum_from_bytes(p, b); @@ -476,96 +621,105 @@ int ssh1_read_bignum(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; - while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0) - bitcount--; +int bignum_bitcount(Bignum bn) +{ + int bitcount = bn[0] * BIGNUM_INT_BITS - 1; + while (bitcount >= 0 + && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--; return bitcount + 1; } /* - * Return the byte length of a bignum when ssh1 encoded. + * Return the byte length of a bignum when SSH-1 encoded. */ -int ssh1_bignum_length(Bignum bn) { - return 2 + (bignum_bitcount(bn)+7)/8; +int ssh1_bignum_length(Bignum bn) +{ + return 2 + (bignum_bitcount(bn) + 7) / 8; } /* - * Return the byte length of a bignum when ssh2 encoded. + * Return the byte length of a bignum when SSH-2 encoded. */ -int ssh2_bignum_length(Bignum bn) { - return 4 + (bignum_bitcount(bn)+8)/8; +int ssh2_bignum_length(Bignum bn) +{ + return 4 + (bignum_bitcount(bn) + 8) / 8; } /* * Return a byte from a bignum; 0 is least significant, etc. */ -int bignum_byte(Bignum bn, int i) { - if (i >= 2*bn[0]) - return 0; /* beyond the end */ - else if (i & 1) - return (bn[i/2+1] >> 8) & 0xFF; +int bignum_byte(Bignum bn, int i) +{ + if (i >= (int)(BIGNUM_INT_BYTES * bn[0])) + return 0; /* beyond the end */ else - return (bn[i/2+1] ) & 0xFF; + return (bn[i / BIGNUM_INT_BYTES + 1] >> + ((i % BIGNUM_INT_BYTES)*8)) & 0xFF; } /* * Return a bit from a bignum; 0 is least significant, etc. */ -int bignum_bit(Bignum bn, int i) { - if (i >= 16*bn[0]) - return 0; /* beyond the end */ +int bignum_bit(Bignum bn, int i) +{ + if (i >= (int)(BIGNUM_INT_BITS * bn[0])) + return 0; /* beyond the end */ else - return (bn[i/16+1] >> (i%16)) & 1; + return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1; } /* * Set a bit in a bignum; 0 is least significant, etc. */ -void bignum_set_bit(Bignum bn, int bitnum, int value) { - if (bitnum >= 16*bn[0]) - abort(); /* beyond the end */ +void bignum_set_bit(Bignum bn, int bitnum, int value) +{ + if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0])) + abort(); /* beyond the end */ else { - int v = bitnum/16+1; - int mask = 1 << (bitnum%16); - if (value) - bn[v] |= mask; - else - bn[v] &= ~mask; + int v = bitnum / BIGNUM_INT_BITS + 1; + int mask = 1 << (bitnum % BIGNUM_INT_BITS); + if (value) + bn[v] |= mask; + else + bn[v] &= ~mask; } } /* - * Write a ssh1-format bignum into a buffer. It is assumed the + * Write a SSH-1-format bignum into a buffer. It is assumed the * buffer is big enough. Returns the number of bytes used. */ -int ssh1_write_bignum(void *data, Bignum bn) { +int ssh1_write_bignum(void *data, Bignum bn) +{ unsigned char *p = data; int len = ssh1_bignum_length(bn); int i; int bitc = bignum_bitcount(bn); *p++ = (bitc >> 8) & 0xFF; - *p++ = (bitc ) & 0xFF; - for (i = len-2; i-- ;) - *p++ = bignum_byte(bn, i); + *p++ = (bitc) & 0xFF; + for (i = len - 2; i--;) + *p++ = bignum_byte(bn, i); return len; } /* * Compare two bignums. Returns like strcmp. */ -int bignum_cmp(Bignum a, Bignum b) { +int bignum_cmp(Bignum a, Bignum b) +{ int amax = a[0], bmax = b[0]; int i = (amax > bmax ? amax : bmax); while (i) { - unsigned short aval = (i > amax ? 0 : a[i]); - unsigned short bval = (i > bmax ? 0 : b[i]); - if (aval < bval) return -1; - if (aval > bval) return +1; - i--; + BignumInt aval = (i > amax ? 0 : a[i]); + BignumInt bval = (i > bmax ? 0 : b[i]); + if (aval < bval) + return -1; + if (aval > bval) + return +1; + i--; } return 0; } @@ -573,25 +727,26 @@ int bignum_cmp(Bignum a, Bignum b) { /* * Right-shift one bignum to form another. */ -Bignum bignum_rshift(Bignum a, int shift) { +Bignum bignum_rshift(Bignum a, int shift) +{ Bignum ret; int i, shiftw, shiftb, shiftbb, bits; - unsigned short ai, ai1; + BignumInt ai, ai1; 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; - - ai1 = a[shiftw+1]; - for (i = 1; i <= ret[0]; i++) { - ai = ai1; - ai1 = (i+shiftw+1 <= a[0] ? a[i+shiftw+1] : 0); - ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & 0xFFFF; - } + shiftw = shift / BIGNUM_INT_BITS; + shiftb = shift % BIGNUM_INT_BITS; + shiftbb = BIGNUM_INT_BITS - shiftb; + + ai1 = a[shiftw + 1]; + for (i = 1; i <= (int)ret[0]; i++) { + ai = ai1; + ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0); + ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK; + } } return ret; @@ -600,56 +755,60 @@ Bignum bignum_rshift(Bignum a, int shift) { /* * Non-modular multiplication and addition. */ -Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) { +Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) +{ int alen = a[0], blen = b[0]; int mlen = (alen > blen ? alen : blen); int rlen, i, maxspot; - unsigned short *workspace; + 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, workspace+2*mlen, mlen); + internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, + workspace + 2 * mlen, mlen); /* now just copy the result back */ rlen = alen + blen + 1; - if (addend && rlen <= addend[0]) - rlen = addend[0] + 1; + if (addend && rlen <= (int)addend[0]) + rlen = addend[0] + 1; ret = newbn(rlen); maxspot = 0; - for (i = 1; i <= ret[0]; i++) { - ret[i] = (i <= 2*mlen ? workspace[4*mlen - i] : 0); - if (ret[i] != 0) - maxspot = i; + for (i = 1; i <= (int)ret[0]; i++) { + ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); + if (ret[i] != 0) + maxspot = i; } ret[0] = maxspot; /* now add in the addend, if any */ if (addend) { - unsigned long carry = 0; - for (i = 1; i <= rlen; i++) { - carry += (i <= ret[0] ? ret[i] : 0); - carry += (i <= addend[0] ? addend[i] : 0); - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; - if (ret[i] != 0 && i > maxspot) - maxspot = i; - } + BignumDblInt carry = 0; + for (i = 1; i <= rlen; i++) { + carry += (i <= (int)ret[0] ? ret[i] : 0); + carry += (i <= (int)addend[0] ? addend[i] : 0); + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0 && i > maxspot) + maxspot = i; + } } ret[0] = maxspot; + sfree(workspace); return ret; } /* * Non-modular multiplication. */ -Bignum bigmul(Bignum a, Bignum b) { +Bignum bigmul(Bignum a, Bignum b) +{ return bigmuladd(a, b, NULL); } @@ -658,54 +817,59 @@ Bignum bigmul(Bignum a, Bignum b) { * is, the smallest integer which is >= N and is also one less than * a power of two. */ -Bignum bignum_bitmask(Bignum n) { +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) - i--; + i--; if (i <= 0) - return ret; /* input was zero */ + return ret; /* input was zero */ j = 1; while (j < n[i]) - j = 2*j+1; + j = 2 * j + 1; ret[i] = j; while (--i > 0) - ret[i] = 0xFFFF; + ret[i] = BIGNUM_INT_MASK; return ret; } /* - * Convert a (max 16-bit) short into a bignum. + * Convert a (max 32-bit) long into a bignum. */ -Bignum bignum_from_short(unsigned short n) { +Bignum bignum_from_long(unsigned long nn) +{ Bignum ret; + BignumDblInt n = nn; - ret = newbn(2); - ret[1] = n & 0xFFFF; - ret[2] = (n >> 16) & 0xFFFF; - ret[0] = (ret[2] ? 2 : 1); - return ret; + ret = newbn(3); + ret[1] = (BignumInt)(n & BIGNUM_INT_MASK); + ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK); + ret[3] = 0; + ret[0] = (ret[2] ? 2 : 1); + return ret; } /* * Add a long to a bignum. */ -Bignum bignum_add_long(Bignum number, unsigned long addend) { - Bignum ret = newbn(number[0]+1); +Bignum bignum_add_long(Bignum number, unsigned long addendx) +{ + Bignum ret = newbn(number[0] + 1); int i, maxspot = 0; - unsigned long carry = 0; - - for (i = 1; i <= ret[0]; i++) { - carry += addend & 0xFFFF; - carry += (i <= number[0] ? number[i] : 0); - addend >>= 16; - ret[i] = (unsigned short) carry & 0xFFFF; - carry >>= 16; - if (ret[i] != 0) - maxspot = i; + BignumDblInt carry = 0, addend = addendx; + + for (i = 1; i <= (int)ret[0]; i++) { + carry += addend & BIGNUM_INT_MASK; + carry += (i <= (int)number[0] ? number[i] : 0); + addend >>= BIGNUM_INT_BITS; + ret[i] = (BignumInt) carry & BIGNUM_INT_MASK; + carry >>= BIGNUM_INT_BITS; + if (ret[i] != 0) + maxspot = i; } ret[0] = maxspot; return ret; @@ -714,49 +878,77 @@ Bignum bignum_add_long(Bignum number, unsigned long addend) { /* * Compute the residue of a bignum, modulo a (max 16-bit) short. */ -unsigned short bignum_mod_short(Bignum number, unsigned short modulus) { - unsigned long mod, r; +unsigned short bignum_mod_short(Bignum number, unsigned short modulus) +{ + BignumDblInt mod, r; int i; r = 0; mod = modulus; for (i = number[0]; i > 0; i--) - r = (r * 65536 + number[i]) % mod; + r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod; return (unsigned short) r; } -void diagbn(char *prefix, Bignum md) { +#ifdef DEBUG +void diagbn(char *prefix, Bignum md) +{ int i, nibbles, morenibbles; static const char hex[] = "0123456789ABCDEF"; - debugprint(("%s0x", prefix ? prefix : "")); + debug(("%s0x", prefix ? prefix : "")); - nibbles = (3 + bignum_bitcount(md))/4; if (nibbles<1) nibbles=1; - morenibbles = 4*md[0] - nibbles; - for (i=0; i> (4*(i%2))) & 0xF])); + 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) debugprint(("\n")); + 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 biggcd(Bignum av, Bignum bv) +{ Bignum a = copybn(av); Bignum b = copybn(bv); - diagbn("a = ", a); - diagbn("b = ", b); while (bignum_cmp(b, Zero) != 0) { - Bignum t = newbn(b[0]); - bigmod(a, b, t, NULL); - diagbn("t = ", t); - while (t[0] > 1 && t[t[0]] == 0) t[0]--; - freebn(a); - a = b; - b = t; + Bignum t = newbn(b[0]); + bigdivmod(a, b, t, NULL); + while (t[0] > 1 && t[t[0]] == 0) + t[0]--; + freebn(a); + a = b; + b = t; } freebn(b); @@ -766,7 +958,8 @@ Bignum biggcd(Bignum av, Bignum bv) { /* * Modular inverse, using Euclid's extended algorithm. */ -Bignum modinv(Bignum number, Bignum modulus) { +Bignum modinv(Bignum number, Bignum modulus) +{ Bignum a = copybn(modulus); Bignum b = copybn(number); Bignum xp = copybn(Zero); @@ -774,18 +967,20 @@ Bignum modinv(Bignum number, Bignum modulus) { int sign = +1; while (bignum_cmp(b, One) != 0) { - Bignum t = newbn(b[0]); - Bignum q = newbn(a[0]); - bigmod(a, b, t, q); - while (t[0] > 1 && t[t[0]] == 0) t[0]--; - freebn(a); - a = b; - b = t; - t = xp; - xp = x; - x = bigmuladd(q, xp, t); - sign = -sign; - freebn(t); + Bignum t = 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); @@ -794,24 +989,24 @@ Bignum modinv(Bignum number, Bignum modulus) { /* now we know that sign * x == 1, and that x < modulus */ if (sign < 0) { - /* set a new x to be modulus - x */ - Bignum newx = newbn(modulus[0]); - unsigned short carry = 0; - int maxspot = 1; - int i; - - for (i = 1; i <= newx[0]; i++) { - unsigned short aword = (i <= modulus[0] ? modulus[i] : 0); - unsigned short bword = (i <= x[0] ? x[i] : 0); - newx[i] = aword - bword - carry; - bword = ~bword; - carry = carry ? (newx[i] >= bword) : (newx[i] > bword); - if (newx[i] != 0) - maxspot = i; - } - newx[0] = maxspot; - freebn(x); - x = newx; + /* set a new x to be modulus - x */ + Bignum newx = newbn(modulus[0]); + BignumInt carry = 0; + int maxspot = 1; + int i; + + for (i = 1; i <= (int)newx[0]; i++) { + BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0); + BignumInt bword = (i <= (int)x[0] ? x[i] : 0); + newx[i] = aword - bword - carry; + bword = ~bword; + carry = carry ? (newx[i] >= bword) : (newx[i] > bword); + if (newx[i] != 0) + maxspot = i; + } + newx[0] = maxspot; + freebn(x); + x = newx; } /* and return. */ @@ -822,12 +1017,13 @@ Bignum modinv(Bignum number, Bignum modulus) { * Render a bignum into decimal. Return a malloced string holding * the decimal representation. */ -char *bignum_decimal(Bignum x) { +char *bignum_decimal(Bignum x) +{ int ndigits, ndigit; int i, iszero; - unsigned long carry; + BignumDblInt carry; char *ret; - unsigned short *workspace; + BignumInt *workspace; /* * First, estimate the number of digits. Since log(10)/log(2) @@ -841,39 +1037,44 @@ char *bignum_decimal(Bignum x) { * round up (rounding down might make it less than x again). * Therefore if we multiply the bit count by 28/93, rounding * up, we will have enough digits. + * + * i=0 (i.e., x=0) is an irritating special case. */ i = bignum_bitcount(x); - ndigits = (28*i + 92)/93; /* multiply by 28/93 and round up */ - ndigits++; /* allow for trailing \0 */ - ret = smalloc(ndigits); + 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 = smalloc(sizeof(unsigned short) * x[0]); - for (i = 0; i < x[0]; i++) - workspace[i] = x[x[0] - i]; + workspace = snewn(x[0], BignumInt); + for (i = 0; i < (int)x[0]; i++) + workspace[i] = x[x[0] - i]; /* * Next, write the decimal number starting with the last digit. * We use ordinary short division, dividing 10 into the * workspace. */ - ndigit = ndigits-1; + ndigit = ndigits - 1; ret[ndigit] = '\0'; do { - iszero = 1; - carry = 0; - for (i = 0; i < x[0]; i++) { - carry = (carry << 16) + workspace[i]; - workspace[i] = (unsigned short) (carry / 10); - if (workspace[i]) - iszero = 0; - carry %= 10; - } - ret[--ndigit] = (char)(carry + '0'); + iszero = 1; + carry = 0; + for (i = 0; i < (int)x[0]; i++) { + carry = (carry << BIGNUM_INT_BITS) + workspace[i]; + workspace[i] = (BignumInt) (carry / 10); + if (workspace[i]) + iszero = 0; + carry %= 10; + } + ret[--ndigit] = (char) (carry + '0'); } while (!iszero); /* @@ -881,10 +1082,11 @@ char *bignum_decimal(Bignum x) { * string. Correct if so. */ if (ndigit > 0) - memmove(ret, ret+ndigit, ndigits-ndigit); + memmove(ret, ret + ndigit, ndigits - ndigit); /* * Done. */ + sfree(workspace); return ret; }