diff options
Diffstat (limited to 'tools/plink/sshbn.c')
| -rw-r--r-- | tools/plink/sshbn.c | 1092 |
1 files changed, 0 insertions, 1092 deletions
diff --git a/tools/plink/sshbn.c b/tools/plink/sshbn.c deleted file mode 100644 index e9ff0cde4..000000000 --- a/tools/plink/sshbn.c +++ /dev/null @@ -1,1092 +0,0 @@ -/*
- * Bignum routines for RSA and DH and stuff.
- */
-
-#include <stdio.h>
-#include <assert.h>
-#include <stdlib.h>
-#include <string.h>
-
-#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.
- * <http://msdn2.microsoft.com/en-us/library/bf1dw62z.aspx> */
-#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 BignumInt *Bignum;
-
-#include "ssh.h"
-
-BignumInt bnZero[1] = { 0 };
-BignumInt bnOne[2] = { 1, 1 };
-
-/*
- * The Bignum format is an array of `BignumInt'. The first
- * element of the array counts the remaining elements. The
- * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_
- * significant digit first. (So it's trivial to extract the bit
- * with value 2^n for any n.)
- *
- * All Bignums in this module are positive. Negative numbers must
- * be dealt with outside it.
- *
- * INVARIANT: the most significant word of any Bignum must be
- * nonzero.
- */
-
-Bignum Zero = bnZero, One = bnOne;
-
-static Bignum newbn(int length)
-{
- Bignum b = snewn(length + 1, BignumInt);
- if (!b)
- abort(); /* FIXME */
- memset(b, 0, (length + 1) * sizeof(*b));
- b[0] = length;
- return b;
-}
-
-void bn_restore_invariant(Bignum b)
-{
- while (b[0] > 1 && b[b[0]] == 0)
- b[0]--;
-}
-
-Bignum copybn(Bignum orig)
-{
- Bignum b = snewn(orig[0] + 1, BignumInt);
- if (!b)
- abort(); /* FIXME */
- memcpy(b, orig, (orig[0] + 1) * sizeof(*b));
- return b;
-}
-
-void freebn(Bignum b)
-{
- /*
- * Burn the evidence, just in case.
- */
- memset(b, 0, sizeof(b[0]) * (b[0] + 1));
- sfree(b);
-}
-
-Bignum bn_power_2(int n)
-{
- Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
- bignum_set_bit(ret, n, 1);
- return ret;
-}
-
-/*
- * Compute c = a * b.
- * Input is in the first len words of a and b.
- * Result is returned in the first 2*len words of c.
- */
-static void internal_mul(BignumInt *a, BignumInt *b,
- BignumInt *c, int len)
-{
- int i, j;
- BignumDblInt t;
-
- for (j = 0; j < 2 * len; j++)
- c[j] = 0;
-
- for (i = len - 1; i >= 0; i--) {
- t = 0;
- for (j = len - 1; j >= 0; j--) {
- 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] = (BignumInt) t;
- }
-}
-
-static void internal_add_shifted(BignumInt *number,
- unsigned n, int shift)
-{
- int word = 1 + (shift / BIGNUM_INT_BITS);
- int bshift = shift % BIGNUM_INT_BITS;
- BignumDblInt addend;
-
- addend = (BignumDblInt)n << bshift;
-
- while (addend) {
- addend += number[word];
- number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
- addend >>= BIGNUM_INT_BITS;
- word++;
- }
-}
-
-/*
- * Compute a = a % m.
- * Input in first alen words of a and first mlen words of m.
- * Output in first alen words of a
- * (of which first alen-mlen words will be zero).
- * The MSW of m MUST have its high bit set.
- * Quotient is accumulated in the `quotient' array, which is a Bignum
- * rather than the internal bigendian format. Quotient parts are shifted
- * left by `qshift' before adding into quot.
- */
-static void internal_mod(BignumInt *a, int alen,
- BignumInt *m, int mlen,
- BignumInt *quot, int qshift)
-{
- BignumInt m0, m1;
- unsigned int h;
- int i, k;
-
- m0 = m[0];
- if (mlen > 1)
- m1 = m[1];
- else
- m1 = 0;
-
- for (i = 0; i <= alen - mlen; i++) {
- BignumDblInt t;
- unsigned int q, r, c, ai1;
-
- if (i == 0) {
- h = 0;
- } else {
- h = a[i - 1];
- a[i - 1] = 0;
- }
-
- if (i == alen - 1)
- ai1 = 0;
- else
- ai1 = a[i + 1];
-
- /* Find q = h:a[i] / m0 */
- if (h >= m0) {
- /*
- * Special case.
- *
- * To illustrate it, suppose a BignumInt is 8 bits, and
- * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then
- * our initial division will be 0xA123 / 0xA1, which
- * will give a quotient of 0x100 and a divide overflow.
- * However, the invariants in this division algorithm
- * are not violated, since the full number A1:23:... is
- * _less_ than the quotient prefix A1:B2:... and so the
- * following correction loop would have sorted it out.
- *
- * In this situation we set q to be the largest
- * quotient we _can_ stomach (0xFF, of course).
- */
- q = BIGNUM_INT_MASK;
- } else {
- /* Macro doesn't want an array subscript expression passed
- * into it (see definition), so use a temporary. */
- BignumInt tmplo = a[i];
- DIVMOD_WORD(q, r, h, tmplo, m0);
-
- /* Refine our estimate of q by looking at
- h:a[i]:a[i+1] / m0:m1 */
- t = MUL_WORD(m1, q);
- if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
- q--;
- t -= m1;
- r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
- if (r >= (BignumDblInt) m0 &&
- t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
- }
- }
-
- /* Subtract q * m from a[i...] */
- c = 0;
- for (k = mlen - 1; k >= 0; k--) {
- t = MUL_WORD(q, m[k]);
- t += c;
- c = (unsigned)(t >> BIGNUM_INT_BITS);
- if ((BignumInt) t > a[i + k])
- c++;
- a[i + k] -= (BignumInt) t;
- }
-
- /* Add back m in case of borrow */
- if (c != h) {
- t = 0;
- for (k = mlen - 1; k >= 0; k--) {
- t += m[k];
- t += a[i + k];
- a[i + k] = (BignumInt) t;
- t = t >> BIGNUM_INT_BITS;
- }
- q--;
- }
- if (quot)
- internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
- }
-}
-
-/*
- * Compute (base ^ exp) % mod.
- */
-Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
-{
- BignumInt *a, *b, *n, *m;
- int mshift;
- int mlen, i, j;
- Bignum base, result;
-
- /*
- * The most significant word of mod needs to be non-zero. It
- * should already be, but let's make sure.
- */
- assert(mod[mod[0]] != 0);
-
- /*
- * Make sure the base is smaller than the modulus, by reducing
- * it modulo the modulus if not.
- */
- base = bigmod(base_in, mod);
-
- /* Allocate m of size mlen, copy mod to m */
- /* We use big endian internally */
- mlen = mod[0];
- m = snewn(mlen, BignumInt);
- for (j = 0; j < mlen; j++)
- m[j] = mod[mod[0] - j];
-
- /* Shift m left to make msb bit set */
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
- break;
- if (mshift) {
- for (i = 0; i < mlen - 1; i++)
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
- m[mlen - 1] = m[mlen - 1] << mshift;
- }
-
- /* Allocate n of size mlen, copy base to n */
- n = snewn(mlen, BignumInt);
- i = mlen - base[0];
- for (j = 0; j < i; j++)
- n[j] = 0;
- for (j = 0; j < (int)base[0]; j++)
- n[i + j] = base[base[0] - j];
-
- /* Allocate a and b of size 2*mlen. Set a = 1 */
- a = snewn(2 * mlen, BignumInt);
- b = snewn(2 * mlen, BignumInt);
- for (i = 0; i < 2 * mlen; i++)
- a[i] = 0;
- a[2 * mlen - 1] = 1;
-
- /* Skip leading zero bits of exp. */
- i = 0;
- j = BIGNUM_INT_BITS-1;
- while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
- j--;
- if (j < 0) {
- i++;
- j = BIGNUM_INT_BITS-1;
- }
- }
-
- /* Main computation */
- while (i < (int)exp[0]) {
- while (j >= 0) {
- internal_mul(a + mlen, a + mlen, b, mlen);
- 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);
- } else {
- BignumInt *t;
- t = a;
- a = b;
- b = t;
- }
- j--;
- }
- i++;
- j = BIGNUM_INT_BITS-1;
- }
-
- /* Fixup result in case the modulus was shifted */
- if (mshift) {
- for (i = mlen - 1; i < 2 * mlen - 1; i++)
- a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
- a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;
- internal_mod(a, mlen * 2, m, mlen, NULL, 0);
- for (i = 2 * mlen - 1; i >= mlen; i--)
- a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
- }
-
- /* Copy result to buffer */
- result = newbn(mod[0]);
- for (i = 0; i < mlen; i++)
- result[result[0] - i] = a[i + mlen];
- while (result[0] > 1 && result[result[0]] == 0)
- result[0]--;
-
- /* Free temporary arrays */
- for (i = 0; i < 2 * mlen; i++)
- a[i] = 0;
- sfree(a);
- for (i = 0; i < 2 * mlen; i++)
- b[i] = 0;
- sfree(b);
- for (i = 0; i < mlen; i++)
- m[i] = 0;
- sfree(m);
- for (i = 0; i < mlen; i++)
- n[i] = 0;
- sfree(n);
-
- freebn(base);
-
- return result;
-}
-
-/*
- * Compute (p * q) % mod.
- * The most significant word of mod MUST be non-zero.
- * We assume that the result array is the same size as the mod array.
- */
-Bignum modmul(Bignum p, Bignum q, Bignum mod)
-{
- BignumInt *a, *n, *m, *o;
- int mshift;
- int pqlen, mlen, rlen, i, j;
- Bignum result;
-
- /* Allocate m of size mlen, copy mod to m */
- /* We use big endian internally */
- mlen = mod[0];
- m = snewn(mlen, BignumInt);
- for (j = 0; j < mlen; j++)
- m[j] = mod[mod[0] - j];
-
- /* Shift m left to make msb bit set */
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
- break;
- if (mshift) {
- for (i = 0; i < mlen - 1; i++)
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
- m[mlen - 1] = m[mlen - 1] << mshift;
- }
-
- pqlen = (p[0] > q[0] ? p[0] : q[0]);
-
- /* Allocate n of size pqlen, copy p to n */
- n = snewn(pqlen, BignumInt);
- i = pqlen - p[0];
- for (j = 0; j < i; j++)
- n[j] = 0;
- for (j = 0; j < (int)p[0]; j++)
- n[i + j] = p[p[0] - j];
-
- /* Allocate o of size pqlen, copy q to o */
- o = snewn(pqlen, BignumInt);
- i = pqlen - q[0];
- for (j = 0; j < i; j++)
- o[j] = 0;
- for (j = 0; j < (int)q[0]; j++)
- o[i + j] = q[q[0] - j];
-
- /* Allocate a of size 2*pqlen for result */
- a = snewn(2 * pqlen, BignumInt);
-
- /* Main computation */
- internal_mul(n, o, a, pqlen);
- internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
-
- /* Fixup result in case the modulus was shifted */
- if (mshift) {
- for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)
- a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
- a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;
- internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
- for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)
- a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
- }
-
- /* Copy result to buffer */
- rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);
- result = newbn(rlen);
- for (i = 0; i < rlen; i++)
- result[result[0] - i] = a[i + 2 * pqlen - rlen];
- while (result[0] > 1 && result[result[0]] == 0)
- result[0]--;
-
- /* Free temporary arrays */
- for (i = 0; i < 2 * pqlen; i++)
- a[i] = 0;
- sfree(a);
- for (i = 0; i < mlen; i++)
- m[i] = 0;
- sfree(m);
- for (i = 0; i < pqlen; i++)
- n[i] = 0;
- sfree(n);
- for (i = 0; i < pqlen; i++)
- o[i] = 0;
- sfree(o);
-
- return result;
-}
-
-/*
- * Compute p % mod.
- * The most significant word of mod MUST be non-zero.
- * We assume that the result array is the same size as the mod array.
- * We optionally write out a quotient if `quotient' is non-NULL.
- * We can avoid writing out the result if `result' is NULL.
- */
-static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)
-{
- BignumInt *n, *m;
- int mshift;
- int plen, mlen, i, j;
-
- /* Allocate m of size mlen, copy mod to m */
- /* We use big endian internally */
- mlen = mod[0];
- m = snewn(mlen, BignumInt);
- for (j = 0; j < mlen; j++)
- m[j] = mod[mod[0] - j];
-
- /* Shift m left to make msb bit set */
- for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
- if ((m[0] << mshift) & BIGNUM_TOP_BIT)
- break;
- if (mshift) {
- for (i = 0; i < mlen - 1; i++)
- m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
- m[mlen - 1] = m[mlen - 1] << mshift;
- }
-
- plen = p[0];
- /* Ensure plen > mlen */
- if (plen <= mlen)
- plen = mlen + 1;
-
- /* Allocate n of size plen, copy p to n */
- n = snewn(plen, BignumInt);
- for (j = 0; j < plen; j++)
- n[j] = 0;
- for (j = 1; j <= (int)p[0]; j++)
- n[plen - j] = p[j];
-
- /* Main computation */
- internal_mod(n, plen, m, mlen, quotient, mshift);
-
- /* Fixup result in case the modulus was shifted */
- if (mshift) {
- for (i = plen - mlen - 1; i < plen - 1; i++)
- n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));
- n[plen - 1] = n[plen - 1] << mshift;
- internal_mod(n, plen, m, mlen, quotient, 0);
- for (i = plen - 1; i >= plen - mlen; i--)
- n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));
- }
-
- /* Copy result to buffer */
- if (result) {
- for (i = 1; i <= (int)result[0]; i++) {
- int j = plen - i;
- result[i] = j >= 0 ? n[j] : 0;
- }
- }
-
- /* Free temporary arrays */
- for (i = 0; i < mlen; i++)
- m[i] = 0;
- sfree(m);
- for (i = 0; i < plen; i++)
- n[i] = 0;
- sfree(n);
-}
-
-/*
- * Decrement a number.
- */
-void decbn(Bignum bn)
-{
- int i = 1;
- while (i < (int)bn[0] && bn[i] == 0)
- bn[i++] = BIGNUM_INT_MASK;
- bn[i]--;
-}
-
-Bignum bignum_from_bytes(const unsigned char *data, int nbytes)
-{
- Bignum result;
- int w, i;
-
- w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */
-
- result = newbn(w);
- for (i = 1; i <= w; i++)
- result[i] = 0;
- for (i = nbytes; i--;) {
- unsigned char byte = *data++;
- result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);
- }
-
- while (result[0] > 1 && result[result[0]] == 0)
- result[0]--;
- return result;
-}
-
-/*
- * Read an SSH-1-format bignum from a data buffer. Return the number
- * of bytes consumed, or -1 if there wasn't enough data.
- */
-int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)
-{
- const unsigned char *p = data;
- int i;
- int w, b;
-
- if (len < 2)
- return -1;
-
- w = 0;
- for (i = 0; i < 2; i++)
- w = (w << 8) + *p++;
- b = (w + 7) / 8; /* bits -> bytes */
-
- if (len < b+2)
- return -1;
-
- if (!result) /* just return length */
- return b + 2;
-
- *result = bignum_from_bytes(p, b);
-
- return p + b - data;
-}
-
-/*
- * Return the bit count of a bignum, for SSH-1 encoding.
- */
-int bignum_bitcount(Bignum bn)
-{
- int bitcount = bn[0] * BIGNUM_INT_BITS - 1;
- while (bitcount >= 0
- && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;
- return bitcount + 1;
-}
-
-/*
- * Return the byte length of a bignum when SSH-1 encoded.
- */
-int ssh1_bignum_length(Bignum bn)
-{
- return 2 + (bignum_bitcount(bn) + 7) / 8;
-}
-
-/*
- * Return the byte length of a bignum when SSH-2 encoded.
- */
-int ssh2_bignum_length(Bignum bn)
-{
- return 4 + (bignum_bitcount(bn) + 8) / 8;
-}
-
-/*
- * Return a byte from a bignum; 0 is least significant, etc.
- */
-int bignum_byte(Bignum bn, int i)
-{
- if (i >= (int)(BIGNUM_INT_BYTES * bn[0]))
- return 0; /* beyond the end */
- else
- return (bn[i / BIGNUM_INT_BYTES + 1] >>
- ((i % BIGNUM_INT_BYTES)*8)) & 0xFF;
-}
-
-/*
- * Return a bit from a bignum; 0 is least significant, etc.
- */
-int bignum_bit(Bignum bn, int i)
-{
- if (i >= (int)(BIGNUM_INT_BITS * bn[0]))
- return 0; /* beyond the end */
- else
- return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;
-}
-
-/*
- * Set a bit in a bignum; 0 is least significant, etc.
- */
-void bignum_set_bit(Bignum bn, int bitnum, int value)
-{
- if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
- abort(); /* beyond the end */
- else {
- int v = bitnum / BIGNUM_INT_BITS + 1;
- int mask = 1 << (bitnum % BIGNUM_INT_BITS);
- if (value)
- bn[v] |= mask;
- else
- bn[v] &= ~mask;
- }
-}
-
-/*
- * Write a SSH-1-format bignum into a buffer. It is assumed the
- * buffer is big enough. Returns the number of bytes used.
- */
-int ssh1_write_bignum(void *data, Bignum bn)
-{
- unsigned char *p = data;
- int len = ssh1_bignum_length(bn);
- int i;
- int bitc = bignum_bitcount(bn);
-
- *p++ = (bitc >> 8) & 0xFF;
- *p++ = (bitc) & 0xFF;
- for (i = len - 2; i--;)
- *p++ = bignum_byte(bn, i);
- return len;
-}
-
-/*
- * Compare two bignums. Returns like strcmp.
- */
-int bignum_cmp(Bignum a, Bignum b)
-{
- int amax = a[0], bmax = b[0];
- int i = (amax > bmax ? amax : bmax);
- while (i) {
- BignumInt aval = (i > amax ? 0 : a[i]);
- BignumInt bval = (i > bmax ? 0 : b[i]);
- if (aval < bval)
- return -1;
- if (aval > bval)
- return +1;
- i--;
- }
- return 0;
-}
-
-/*
- * Right-shift one bignum to form another.
- */
-Bignum bignum_rshift(Bignum a, int shift)
-{
- Bignum ret;
- int i, shiftw, shiftb, shiftbb, bits;
- BignumInt ai, ai1;
-
- bits = bignum_bitcount(a) - shift;
- ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
-
- if (ret) {
- shiftw = shift / BIGNUM_INT_BITS;
- shiftb = shift % BIGNUM_INT_BITS;
- shiftbb = BIGNUM_INT_BITS - shiftb;
-
- ai1 = a[shiftw + 1];
- for (i = 1; i <= (int)ret[0]; i++) {
- ai = ai1;
- ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0);
- ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK;
- }
- }
-
- return ret;
-}
-
-/*
- * Non-modular multiplication and addition.
- */
-Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)
-{
- int alen = a[0], blen = b[0];
- int mlen = (alen > blen ? alen : blen);
- int rlen, i, maxspot;
- BignumInt *workspace;
- Bignum ret;
-
- /* mlen space for a, mlen space for b, 2*mlen for result */
- workspace = snewn(mlen * 4, BignumInt);
- for (i = 0; i < mlen; i++) {
- workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);
- workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);
- }
-
- internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,
- workspace + 2 * mlen, mlen);
-
- /* now just copy the result back */
- rlen = alen + blen + 1;
- if (addend && rlen <= (int)addend[0])
- rlen = addend[0] + 1;
- ret = newbn(rlen);
- maxspot = 0;
- for (i = 1; i <= (int)ret[0]; i++) {
- ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);
- if (ret[i] != 0)
- maxspot = i;
- }
- ret[0] = maxspot;
-
- /* now add in the addend, if any */
- if (addend) {
- BignumDblInt carry = 0;
- for (i = 1; i <= rlen; i++) {
- carry += (i <= (int)ret[0] ? ret[i] : 0);
- carry += (i <= (int)addend[0] ? addend[i] : 0);
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
- carry >>= BIGNUM_INT_BITS;
- if (ret[i] != 0 && i > maxspot)
- maxspot = i;
- }
- }
- ret[0] = maxspot;
-
- sfree(workspace);
- return ret;
-}
-
-/*
- * Non-modular multiplication.
- */
-Bignum bigmul(Bignum a, Bignum b)
-{
- return bigmuladd(a, b, NULL);
-}
-
-/*
- * Create a bignum which is the bitmask covering another one. That
- * is, the smallest integer which is >= N and is also one less than
- * a power of two.
- */
-Bignum bignum_bitmask(Bignum n)
-{
- Bignum ret = copybn(n);
- int i;
- BignumInt j;
-
- i = ret[0];
- while (n[i] == 0 && i > 0)
- i--;
- if (i <= 0)
- return ret; /* input was zero */
- j = 1;
- while (j < n[i])
- j = 2 * j + 1;
- ret[i] = j;
- while (--i > 0)
- ret[i] = BIGNUM_INT_MASK;
- return ret;
-}
-
-/*
- * Convert a (max 32-bit) long into a bignum.
- */
-Bignum bignum_from_long(unsigned long nn)
-{
- Bignum ret;
- BignumDblInt n = nn;
-
- ret = newbn(3);
- ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);
- ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);
- ret[3] = 0;
- ret[0] = (ret[2] ? 2 : 1);
- return ret;
-}
-
-/*
- * Add a long to a bignum.
- */
-Bignum bignum_add_long(Bignum number, unsigned long addendx)
-{
- Bignum ret = newbn(number[0] + 1);
- int i, maxspot = 0;
- BignumDblInt carry = 0, addend = addendx;
-
- for (i = 1; i <= (int)ret[0]; i++) {
- carry += addend & BIGNUM_INT_MASK;
- carry += (i <= (int)number[0] ? number[i] : 0);
- addend >>= BIGNUM_INT_BITS;
- ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
- carry >>= BIGNUM_INT_BITS;
- if (ret[i] != 0)
- maxspot = i;
- }
- ret[0] = maxspot;
- return ret;
-}
-
-/*
- * Compute the residue of a bignum, modulo a (max 16-bit) short.
- */
-unsigned short bignum_mod_short(Bignum number, unsigned short modulus)
-{
- BignumDblInt mod, r;
- int i;
-
- r = 0;
- mod = modulus;
- for (i = number[0]; i > 0; i--)
- r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;
- return (unsigned short) r;
-}
-
-#ifdef DEBUG
-void diagbn(char *prefix, Bignum md)
-{
- int i, nibbles, morenibbles;
- static const char hex[] = "0123456789ABCDEF";
-
- debug(("%s0x", prefix ? prefix : ""));
-
- nibbles = (3 + bignum_bitcount(md)) / 4;
- if (nibbles < 1)
- nibbles = 1;
- morenibbles = 4 * md[0] - nibbles;
- for (i = 0; i < morenibbles; i++)
- debug(("-"));
- for (i = nibbles; i--;)
- debug(("%c",
- hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));
-
- if (prefix)
- debug(("\n"));
-}
-#endif
-
-/*
- * Simple division.
- */
-Bignum bigdiv(Bignum a, Bignum b)
-{
- Bignum q = newbn(a[0]);
- bigdivmod(a, b, NULL, q);
- return q;
-}
-
-/*
- * Simple remainder.
- */
-Bignum bigmod(Bignum a, Bignum b)
-{
- Bignum r = newbn(b[0]);
- bigdivmod(a, b, r, NULL);
- return r;
-}
-
-/*
- * Greatest common divisor.
- */
-Bignum biggcd(Bignum av, Bignum bv)
-{
- Bignum a = copybn(av);
- Bignum b = copybn(bv);
-
- while (bignum_cmp(b, Zero) != 0) {
- Bignum t = newbn(b[0]);
- bigdivmod(a, b, t, NULL);
- while (t[0] > 1 && t[t[0]] == 0)
- t[0]--;
- freebn(a);
- a = b;
- b = t;
- }
-
- freebn(b);
- return a;
-}
-
-/*
- * Modular inverse, using Euclid's extended algorithm.
- */
-Bignum modinv(Bignum number, Bignum modulus)
-{
- Bignum a = copybn(modulus);
- Bignum b = copybn(number);
- Bignum xp = copybn(Zero);
- Bignum x = copybn(One);
- int sign = +1;
-
- while (bignum_cmp(b, One) != 0) {
- Bignum t = newbn(b[0]);
- Bignum q = newbn(a[0]);
- bigdivmod(a, b, t, q);
- while (t[0] > 1 && t[t[0]] == 0)
- t[0]--;
- freebn(a);
- a = b;
- b = t;
- t = xp;
- xp = x;
- x = bigmuladd(q, xp, t);
- sign = -sign;
- freebn(t);
- freebn(q);
- }
-
- freebn(b);
- freebn(a);
- freebn(xp);
-
- /* now we know that sign * x == 1, and that x < modulus */
- if (sign < 0) {
- /* set a new x to be modulus - x */
- Bignum newx = newbn(modulus[0]);
- BignumInt carry = 0;
- int maxspot = 1;
- int i;
-
- for (i = 1; i <= (int)newx[0]; i++) {
- BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);
- BignumInt bword = (i <= (int)x[0] ? x[i] : 0);
- newx[i] = aword - bword - carry;
- bword = ~bword;
- carry = carry ? (newx[i] >= bword) : (newx[i] > bword);
- if (newx[i] != 0)
- maxspot = i;
- }
- newx[0] = maxspot;
- freebn(x);
- x = newx;
- }
-
- /* and return. */
- return x;
-}
-
-/*
- * Render a bignum into decimal. Return a malloced string holding
- * the decimal representation.
- */
-char *bignum_decimal(Bignum x)
-{
- int ndigits, ndigit;
- int i, iszero;
- BignumDblInt carry;
- char *ret;
- BignumInt *workspace;
-
- /*
- * First, estimate the number of digits. Since log(10)/log(2)
- * is just greater than 93/28 (the joys of continued fraction
- * approximations...) we know that for every 93 bits, we need
- * at most 28 digits. This will tell us how much to malloc.
- *
- * Formally: if x has i bits, that means x is strictly less
- * than 2^i. Since 2 is less than 10^(28/93), this is less than
- * 10^(28i/93). We need an integer power of ten, so we must
- * round up (rounding down might make it less than x again).
- * Therefore if we multiply the bit count by 28/93, rounding
- * up, we will have enough digits.
- *
- * i=0 (i.e., x=0) is an irritating special case.
- */
- i = bignum_bitcount(x);
- if (!i)
- ndigits = 1; /* x = 0 */
- else
- ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */
- ndigits++; /* allow for trailing \0 */
- ret = snewn(ndigits, char);
-
- /*
- * Now allocate some workspace to hold the binary form as we
- * repeatedly divide it by ten. Initialise this to the
- * big-endian form of the number.
- */
- workspace = snewn(x[0], BignumInt);
- for (i = 0; i < (int)x[0]; i++)
- workspace[i] = x[x[0] - i];
-
- /*
- * Next, write the decimal number starting with the last digit.
- * We use ordinary short division, dividing 10 into the
- * workspace.
- */
- ndigit = ndigits - 1;
- ret[ndigit] = '\0';
- do {
- iszero = 1;
- carry = 0;
- for (i = 0; i < (int)x[0]; i++) {
- carry = (carry << BIGNUM_INT_BITS) + workspace[i];
- workspace[i] = (BignumInt) (carry / 10);
- if (workspace[i])
- iszero = 0;
- carry %= 10;
- }
- ret[--ndigit] = (char) (carry + '0');
- } while (!iszero);
-
- /*
- * There's a chance we've fallen short of the start of the
- * string. Correct if so.
- */
- if (ndigit > 0)
- memmove(ret, ret + ndigit, ndigits - ndigit);
-
- /*
- * Done.
- */
- sfree(workspace);
- return ret;
-}
|