*/
#include <stdio.h>
+#include <assert.h>
#include <stdlib.h>
#include <string.h>
-#include <stdio.h> /* FIXME */
-#include <stdarg.h> /* FIXME */
-#include <windows.h> /* FIXME */
-#include "putty.h" /* FIXME */
+#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"
-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 `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;
-Bignum newbn(int length) {
- Bignum b = malloc((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;
}
-Bignum copybn(Bignum orig) {
- Bignum b = malloc((orig[0]+1)*sizeof(unsigned short));
+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));
+ memcpy(b, orig, (orig[0] + 1) * sizeof(*b));
return b;
}
-void freebn(Bignum b) {
+void freebn(Bignum b)
+{
/*
* Burn the evidence, just in case.
*/
memset(b, 0, sizeof(b[0]) * (b[0] + 1));
- free(b);
+ sfree(b);
+}
+
+Bignum bn_power_2(int n)
+{
+ Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
+ bignum_set_bit(ret, n, 1);
+ return ret;
}
/*
* Input is in the first len words of a and b.
* Result is returned in the first 2*len words of c.
*/
-static void bigmul(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 = len - 1; j >= 0; j--)
- c[j+len] = 0;
+ 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(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 len2 words of a and first len words of m.
- * Output in first len2 words of a
- * (of which first len2-len words will be zero).
+ * 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 bigmod(unsigned short *a, unsigned short *m,
- int len, int len2)
+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;
- /* Special case for len == 1 */
- if (len == 1) {
- a[1] = (((long) a[0] << 16) + a[1]) % m[0];
- a[0] = 0;
- return;
- }
-
m0 = m[0];
- m1 = m[1];
+ if (mlen > 1)
+ m1 = m[1];
+ else
+ m1 = 0;
- for (i = 0; i <= len2-len; i++) {
- unsigned long t;
- unsigned int q, r, c;
+ 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];
+
/* 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) + a[i+1]) {
- q--;
- t -= m1;
- r = (r + m0) & 0xffff; /* overflow? */
- if (r >= (unsigned long)m0 &&
- t > ((unsigned long) r << 16) + a[i+1])
+ 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--;
+ }
}
- /* Substract q * m from a[i...] */
+ /* Subtract q * m from a[i...] */
c = 0;
- for (k = len - 1; k >= 0; k--) {
- t = (long) q * (long) m[k];
+ for (k = mlen - 1; k >= 0; 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 */
if (c != h) {
t = 0;
- for (k = len - 1; k >= 0; k--) {
+ 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--;
}
+ 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.
*/
-void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result)
+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 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 = malloc(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 = malloc(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 = malloc(2 * mlen * sizeof(unsigned short));
- b = malloc(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) {
- bigmul(a + mlen, a + mlen, b, mlen);
- bigmod(b, m, mlen, mlen*2);
+ 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) {
- bigmul(b + mlen, n, a, mlen);
- bigmod(a, m, mlen, mlen*2);
+ internal_mul(b + mlen, n, a, mlen);
+ 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;
- bigmod(a, m, mlen, mlen*2);
- 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];
+ 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; free(a);
- for (i = 0; i < 2*mlen; i++) b[i] = 0; free(b);
- for (i = 0; i < mlen; i++) m[i] = 0; free(m);
- for (i = 0; i < mlen; i++) n[i] = 0; free(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;
}
/*
* The most significant word of mod MUST be non-zero.
* We assume that the result array is the same size as the mod array.
*/
-void modmul(Bignum p, Bignum q, Bignum mod, Bignum result)
+Bignum modmul(Bignum p, Bignum q, Bignum mod)
{
- unsigned short *a, *n, *m, *o;
+ BignumInt *a, *n, *m, *o;
int mshift;
- int pqlen, mlen, i, j;
+ 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 = malloc(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 = malloc(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 = malloc(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 = malloc(2 * pqlen * sizeof(unsigned short));
+ a = snewn(2 * pqlen, BignumInt);
/* Main computation */
- bigmul(n, o, a, pqlen);
- bigmod(a, m, mlen, 2*pqlen);
+ 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] >> (16-mshift));
- a[2*pqlen-1] = a[2*pqlen-1] << mshift;
- bigmod(a, m, mlen, pqlen*2);
- 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);
+ 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++)
- result[result[0] - i] = a[i+2*pqlen-mlen];
+ 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 < 2*pqlen; i++) a[i] = 0; free(a);
- for (i = 0; i < mlen; i++) m[i] = 0; free(m);
- for (i = 0; i < pqlen; i++) n[i] = 0; free(n);
- for (i = 0; i < pqlen; i++) o[i] = 0; free(o);
+ 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(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 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;
- Bignum bn;
+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 */
- w = (w+15)/16; /* bits -> words */
-
- bn = newbn(w);
-
- for (i=1; i<=w; i++)
- bn[i] = 0;
- for (i=b; i-- ;) {
- unsigned char byte = *p++;
- if (i & 1)
- bn[1+i/2] |= byte<<8;
- else
- bn[1+i/2] |= byte;
- }
+ for (i = 0; i < 2; i++)
+ w = (w << 8) + *p++;
+ b = (w + 7) / 8; /* bits -> bytes */
+
+ if (len < b+2)
+ return -1;
- *result = bn;
+ if (!result) /* just return length */
+ return b + 2;
- return p - data;
+ *result = bignum_from_bytes(p, b);
+
+ return p + b - data;
}
/*
- * Return the bit count of a bignum, for ssh1 encoding.
+ * Return the bit count of a bignum, for SSH-1 encoding.
*/
-int ssh1_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 + (ssh1_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 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 >= 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;
}
/*
- * Write a ssh1-format bignum into a buffer. It is assumed the
+ * 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) {
+int ssh1_write_bignum(void *data, Bignum bn)
+{
unsigned char *p = data;
int len = ssh1_bignum_length(bn);
int i;
- int bitc = ssh1_bignum_bitcount(bn);
+ 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 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;
+}
projects / u / mdw / putty / blobdiff