#include <stdlib.h>
#include <string.h>
-#include <stdio.h> /* FIXME */
-#include <stdarg.h> /* FIXME */
-#include <windows.h> /* FIXME */
-#include "putty.h" /* FIXME */
+#define BIGNUM_INTERNAL
+typedef unsigned short *Bignum;
#include "ssh.h"
unsigned short bnZero[1] = { 0 };
unsigned short bnOne[2] = { 1, 1 };
+/*
+ * The Bignum format is an array of `unsigned short'. The first
+ * element of the array counts the remaining elements. The
+ * remaining elements express the actual number, base 2^16, _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 = smalloc((length+1)*sizeof(unsigned short));
if (!b)
abort(); /* FIXME */
memset(b, 0, (length+1)*sizeof(*b));
return b;
}
+void bn_restore_invariant(Bignum b) {
+ while (b[0] > 1 && b[b[0]] == 0) b[0]--;
+}
+
Bignum copybn(Bignum orig) {
- Bignum b = malloc((orig[0]+1)*sizeof(unsigned short));
+ Bignum b = smalloc((orig[0]+1)*sizeof(unsigned short));
if (!b)
abort(); /* FIXME */
memcpy(b, orig, (orig[0]+1)*sizeof(*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+15)/16);
+ 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(unsigned short *a, unsigned short *b,
+ unsigned short *c, int len)
{
int i, j;
unsigned long ai, 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];
}
}
+static void internal_add_shifted(unsigned short *number,
+ unsigned n, int shift) {
+ int word = 1 + (shift / 16);
+ int bshift = shift % 16;
+ unsigned long addend;
+
+ addend = n << bshift;
+
+ while (addend) {
+ addend += number[word];
+ number[word] = (unsigned short) addend & 0xFFFF;
+ addend >>= 16;
+ 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(unsigned short *a, int alen,
+ unsigned short *m, int mlen,
+ unsigned short *quot, int qshift)
{
unsigned short 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++) {
+ for (i = 0; i <= alen-mlen; i++) {
unsigned long t;
- unsigned int q, r, c;
+ unsigned int q, r, c, ai1;
if (i == 0) {
h = 0;
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;
/* 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]) {
+ 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) + a[i+1])
+ t > ((unsigned long) r << 16) + ai1)
q--;
}
- /* Substract q * m from a[i...] */
+ /* Subtract q * m from a[i...] */
c = 0;
- for (k = len - 1; k >= 0; k--) {
+ for (k = mlen - 1; k >= 0; k--) {
t = (long) q * (long) m[k];
t += c;
c = t >> 16;
/* 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;
}
+ q--;
}
+ if (quot)
+ internal_add_shifted(quot, q, qshift + 16 * (alen-mlen-i));
}
}
* 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, Bignum exp, Bignum mod)
{
unsigned short *a, *b, *n, *m;
int mshift;
int mlen, 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));
+ m = smalloc(mlen * sizeof(unsigned short));
for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
}
/* Allocate n of size mlen, copy base to n */
- n = malloc(mlen * sizeof(unsigned short));
+ n = smalloc(mlen * sizeof(unsigned short));
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];
/* 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));
+ 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;
/* Main computation */
while (i < 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;
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);
+ 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));
}
/* 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; 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);
+
+ 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;
int mshift;
int pqlen, mlen, 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));
+ m = smalloc(mlen * sizeof(unsigned short));
for (j = 0; j < mlen; j++) m[j] = mod[mod[0] - j];
/* Shift m left to make msb bit set */
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 = smalloc(pqlen * sizeof(unsigned short));
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];
/* Allocate o of size pqlen, copy q to o */
- o = malloc(pqlen * sizeof(unsigned short));
+ o = smalloc(pqlen * sizeof(unsigned short));
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];
/* Allocate a of size 2*pqlen for result */
- a = malloc(2 * pqlen * sizeof(unsigned short));
+ a = smalloc(2 * pqlen * sizeof(unsigned short));
/* 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);
+ 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));
}
/* Copy result to buffer */
+ result = newbn(mod[0]);
for (i = 0; i < mlen; i++)
result[result[0] - i] = a[i+2*pqlen-mlen];
+ while (result[0] > 1 && result[result[0]] == 0) result[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 < 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.
+ */
+void bigmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)
+{
+ unsigned short *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];
+
+ /* Shift m left to make msb bit set */
+ for (mshift = 0; mshift < 15; mshift++)
+ if ((m[0] << mshift) & 0x8000) 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;
+ }
+
+ plen = p[0];
+ /* Ensure plen > mlen */
+ 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];
+
+ /* 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] >> (16-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));
+ }
+
+ /* Copy result to buffer */
+ for (i = 1; i <= 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);
}
/*
bn[i]--;
}
+Bignum bignum_from_bytes(unsigned char *data, int nbytes) {
+ Bignum result;
+ int w, i;
+
+ w = (nbytes+1)/2; /* 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;
+ }
+
+ 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.
*/
int ssh1_read_bignum(unsigned char *data, Bignum *result) {
unsigned char *p = data;
- Bignum bn;
int i;
int w, b;
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);
+ if (!result) /* just return length */
+ return b + 2;
- 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;
+ *result = bignum_from_bytes(p, b);
+
+ return p + b - data;
+}
+
+/*
+ * Return the bit count of a bignum, for ssh1 encoding.
+ */
+int ssh1_bignum_bitcount(Bignum bn) {
+ int bitcount = bn[0] * 16 - 1;
+ while (bitcount >= 0 && (bn[bitcount/16+1] >> (bitcount % 16)) == 0)
+ bitcount--;
+ return bitcount + 1;
+}
+
+/*
+ * Return the byte length of a bignum when ssh1 encoded.
+ */
+int ssh1_bignum_length(Bignum bn) {
+ return 2 + (ssh1_bignum_bitcount(bn)+7)/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;
+ else
+ return (bn[i/2+1] ) & 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 */
+ else
+ return (bn[i/16+1] >> (i%16)) & 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 */
+ else {
+ int v = bitnum/16+1;
+ int mask = 1 << (bitnum%16);
+ if (value)
+ bn[v] |= mask;
else
- bn[1+i/2] |= byte;
+ bn[v] &= ~mask;
}
+}
- *result = bn;
+/*
+ * Write a ssh1-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 = ssh1_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) {
+ 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--;
+ }
+ return 0;
+}
+
+/*
+ * Right-shift one bignum to form another.
+ */
+Bignum bignum_rshift(Bignum a, int shift) {
+ Bignum ret;
+ int i, shiftw, shiftb, shiftbb, bits;
+ unsigned short ai, ai1;
+
+ bits = ssh1_bignum_bitcount(a) - shift;
+ ret = newbn((bits+15)/16);
+
+ 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;
+ }
+ }
+
+ 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;
+ unsigned short *workspace;
+ Bignum ret;
+
+ /* mlen space for a, mlen space for b, 2*mlen for result */
+ workspace = smalloc(mlen * 4 * sizeof(unsigned short));
+ 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);
+ }
+
+ 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;
+ 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;
+ }
+ 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;
+ }
+ }
+ ret[0] = maxspot;
+
+ 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;
+ unsigned short 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] = 0xFFFF;
+ return ret;
+}
+
+/*
+ * Convert a (max 16-bit) short into a bignum.
+ */
+Bignum bignum_from_short(unsigned short n) {
+ Bignum ret;
+
+ ret = newbn(2);
+ ret[1] = n & 0xFFFF;
+ ret[2] = (n >> 16) & 0xFFFF;
+ 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);
+ 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;
+ }
+ 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) {
+ unsigned long mod, r;
+ int i;
+
+ r = 0;
+ mod = modulus;
+ for (i = number[0]; i > 0; i--)
+ r = (r * 65536 + number[i]) % mod;
+ return (unsigned short) r;
+}
+
+void diagbn(char *prefix, Bignum md) {
+ int i, nibbles, morenibbles;
+ static const char hex[] = "0123456789ABCDEF";
+
+ printf("%s0x", prefix ? prefix : "");
+
+ nibbles = (3 + ssh1_bignum_bitcount(md))/4; if (nibbles<1) nibbles=1;
+ morenibbles = 4*md[0] - nibbles;
+ for (i=0; i<morenibbles; i++) putchar('-');
+ for (i=nibbles; i-- ;)
+ putchar(hex[(bignum_byte(md, i/2) >> (4*(i%2))) & 0xF]);
+
+ if (prefix) putchar('\n');
+}
+
+/*
+ * Greatest common divisor.
+ */
+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;
+ }
+
+ 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]);
+ 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);
+ }
- return p - data;
+ 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]);
+ 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;
+ }
+
+ /* 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;
+ unsigned long carry;
+ char *ret;
+ unsigned short *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 = ssh1_bignum_bitcount(x);
+ ndigits = (28*i + 92)/93; /* multiply by 28/93 and round up */
+ ndigits++; /* allow for trailing \0 */
+ ret = smalloc(ndigits);
+
+ /*
+ * 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];
+
+ /*
+ * 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 < 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');
+ } 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.
+ */
+ return ret;
}
projects / u / mdw / putty / blobdiff