X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/a52f067e0510f49ff0473878280521bd11cd3c78..80b105717eaccb493391330a0a812be0af2a40e7:/sshbn.c diff --git a/sshbn.c b/sshbn.c index dbf223d6..587fc8f3 100644 --- a/sshbn.c +++ b/sshbn.c @@ -6,20 +6,32 @@ #include #include -#include /* FIXME */ -#include /* FIXME */ -#include /* 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)); @@ -27,8 +39,12 @@ Bignum newbn(int 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 = 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)); @@ -40,7 +56,13 @@ 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+15)/16); + bignum_set_bit(ret, n, 1); + return ret; } /* @@ -48,14 +70,14 @@ void freebn(Bignum 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 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]; @@ -70,33 +92,49 @@ static void bigmul(unsigned short *a, unsigned short *b, unsigned short *c, } } +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; @@ -105,6 +143,11 @@ static void bigmod(unsigned short *a, unsigned short *m, 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; @@ -113,18 +156,18 @@ static void bigmod(unsigned short *a, unsigned short *m, /* 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; @@ -135,13 +178,16 @@ static void bigmod(unsigned short *a, unsigned short *m, /* 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)); } } @@ -151,16 +197,17 @@ static void bigmod(unsigned short *a, unsigned short *m, * 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 */ @@ -173,14 +220,14 @@ void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) } /* 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; @@ -194,11 +241,11 @@ void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) /* 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; @@ -213,20 +260,24 @@ void modpow(Bignum base, Bignum exp, Bignum mod, Bignum result) 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; } /* @@ -234,16 +285,17 @@ void modpow(Bignum base, Bignum exp, Bignum mod, Bignum 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; + 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)); + 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 */ @@ -258,43 +310,108 @@ void modmul(Bignum p, Bignum q, Bignum mod, Bignum result) 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 */ - for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i+2*pqlen-mlen]; + 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; 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); } /* @@ -307,41 +424,47 @@ void decbn(Bignum bn) { 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 */ if (!result) /* just return length */ return b + 2; - 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; - } - - *result = bn; + *result = bignum_from_bytes(p, b); - return p - data; + return p + b - data; } /* @@ -349,7 +472,6 @@ int ssh1_read_bignum(unsigned char *data, Bignum *result) { */ 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; @@ -375,6 +497,32 @@ int bignum_byte(Bignum bn, int i) { } /* + * 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[v] &= ~mask; + } +} + +/* * Write a ssh1-format bignum into a buffer. It is assumed the * buffer is big enough. Returns the number of bytes used. */ @@ -390,3 +538,338 @@ int ssh1_write_bignum(void *data, Bignum bn) { *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> (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); + } + + 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; +}