#include <assert.h>
#include <stdlib.h>
#include <string.h>
+#include <limits.h>
+#include <ctype.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)
-#elif defined _LP64
-/* 64-bit architectures can do 32x32->64 chunks at a time */
-typedef unsigned int BignumInt;
-typedef unsigned long BignumDblInt;
-#define BIGNUM_INT_MASK 0xFFFFFFFFU
-#define BIGNUM_TOP_BIT 0x80000000U
-#define BIGNUM_INT_BITS 32
-#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)
-#elif defined _LLP64
-/* 64-bit architectures in which unsigned long is 32 bits, not 64 */
-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) do { \
- BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
- q = n / w; \
- r = n % w; \
-} while (0)
-#else
-/* Fallback for all other cases */
-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)
+#include "sshbn.h"
#define BIGNUM_INTERNAL
typedef BignumInt *Bignum;
BignumInt bnZero[1] = { 0 };
BignumInt bnOne[2] = { 1, 1 };
+BignumInt bnTen[2] = { 1, 10 };
/*
* The Bignum format is an array of `BignumInt'. The first
* nonzero.
*/
-Bignum Zero = bnZero, One = bnOne;
+Bignum Zero = bnZero, One = bnOne, Ten = bnTen;
static Bignum newbn(int length)
{
- Bignum b = snewn(length + 1, BignumInt);
- if (!b)
- abort(); /* FIXME */
+ Bignum b;
+
+ assert(length >= 0 && length < INT_MAX / BIGNUM_INT_BITS);
+
+ b = snewn(length + 1, BignumInt);
memset(b, 0, (length + 1) * sizeof(*b));
b[0] = length;
return b;
Bignum bn_power_2(int n)
{
- Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
+ Bignum ret;
+
+ assert(n >= 0);
+
+ ret = newbn(n / BIGNUM_INT_BITS + 1);
bignum_set_bit(ret, n, 1);
return ret;
}
}
static void internal_add_shifted(BignumInt *number,
- unsigned n, int shift)
+ BignumInt n, int shift)
{
int word = 1 + (shift / BIGNUM_INT_BITS);
int bshift = shift % BIGNUM_INT_BITS;
addend = (BignumDblInt)n << bshift;
while (addend) {
+ assert(word <= number[0]);
addend += number[word];
number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
addend >>= BIGNUM_INT_BITS;
BignumInt *m, int mlen,
BignumInt *quot, int qshift)
{
- BignumInt m0, m1;
- unsigned int h;
+ BignumInt m0, m1, h;
int i, k;
m0 = m[0];
+ assert(m0 >> (BIGNUM_INT_BITS-1) == 1);
if (mlen > 1)
m1 = m[1];
else
for (i = 0; i <= alen - mlen; i++) {
BignumDblInt t;
- unsigned int q, r, c, ai1;
+ BignumInt q, r, c, ai1;
if (i == 0) {
h = 0;
for (k = mlen - 1; k >= 0; k--) {
t = MUL_WORD(q, m[k]);
t += c;
- c = (unsigned)(t >> BIGNUM_INT_BITS);
+ c = (BignumInt)(t >> BIGNUM_INT_BITS);
if ((BignumInt) t > a[i + k])
c++;
a[i + k] -= (BignumInt) t;
/* 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) {
+ while (i < (int)exp[0] && (exp[exp[0] - i] & ((BignumInt)1 << j)) == 0) {
j--;
if (j < 0) {
i++;
while (j >= 0) {
internal_mul(a + mlen, a + mlen, b, mlen, scratch);
internal_mod(b, mlen * 2, m, mlen, NULL, 0);
- if ((exp[exp[0] - i] & (1 << j)) != 0) {
+ if ((exp[exp[0] - i] & ((BignumInt)1 << j)) != 0) {
internal_mul(b + mlen, n, a, mlen, scratch);
internal_mod(a, mlen * 2, m, mlen, NULL, 0);
} else {
result[0]--;
/* Free temporary arrays */
- for (i = 0; i < 2 * mlen; i++)
- a[i] = 0;
+ smemclr(a, 2 * mlen * sizeof(*a));
sfree(a);
- for (i = 0; i < scratchlen; i++)
- scratch[i] = 0;
+ smemclr(scratch, scratchlen * sizeof(*scratch));
sfree(scratch);
- for (i = 0; i < 2 * mlen; i++)
- b[i] = 0;
+ smemclr(b, 2 * mlen * sizeof(*b));
sfree(b);
- for (i = 0; i < mlen; i++)
- m[i] = 0;
+ smemclr(m, mlen * sizeof(*m));
sfree(m);
- for (i = 0; i < mlen; i++)
- n[i] = 0;
+ smemclr(n, mlen * sizeof(*n));
sfree(n);
freebn(base);
len = mod[0];
r = bn_power_2(BIGNUM_INT_BITS * len);
inv = modinv(mod, r);
+ assert(inv); /* cannot fail, since mod is odd and r is a power of 2 */
/*
* Multiply the base by r mod n, to get it into Montgomery
/* 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) {
+ while (i < (int)exp[0] && (exp[exp[0] - i] & ((BignumInt)1 << j)) == 0) {
j--;
if (j < 0) {
i++;
while (j >= 0) {
internal_mul(a + len, a + len, b, len, scratch);
monty_reduce(b, n, mninv, scratch, len);
- if ((exp[exp[0] - i] & (1 << j)) != 0) {
+ if ((exp[exp[0] - i] & ((BignumInt)1 << j)) != 0) {
internal_mul(b + len, x, a, len, scratch);
monty_reduce(a, n, mninv, scratch, len);
} else {
result[0]--;
/* Free temporary arrays */
- for (i = 0; i < scratchlen; i++)
- scratch[i] = 0;
+ smemclr(scratch, scratchlen * sizeof(*scratch));
sfree(scratch);
- for (i = 0; i < 2 * len; i++)
- a[i] = 0;
+ smemclr(a, 2 * len * sizeof(*a));
sfree(a);
- for (i = 0; i < 2 * len; i++)
- b[i] = 0;
+ smemclr(b, 2 * len * sizeof(*b));
sfree(b);
- for (i = 0; i < len; i++)
- mninv[i] = 0;
+ smemclr(mninv, len * sizeof(*mninv));
sfree(mninv);
- for (i = 0; i < len; i++)
- n[i] = 0;
+ smemclr(n, len * sizeof(*n));
sfree(n);
- for (i = 0; i < len; i++)
- x[i] = 0;
+ smemclr(x, len * sizeof(*x));
sfree(x);
return result;
int pqlen, mlen, rlen, i, j;
Bignum 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);
+
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
pqlen = (p[0] > q[0] ? p[0] : q[0]);
+ /*
+ * Make sure that we're allowing enough space. The shifting below
+ * will underflow the vectors we allocate if pqlen is too small.
+ */
+ if (2*pqlen <= mlen)
+ pqlen = mlen/2 + 1;
+
/* Allocate n of size pqlen, copy p to n */
n = snewn(pqlen, BignumInt);
i = pqlen - p[0];
result[0]--;
/* Free temporary arrays */
- for (i = 0; i < scratchlen; i++)
- scratch[i] = 0;
+ smemclr(scratch, scratchlen * sizeof(*scratch));
sfree(scratch);
- for (i = 0; i < 2 * pqlen; i++)
- a[i] = 0;
+ smemclr(a, 2 * pqlen * sizeof(*a));
sfree(a);
- for (i = 0; i < mlen; i++)
- m[i] = 0;
+ smemclr(m, mlen * sizeof(*m));
sfree(m);
- for (i = 0; i < pqlen; i++)
- n[i] = 0;
+ smemclr(n, pqlen * sizeof(*n));
sfree(n);
- for (i = 0; i < pqlen; i++)
- o[i] = 0;
+ smemclr(o, pqlen * sizeof(*o));
sfree(o);
return result;
}
+Bignum modsub(const Bignum a, const Bignum b, const Bignum n)
+{
+ Bignum a1, b1, ret;
+
+ if (bignum_cmp(a, n) >= 0) a1 = bigmod(a, n);
+ else a1 = a;
+ if (bignum_cmp(b, n) >= 0) b1 = bigmod(b, n);
+ else b1 = b;
+
+ if (bignum_cmp(a1, b1) >= 0) /* a >= b */
+ {
+ ret = bigsub(a1, b1);
+ }
+ else
+ {
+ /* Handle going round the corner of the modulus without having
+ * negative support in Bignum */
+ Bignum tmp = bigsub(n, b1);
+ assert(tmp);
+ ret = bigadd(tmp, a1);
+ freebn(tmp);
+ }
+
+ if (a != a1) freebn(a1);
+ if (b != b1) freebn(b1);
+
+ return ret;
+}
+
/*
* Compute p % mod.
* The most significant word of mod MUST be non-zero.
int mshift;
int plen, mlen, i, j;
+ /*
+ * 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);
+
/* Allocate m of size mlen, copy mod to m */
/* We use big endian internally */
mlen = mod[0];
}
/* Free temporary arrays */
- for (i = 0; i < mlen; i++)
- m[i] = 0;
+ smemclr(m, mlen * sizeof(*m));
sfree(m);
- for (i = 0; i < plen; i++)
- n[i] = 0;
+ smemclr(n, plen * sizeof(*n));
sfree(n);
}
Bignum result;
int w, i;
+ assert(nbytes >= 0 && nbytes < INT_MAX/8);
+
w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */
result = newbn(w);
result[i] = 0;
for (i = nbytes; i--;) {
unsigned char byte = *data++;
- result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);
+ result[1 + i / BIGNUM_INT_BYTES] |=
+ (BignumInt)byte << (8*i % BIGNUM_INT_BITS);
+ }
+
+ bn_restore_invariant(result);
+ return result;
+}
+
+Bignum bignum_from_bytes_le(const unsigned char *data, int nbytes)
+{
+ Bignum result;
+ int w, i;
+
+ assert(nbytes >= 0 && nbytes < INT_MAX/8);
+
+ 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 = 0; i < nbytes; ++i) {
+ unsigned char byte = *data++;
+ result[1 + i / BIGNUM_INT_BYTES] |=
+ (BignumInt)byte << (8*i % BIGNUM_INT_BITS);
+ }
+
+ bn_restore_invariant(result);
+ return result;
+}
+
+Bignum bignum_from_decimal(const char *decimal)
+{
+ Bignum result = copybn(Zero);
+
+ while (*decimal) {
+ Bignum tmp, tmp2;
+
+ if (!isdigit((unsigned char)*decimal)) {
+ freebn(result);
+ return 0;
+ }
+
+ tmp = bigmul(result, Ten);
+ tmp2 = bignum_from_long(*decimal - '0');
+ result = bigadd(tmp, tmp2);
+ freebn(tmp);
+ freebn(tmp2);
+
+ decimal++;
}
- while (result[0] > 1 && result[result[0]] == 0)
- result[0]--;
return result;
}
+Bignum bignum_random_in_range(const Bignum lower, const Bignum upper)
+{
+ Bignum ret = NULL;
+ unsigned char *bytes;
+ int upper_len = bignum_bitcount(upper);
+ int upper_bytes = upper_len / 8;
+ int upper_bits = upper_len % 8;
+ if (upper_bits) ++upper_bytes;
+
+ bytes = snewn(upper_bytes, unsigned char);
+ do {
+ int i;
+
+ if (ret) freebn(ret);
+
+ for (i = 0; i < upper_bytes; ++i)
+ {
+ bytes[i] = (unsigned char)random_byte();
+ }
+ /* Mask the top to reduce failure rate to 50/50 */
+ if (upper_bits)
+ {
+ bytes[i - 1] &= 0xFF >> (8 - upper_bits);
+ }
+
+ ret = bignum_from_bytes(bytes, upper_bytes);
+ } while (bignum_cmp(ret, lower) < 0 || bignum_cmp(ret, upper) > 0);
+ smemclr(bytes, upper_bytes);
+ sfree(bytes);
+
+ return ret;
+}
+
/*
* 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 bignum_byte(Bignum bn, int i)
{
- if (i >= (int)(BIGNUM_INT_BYTES * bn[0]))
+ if (i < 0 || i >= (int)(BIGNUM_INT_BYTES * bn[0]))
return 0; /* beyond the end */
else
return (bn[i / BIGNUM_INT_BYTES + 1] >>
*/
int bignum_bit(Bignum bn, int i)
{
- if (i >= (int)(BIGNUM_INT_BITS * bn[0]))
+ if (i < 0 || 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;
*/
void bignum_set_bit(Bignum bn, int bitnum, int value)
{
- if (bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
- abort(); /* beyond the end */
- else {
+ if (bitnum < 0 || bitnum >= (int)(BIGNUM_INT_BITS * bn[0])) {
+ if (value) abort(); /* beyond the end */
+ } else {
int v = bitnum / BIGNUM_INT_BITS + 1;
- int mask = 1 << (bitnum % BIGNUM_INT_BITS);
+ BignumInt mask = (BignumInt)1 << (bitnum % BIGNUM_INT_BITS);
if (value)
bn[v] |= mask;
else
int bignum_cmp(Bignum a, Bignum b)
{
int amax = a[0], bmax = b[0];
- int i = (amax > bmax ? amax : bmax);
+ int i;
+
+ /* Annoyingly we have two representations of zero */
+ if (amax == 1 && a[amax] == 0)
+ amax = 0;
+ if (bmax == 1 && b[bmax] == 0)
+ bmax = 0;
+
+ assert(amax == 0 || a[amax] != 0);
+ assert(bmax == 0 || b[bmax] != 0);
+
+ i = (amax > bmax ? amax : bmax);
while (i) {
BignumInt aval = (i > amax ? 0 : a[i]);
BignumInt bval = (i > bmax ? 0 : b[i]);
int i, shiftw, shiftb, shiftbb, bits;
BignumInt ai, ai1;
+ assert(shift >= 0);
+
bits = bignum_bitcount(a) - shift;
ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
return ret;
}
+/*
+ * Left-shift one bignum to form another.
+ */
+Bignum bignum_lshift(Bignum a, int shift)
+{
+ Bignum ret;
+ int bits, shiftWords, shiftBits;
+
+ assert(shift >= 0);
+
+ bits = bignum_bitcount(a) + shift;
+ ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
+
+ shiftWords = shift / BIGNUM_INT_BITS;
+ shiftBits = shift % BIGNUM_INT_BITS;
+
+ if (shiftBits == 0)
+ {
+ memcpy(&ret[1 + shiftWords], &a[1], sizeof(BignumInt) * a[0]);
+ }
+ else
+ {
+ int i;
+ BignumInt carry = 0;
+
+ /* Remember that Bignum[0] is length, so add 1 */
+ for (i = shiftWords + 1; i < ((int)a[0]) + shiftWords + 1; ++i)
+ {
+ BignumInt from = a[i - shiftWords];
+ ret[i] = (from << shiftBits) | carry;
+ carry = from >> (BIGNUM_INT_BITS - shiftBits);
+ }
+ if (carry) ret[i] = carry;
+ }
+
+ return ret;
+}
+
/*
* Non-modular multiplication and addition.
*/
}
ret[0] = maxspot;
- for (i = 0; i < wslen; i++)
- workspace[i] = 0;
+ smemclr(workspace, wslen * sizeof(*workspace));
sfree(workspace);
return ret;
}
{
Bignum q = newbn(a[0]);
bigdivmod(a, b, NULL, q);
+ while (q[0] > 1 && q[q[0]] == 0)
+ q[0]--;
return q;
}
{
Bignum r = newbn(b[0]);
bigdivmod(a, b, r, NULL);
+ while (r[0] > 1 && r[r[0]] == 0)
+ r[0]--;
return r;
}
Bignum x = copybn(One);
int sign = +1;
+ assert(number[number[0]] != 0);
+ assert(modulus[modulus[0]] != 0);
+
while (bignum_cmp(b, One) != 0) {
- Bignum t = newbn(b[0]);
- Bignum q = newbn(a[0]);
+ Bignum t, q;
+
+ if (bignum_cmp(b, Zero) == 0) {
+ /*
+ * Found a common factor between the inputs, so we cannot
+ * return a modular inverse at all.
+ */
+ freebn(b);
+ freebn(a);
+ freebn(xp);
+ freebn(x);
+ return NULL;
+ }
+
+ t = newbn(b[0]);
+ q = newbn(a[0]);
bigdivmod(a, b, t, q);
while (t[0] > 1 && t[t[0]] == 0)
t[0]--;
+ while (q[0] > 1 && q[q[0]] == 0)
+ q[0]--;
freebn(a);
a = b;
b = t;
/*
* Done.
*/
+ smemclr(workspace, x[0] * sizeof(*workspace));
sfree(workspace);
return ret;
}
#include <ctype.h>
/*
- * gcc -g -O0 -DTESTBN -o testbn sshbn.c misc.c -I unix -I charset
+ * gcc -Wall -g -O0 -DTESTBN -o testbn sshbn.c misc.c conf.c tree234.c unix/uxmisc.c -I. -I unix -I charset
*
* Then feed to this program's standard input the output of
* testdata/bignum.py .
*/
-void modalfatalbox(char *p, ...)
+void modalfatalbox(const char *p, ...)
{
va_list ap;
fprintf(stderr, "FATAL ERROR: ");
exit(1);
}
+int random_byte(void)
+{
+ modalfatalbox("random_byte called in testbn");
+ return 0;
+}
+
#define fromxdigit(c) ( (c)>'9' ? ((c)&0xDF) - 'A' + 10 : (c) - '0' )
int main(int argc, char **argv)
freebn(b);
freebn(c);
freebn(p);
+ } else if (!strcmp(buf, "modmul")) {
+ Bignum a, b, m, c, p;
+
+ if (ptrnum != 4) {
+ printf("%d: modmul with %d parameters, expected 4\n",
+ line, ptrnum);
+ exit(1);
+ }
+ a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
+ b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
+ m = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
+ c = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);
+ p = modmul(a, b, m);
+
+ if (bignum_cmp(c, p) == 0) {
+ passes++;
+ } else {
+ char *as = bignum_decimal(a);
+ char *bs = bignum_decimal(b);
+ char *ms = bignum_decimal(m);
+ char *cs = bignum_decimal(c);
+ char *ps = bignum_decimal(p);
+
+ printf("%d: fail: %s * %s mod %s gave %s expected %s\n",
+ line, as, bs, ms, ps, cs);
+ fails++;
+
+ sfree(as);
+ sfree(bs);
+ sfree(ms);
+ sfree(cs);
+ sfree(ps);
+ }
+ freebn(a);
+ freebn(b);
+ freebn(m);
+ freebn(c);
+ freebn(p);
} else if (!strcmp(buf, "pow")) {
Bignum base, expt, modulus, expected, answer;
if (ptrnum != 4) {
- printf("%d: mul with %d parameters, expected 4\n", line, ptrnum);
+ printf("%d: pow with %d parameters, expected 4\n", line, ptrnum);
exit(1);
}
projects / PuTTY.git / blobdiff