зеркало из https://github.com/github/putty.git
1054 строки
24 KiB
C
1054 строки
24 KiB
C
/*
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* Bignum routines for RSA and DH and stuff.
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*/
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#include <stdio.h>
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#include <assert.h>
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#include <stdlib.h>
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#include <string.h>
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#include "misc.h"
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#if defined __GNUC__ && defined __i386__
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typedef unsigned long BignumInt;
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typedef unsigned long long BignumDblInt;
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#define BIGNUM_INT_MASK 0xFFFFFFFFUL
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#define BIGNUM_TOP_BIT 0x80000000UL
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#define BIGNUM_INT_BITS 32
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#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
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#define DIVMOD_WORD(q, r, hi, lo, w) \
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__asm__("div %2" : \
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"=d" (r), "=a" (q) : \
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"r" (w), "d" (hi), "a" (lo))
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#else
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typedef unsigned short BignumInt;
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typedef unsigned long BignumDblInt;
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#define BIGNUM_INT_MASK 0xFFFFU
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#define BIGNUM_TOP_BIT 0x8000U
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#define BIGNUM_INT_BITS 16
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#define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
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#define DIVMOD_WORD(q, r, hi, lo, w) do { \
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BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
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q = n / w; \
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r = n % w; \
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} while (0)
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#endif
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#define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8)
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#define BIGNUM_INTERNAL
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typedef BignumInt *Bignum;
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#include "ssh.h"
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BignumInt bnZero[1] = { 0 };
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BignumInt bnOne[2] = { 1, 1 };
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/*
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* The Bignum format is an array of `BignumInt'. The first
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* element of the array counts the remaining elements. The
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* remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_
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* significant digit first. (So it's trivial to extract the bit
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* with value 2^n for any n.)
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*
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* All Bignums in this module are positive. Negative numbers must
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* be dealt with outside it.
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*
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* INVARIANT: the most significant word of any Bignum must be
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* nonzero.
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*/
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Bignum Zero = bnZero, One = bnOne;
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static Bignum newbn(int length)
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{
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Bignum b = snewn(length + 1, BignumInt);
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if (!b)
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abort(); /* FIXME */
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memset(b, 0, (length + 1) * sizeof(*b));
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b[0] = length;
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return b;
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}
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void bn_restore_invariant(Bignum b)
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{
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while (b[0] > 1 && b[b[0]] == 0)
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b[0]--;
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}
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Bignum copybn(Bignum orig)
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{
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Bignum b = snewn(orig[0] + 1, BignumInt);
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if (!b)
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abort(); /* FIXME */
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memcpy(b, orig, (orig[0] + 1) * sizeof(*b));
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return b;
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}
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void freebn(Bignum b)
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{
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/*
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* Burn the evidence, just in case.
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*/
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memset(b, 0, sizeof(b[0]) * (b[0] + 1));
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sfree(b);
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}
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Bignum bn_power_2(int n)
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{
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Bignum ret = newbn(n / BIGNUM_INT_BITS + 1);
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bignum_set_bit(ret, n, 1);
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return ret;
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}
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/*
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* Compute c = a * b.
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* Input is in the first len words of a and b.
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* Result is returned in the first 2*len words of c.
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*/
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static void internal_mul(BignumInt *a, BignumInt *b,
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BignumInt *c, int len)
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{
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int i, j;
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BignumDblInt t;
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for (j = 0; j < 2 * len; j++)
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c[j] = 0;
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for (i = len - 1; i >= 0; i--) {
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t = 0;
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for (j = len - 1; j >= 0; j--) {
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t += MUL_WORD(a[i], (BignumDblInt) b[j]);
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t += (BignumDblInt) c[i + j + 1];
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c[i + j + 1] = (BignumInt) t;
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t = t >> BIGNUM_INT_BITS;
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}
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c[i] = (BignumInt) t;
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}
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}
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static void internal_add_shifted(BignumInt *number,
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unsigned n, int shift)
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{
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int word = 1 + (shift / BIGNUM_INT_BITS);
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int bshift = shift % BIGNUM_INT_BITS;
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BignumDblInt addend;
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addend = (BignumDblInt)n << bshift;
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while (addend) {
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addend += number[word];
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number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
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addend >>= BIGNUM_INT_BITS;
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word++;
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}
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}
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/*
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* Compute a = a % m.
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* Input in first alen words of a and first mlen words of m.
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* Output in first alen words of a
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* (of which first alen-mlen words will be zero).
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* The MSW of m MUST have its high bit set.
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* Quotient is accumulated in the `quotient' array, which is a Bignum
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* rather than the internal bigendian format. Quotient parts are shifted
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* left by `qshift' before adding into quot.
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*/
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static void internal_mod(BignumInt *a, int alen,
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BignumInt *m, int mlen,
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BignumInt *quot, int qshift)
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{
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BignumInt m0, m1;
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unsigned int h;
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int i, k;
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m0 = m[0];
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if (mlen > 1)
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m1 = m[1];
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else
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m1 = 0;
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for (i = 0; i <= alen - mlen; i++) {
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BignumDblInt t;
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unsigned int q, r, c, ai1;
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if (i == 0) {
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h = 0;
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} else {
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h = a[i - 1];
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a[i - 1] = 0;
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}
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if (i == alen - 1)
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ai1 = 0;
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else
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ai1 = a[i + 1];
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/* Find q = h:a[i] / m0 */
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if (h >= m0) {
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/*
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* Special case.
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*
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* To illustrate it, suppose a BignumInt is 8 bits, and
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* we are dividing (say) A1:23:45:67 by A1:B2:C3. Then
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* our initial division will be 0xA123 / 0xA1, which
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* will give a quotient of 0x100 and a divide overflow.
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* However, the invariants in this division algorithm
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* are not violated, since the full number A1:23:... is
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* _less_ than the quotient prefix A1:B2:... and so the
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* following correction loop would have sorted it out.
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*
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* In this situation we set q to be the largest
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* quotient we _can_ stomach (0xFF, of course).
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*/
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q = BIGNUM_INT_MASK;
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} else {
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DIVMOD_WORD(q, r, h, a[i], m0);
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/* Refine our estimate of q by looking at
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h:a[i]:a[i+1] / m0:m1 */
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t = MUL_WORD(m1, q);
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if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
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q--;
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t -= m1;
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r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
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if (r >= (BignumDblInt) m0 &&
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t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
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}
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}
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/* Subtract q * m from a[i...] */
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c = 0;
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for (k = mlen - 1; k >= 0; k--) {
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t = MUL_WORD(q, m[k]);
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t += c;
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c = t >> BIGNUM_INT_BITS;
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if ((BignumInt) t > a[i + k])
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c++;
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a[i + k] -= (BignumInt) t;
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}
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/* Add back m in case of borrow */
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if (c != h) {
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t = 0;
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for (k = mlen - 1; k >= 0; k--) {
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t += m[k];
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t += a[i + k];
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a[i + k] = (BignumInt) t;
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t = t >> BIGNUM_INT_BITS;
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}
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q--;
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}
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if (quot)
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internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
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}
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}
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/*
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* Compute (base ^ exp) % mod.
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*/
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Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
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{
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BignumInt *a, *b, *n, *m;
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int mshift;
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int mlen, i, j;
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Bignum base, result;
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/*
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* The most significant word of mod needs to be non-zero. It
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* should already be, but let's make sure.
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*/
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assert(mod[mod[0]] != 0);
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/*
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* Make sure the base is smaller than the modulus, by reducing
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* it modulo the modulus if not.
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*/
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base = bigmod(base_in, mod);
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/* Allocate m of size mlen, copy mod to m */
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/* We use big endian internally */
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mlen = mod[0];
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m = snewn(mlen, BignumInt);
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for (j = 0; j < mlen; j++)
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m[j] = mod[mod[0] - j];
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/* Shift m left to make msb bit set */
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for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
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if ((m[0] << mshift) & BIGNUM_TOP_BIT)
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break;
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if (mshift) {
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for (i = 0; i < mlen - 1; i++)
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m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
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m[mlen - 1] = m[mlen - 1] << mshift;
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}
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/* Allocate n of size mlen, copy base to n */
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n = snewn(mlen, BignumInt);
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i = mlen - base[0];
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for (j = 0; j < i; j++)
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n[j] = 0;
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for (j = 0; j < base[0]; j++)
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n[i + j] = base[base[0] - j];
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/* Allocate a and b of size 2*mlen. Set a = 1 */
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a = snewn(2 * mlen, BignumInt);
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b = snewn(2 * mlen, BignumInt);
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for (i = 0; i < 2 * mlen; i++)
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a[i] = 0;
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a[2 * mlen - 1] = 1;
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/* Skip leading zero bits of exp. */
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i = 0;
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j = BIGNUM_INT_BITS-1;
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while (i < exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
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j--;
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if (j < 0) {
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i++;
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j = BIGNUM_INT_BITS-1;
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}
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}
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/* Main computation */
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while (i < exp[0]) {
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while (j >= 0) {
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internal_mul(a + mlen, a + mlen, b, mlen);
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internal_mod(b, mlen * 2, m, mlen, NULL, 0);
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if ((exp[exp[0] - i] & (1 << j)) != 0) {
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internal_mul(b + mlen, n, a, mlen);
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internal_mod(a, mlen * 2, m, mlen, NULL, 0);
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} else {
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BignumInt *t;
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t = a;
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a = b;
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b = t;
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}
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j--;
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}
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i++;
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j = BIGNUM_INT_BITS-1;
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}
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/* Fixup result in case the modulus was shifted */
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if (mshift) {
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for (i = mlen - 1; i < 2 * mlen - 1; i++)
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a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
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a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;
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internal_mod(a, mlen * 2, m, mlen, NULL, 0);
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for (i = 2 * mlen - 1; i >= mlen; i--)
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a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
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}
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/* Copy result to buffer */
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result = newbn(mod[0]);
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for (i = 0; i < mlen; i++)
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result[result[0] - i] = a[i + mlen];
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while (result[0] > 1 && result[result[0]] == 0)
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result[0]--;
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/* Free temporary arrays */
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for (i = 0; i < 2 * mlen; i++)
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a[i] = 0;
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sfree(a);
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for (i = 0; i < 2 * mlen; i++)
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b[i] = 0;
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sfree(b);
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for (i = 0; i < mlen; i++)
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m[i] = 0;
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sfree(m);
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for (i = 0; i < mlen; i++)
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n[i] = 0;
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sfree(n);
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freebn(base);
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return result;
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}
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/*
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* Compute (p * q) % mod.
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* The most significant word of mod MUST be non-zero.
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* We assume that the result array is the same size as the mod array.
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*/
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Bignum modmul(Bignum p, Bignum q, Bignum mod)
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{
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BignumInt *a, *n, *m, *o;
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int mshift;
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int pqlen, mlen, rlen, i, j;
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Bignum result;
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/* Allocate m of size mlen, copy mod to m */
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/* We use big endian internally */
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mlen = mod[0];
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m = snewn(mlen, BignumInt);
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for (j = 0; j < mlen; j++)
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m[j] = mod[mod[0] - j];
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/* Shift m left to make msb bit set */
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for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
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if ((m[0] << mshift) & BIGNUM_TOP_BIT)
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break;
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if (mshift) {
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for (i = 0; i < mlen - 1; i++)
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m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
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m[mlen - 1] = m[mlen - 1] << mshift;
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}
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pqlen = (p[0] > q[0] ? p[0] : q[0]);
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/* Allocate n of size pqlen, copy p to n */
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n = snewn(pqlen, BignumInt);
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i = pqlen - p[0];
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for (j = 0; j < i; j++)
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n[j] = 0;
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for (j = 0; j < p[0]; j++)
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n[i + j] = p[p[0] - j];
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/* Allocate o of size pqlen, copy q to o */
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o = snewn(pqlen, BignumInt);
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i = pqlen - q[0];
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for (j = 0; j < i; j++)
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o[j] = 0;
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for (j = 0; j < q[0]; j++)
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o[i + j] = q[q[0] - j];
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/* Allocate a of size 2*pqlen for result */
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a = snewn(2 * pqlen, BignumInt);
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/* Main computation */
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internal_mul(n, o, a, pqlen);
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internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
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/* Fixup result in case the modulus was shifted */
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if (mshift) {
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for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)
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a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
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a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;
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internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
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for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)
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a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
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}
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/* Copy result to buffer */
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rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);
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result = newbn(rlen);
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for (i = 0; i < rlen; i++)
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result[result[0] - i] = a[i + 2 * pqlen - rlen];
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while (result[0] > 1 && result[result[0]] == 0)
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result[0]--;
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/* Free temporary arrays */
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for (i = 0; i < 2 * pqlen; i++)
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a[i] = 0;
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sfree(a);
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for (i = 0; i < mlen; i++)
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m[i] = 0;
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sfree(m);
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for (i = 0; i < pqlen; i++)
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n[i] = 0;
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sfree(n);
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for (i = 0; i < pqlen; i++)
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o[i] = 0;
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sfree(o);
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return result;
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}
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/*
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* Compute p % mod.
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* The most significant word of mod MUST be non-zero.
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* We assume that the result array is the same size as the mod array.
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* We optionally write out a quotient if `quotient' is non-NULL.
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* We can avoid writing out the result if `result' is NULL.
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*/
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static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)
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{
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BignumInt *n, *m;
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int mshift;
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int plen, mlen, i, j;
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/* Allocate m of size mlen, copy mod to m */
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/* We use big endian internally */
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mlen = mod[0];
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m = snewn(mlen, BignumInt);
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for (j = 0; j < mlen; j++)
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m[j] = mod[mod[0] - j];
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/* Shift m left to make msb bit set */
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for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
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if ((m[0] << mshift) & BIGNUM_TOP_BIT)
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break;
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if (mshift) {
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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 <= 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 <= result[0]; i++) {
|
|
int j = plen - i;
|
|
result[i] = j >= 0 ? n[j] : 0;
|
|
}
|
|
}
|
|
|
|
/* Free temporary arrays */
|
|
for (i = 0; i < mlen; i++)
|
|
m[i] = 0;
|
|
sfree(m);
|
|
for (i = 0; i < plen; i++)
|
|
n[i] = 0;
|
|
sfree(n);
|
|
}
|
|
|
|
/*
|
|
* Decrement a number.
|
|
*/
|
|
void decbn(Bignum bn)
|
|
{
|
|
int i = 1;
|
|
while (i < 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, or -1 if there wasn't enough data.
|
|
*/
|
|
int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)
|
|
{
|
|
const unsigned char *p = data;
|
|
int i;
|
|
int w, b;
|
|
|
|
if (len < 2)
|
|
return -1;
|
|
|
|
w = 0;
|
|
for (i = 0; i < 2; i++)
|
|
w = (w << 8) + *p++;
|
|
b = (w + 7) / 8; /* bits -> bytes */
|
|
|
|
if (len < b+2)
|
|
return -1;
|
|
|
|
if (!result) /* just return length */
|
|
return b + 2;
|
|
|
|
*result = bignum_from_bytes(p, b);
|
|
|
|
return p + b - data;
|
|
}
|
|
|
|
/*
|
|
* Return the bit count of a bignum, for ssh1 encoding.
|
|
*/
|
|
int bignum_bitcount(Bignum bn)
|
|
{
|
|
int bitcount = bn[0] * BIGNUM_INT_BITS - 1;
|
|
while (bitcount >= 0
|
|
&& (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;
|
|
return bitcount + 1;
|
|
}
|
|
|
|
/*
|
|
* Return the byte length of a bignum when ssh1 encoded.
|
|
*/
|
|
int ssh1_bignum_length(Bignum bn)
|
|
{
|
|
return 2 + (bignum_bitcount(bn) + 7) / 8;
|
|
}
|
|
|
|
/*
|
|
* Return the byte length of a bignum when ssh2 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 >= BIGNUM_INT_BYTES * bn[0])
|
|
return 0; /* beyond the end */
|
|
else
|
|
return (bn[i / BIGNUM_INT_BYTES + 1] >>
|
|
((i % BIGNUM_INT_BYTES)*8)) & 0xFF;
|
|
}
|
|
|
|
/*
|
|
* Return a bit from a bignum; 0 is least significant, etc.
|
|
*/
|
|
int bignum_bit(Bignum bn, int i)
|
|
{
|
|
if (i >= 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 >= 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 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 = bignum_bitcount(bn);
|
|
|
|
*p++ = (bitc >> 8) & 0xFF;
|
|
*p++ = (bitc) & 0xFF;
|
|
for (i = len - 2; i--;)
|
|
*p++ = bignum_byte(bn, i);
|
|
return len;
|
|
}
|
|
|
|
/*
|
|
* Compare two bignums. Returns like strcmp.
|
|
*/
|
|
int bignum_cmp(Bignum a, Bignum b)
|
|
{
|
|
int amax = a[0], bmax = b[0];
|
|
int i = (amax > bmax ? amax : bmax);
|
|
while (i) {
|
|
BignumInt aval = (i > amax ? 0 : a[i]);
|
|
BignumInt bval = (i > bmax ? 0 : b[i]);
|
|
if (aval < bval)
|
|
return -1;
|
|
if (aval > bval)
|
|
return +1;
|
|
i--;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
/*
|
|
* Right-shift one bignum to form another.
|
|
*/
|
|
Bignum bignum_rshift(Bignum a, int shift)
|
|
{
|
|
Bignum ret;
|
|
int i, shiftw, shiftb, shiftbb, bits;
|
|
BignumInt ai, ai1;
|
|
|
|
bits = bignum_bitcount(a) - shift;
|
|
ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
|
|
|
|
if (ret) {
|
|
shiftw = shift / BIGNUM_INT_BITS;
|
|
shiftb = shift % BIGNUM_INT_BITS;
|
|
shiftbb = BIGNUM_INT_BITS - shiftb;
|
|
|
|
ai1 = a[shiftw + 1];
|
|
for (i = 1; i <= ret[0]; i++) {
|
|
ai = ai1;
|
|
ai1 = (i + shiftw + 1 <= 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 <= 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) {
|
|
BignumDblInt carry = 0;
|
|
for (i = 1; i <= rlen; i++) {
|
|
carry += (i <= ret[0] ? ret[i] : 0);
|
|
carry += (i <= 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 <= ret[0]; i++) {
|
|
carry += addend & BIGNUM_INT_MASK;
|
|
carry += (i <= 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 <= newx[0]; i++) {
|
|
BignumInt aword = (i <= modulus[0] ? modulus[i] : 0);
|
|
BignumInt 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;
|
|
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 = bignum_bitcount(x);
|
|
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 < 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 << 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;
|
|
}
|