2 * Bignum routines for RSA and DH and stuff.
15 * * Do not call the DIVMOD_WORD macro with expressions such as array
16 * subscripts, as some implementations object to this (see below).
17 * * Note that none of the division methods below will cope if the
18 * quotient won't fit into BIGNUM_INT_BITS. Callers should be careful
20 * If this condition occurs, in the case of the x86 DIV instruction,
21 * an overflow exception will occur, which (according to a correspondent)
22 * will manifest on Windows as something like
23 * 0xC0000095: Integer overflow
24 * The C variant won't give the right answer, either.
27 #if defined __GNUC__ && defined __i386__
28 typedef unsigned long BignumInt;
29 typedef unsigned long long BignumDblInt;
30 #define BIGNUM_INT_MASK 0xFFFFFFFFUL
31 #define BIGNUM_TOP_BIT 0x80000000UL
32 #define BIGNUM_INT_BITS 32
33 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
34 #define DIVMOD_WORD(q, r, hi, lo, w) \
36 "=d" (r), "=a" (q) : \
37 "r" (w), "d" (hi), "a" (lo))
38 #elif defined _MSC_VER && defined _M_IX86
39 typedef unsigned __int32 BignumInt;
40 typedef unsigned __int64 BignumDblInt;
41 #define BIGNUM_INT_MASK 0xFFFFFFFFUL
42 #define BIGNUM_TOP_BIT 0x80000000UL
43 #define BIGNUM_INT_BITS 32
44 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
45 /* Note: MASM interprets array subscripts in the macro arguments as
46 * assembler syntax, which gives the wrong answer. Don't supply them.
47 * <http://msdn2.microsoft.com/en-us/library/bf1dw62z.aspx> */
48 #define DIVMOD_WORD(q, r, hi, lo, w) do { \
56 /* 64-bit architectures can do 32x32->64 chunks at a time */
57 typedef unsigned int BignumInt;
58 typedef unsigned long BignumDblInt;
59 #define BIGNUM_INT_MASK 0xFFFFFFFFU
60 #define BIGNUM_TOP_BIT 0x80000000U
61 #define BIGNUM_INT_BITS 32
62 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
63 #define DIVMOD_WORD(q, r, hi, lo, w) do { \
64 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
69 /* 64-bit architectures in which unsigned long is 32 bits, not 64 */
70 typedef unsigned long BignumInt;
71 typedef unsigned long long BignumDblInt;
72 #define BIGNUM_INT_MASK 0xFFFFFFFFUL
73 #define BIGNUM_TOP_BIT 0x80000000UL
74 #define BIGNUM_INT_BITS 32
75 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
76 #define DIVMOD_WORD(q, r, hi, lo, w) do { \
77 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
82 /* Fallback for all other cases */
83 typedef unsigned short BignumInt;
84 typedef unsigned long BignumDblInt;
85 #define BIGNUM_INT_MASK 0xFFFFU
86 #define BIGNUM_TOP_BIT 0x8000U
87 #define BIGNUM_INT_BITS 16
88 #define MUL_WORD(w1, w2) ((BignumDblInt)w1 * w2)
89 #define DIVMOD_WORD(q, r, hi, lo, w) do { \
90 BignumDblInt n = (((BignumDblInt)hi) << BIGNUM_INT_BITS) | lo; \
96 #define BIGNUM_INT_BYTES (BIGNUM_INT_BITS / 8)
98 #define BIGNUM_INTERNAL
99 typedef BignumInt *Bignum;
103 BignumInt bnZero[1] = { 0 };
104 BignumInt bnOne[2] = { 1, 1 };
107 * The Bignum format is an array of `BignumInt'. The first
108 * element of the array counts the remaining elements. The
109 * remaining elements express the actual number, base 2^BIGNUM_INT_BITS, _least_
110 * significant digit first. (So it's trivial to extract the bit
111 * with value 2^n for any n.)
113 * All Bignums in this module are positive. Negative numbers must
114 * be dealt with outside it.
116 * INVARIANT: the most significant word of any Bignum must be
120 Bignum Zero = bnZero, One = bnOne;
122 static Bignum newbn(int length)
126 assert(length >= 0 && length < INT_MAX / BIGNUM_INT_BITS);
128 b = snewn(length + 1, BignumInt);
131 memset(b, 0, (length + 1) * sizeof(*b));
136 void bn_restore_invariant(Bignum b)
138 while (b[0] > 1 && b[b[0]] == 0)
142 Bignum copybn(Bignum orig)
144 Bignum b = snewn(orig[0] + 1, BignumInt);
147 memcpy(b, orig, (orig[0] + 1) * sizeof(*b));
151 void freebn(Bignum b)
154 * Burn the evidence, just in case.
156 smemclr(b, sizeof(b[0]) * (b[0] + 1));
160 Bignum bn_power_2(int n)
166 ret = newbn(n / BIGNUM_INT_BITS + 1);
167 bignum_set_bit(ret, n, 1);
172 * Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all
173 * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried
176 static BignumInt internal_add(const BignumInt *a, const BignumInt *b,
177 BignumInt *c, int len)
180 BignumDblInt carry = 0;
182 for (i = len-1; i >= 0; i--) {
183 carry += (BignumDblInt)a[i] + b[i];
184 c[i] = (BignumInt)carry;
185 carry >>= BIGNUM_INT_BITS;
188 return (BignumInt)carry;
192 * Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are
193 * all big-endian arrays of 'len' BignumInts. Any borrow from the top
196 static void internal_sub(const BignumInt *a, const BignumInt *b,
197 BignumInt *c, int len)
200 BignumDblInt carry = 1;
202 for (i = len-1; i >= 0; i--) {
203 carry += (BignumDblInt)a[i] + (b[i] ^ BIGNUM_INT_MASK);
204 c[i] = (BignumInt)carry;
205 carry >>= BIGNUM_INT_BITS;
211 * Input is in the first len words of a and b.
212 * Result is returned in the first 2*len words of c.
214 * 'scratch' must point to an array of BignumInt of size at least
215 * mul_compute_scratch(len). (This covers the needs of internal_mul
216 * and all its recursive calls to itself.)
218 #define KARATSUBA_THRESHOLD 50
219 static int mul_compute_scratch(int len)
222 while (len > KARATSUBA_THRESHOLD) {
223 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
224 int midlen = botlen + 1;
230 static void internal_mul(const BignumInt *a, const BignumInt *b,
231 BignumInt *c, int len, BignumInt *scratch)
233 if (len > KARATSUBA_THRESHOLD) {
237 * Karatsuba divide-and-conquer algorithm. Cut each input in
238 * half, so that it's expressed as two big 'digits' in a giant
244 * Then the product is of course
246 * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0
248 * and we compute the three coefficients by recursively
249 * calling ourself to do half-length multiplications.
251 * The clever bit that makes this worth doing is that we only
252 * need _one_ half-length multiplication for the central
253 * coefficient rather than the two that it obviouly looks
254 * like, because we can use a single multiplication to compute
256 * (a_1 + a_0) (b_1 + b_0) = a_1 b_1 + a_1 b_0 + a_0 b_1 + a_0 b_0
258 * and then we subtract the other two coefficients (a_1 b_1
259 * and a_0 b_0) which we were computing anyway.
261 * Hence we get to multiply two numbers of length N in about
262 * three times as much work as it takes to multiply numbers of
263 * length N/2, which is obviously better than the four times
264 * as much work it would take if we just did a long
265 * conventional multiply.
268 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
269 int midlen = botlen + 1;
276 * The coefficients a_1 b_1 and a_0 b_0 just avoid overlapping
277 * in the output array, so we can compute them immediately in
282 printf("a1,a0 = 0x");
283 for (i = 0; i < len; i++) {
284 if (i == toplen) printf(", 0x");
285 printf("%0*x", BIGNUM_INT_BITS/4, a[i]);
288 printf("b1,b0 = 0x");
289 for (i = 0; i < len; i++) {
290 if (i == toplen) printf(", 0x");
291 printf("%0*x", BIGNUM_INT_BITS/4, b[i]);
297 internal_mul(a, b, c, toplen, scratch);
300 for (i = 0; i < 2*toplen; i++) {
301 printf("%0*x", BIGNUM_INT_BITS/4, c[i]);
307 internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch);
310 for (i = 0; i < 2*botlen; i++) {
311 printf("%0*x", BIGNUM_INT_BITS/4, c[2*toplen+i]);
316 /* Zero padding. midlen exceeds toplen by at most 2, so just
317 * zero the first two words of each input and the rest will be
319 scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0;
321 for (i = 0; i < toplen; i++) {
322 scratch[midlen - toplen + i] = a[i]; /* a_1 */
323 scratch[2*midlen - toplen + i] = b[i]; /* b_1 */
326 /* compute a_1 + a_0 */
327 scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen);
329 printf("a1plusa0 = 0x");
330 for (i = 0; i < midlen; i++) {
331 printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
335 /* compute b_1 + b_0 */
336 scratch[midlen] = internal_add(scratch+midlen+1, b+toplen,
337 scratch+midlen+1, botlen);
339 printf("b1plusb0 = 0x");
340 for (i = 0; i < midlen; i++) {
341 printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]);
347 * Now we can do the third multiplication.
349 internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen,
352 printf("a1plusa0timesb1plusb0 = 0x");
353 for (i = 0; i < 2*midlen; i++) {
354 printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);
360 * Now we can reuse the first half of 'scratch' to compute the
361 * sum of the outer two coefficients, to subtract from that
362 * product to obtain the middle one.
364 scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0;
365 for (i = 0; i < 2*toplen; i++)
366 scratch[2*midlen - 2*toplen + i] = c[i];
367 scratch[1] = internal_add(scratch+2, c + 2*toplen,
368 scratch+2, 2*botlen);
370 printf("a1b1plusa0b0 = 0x");
371 for (i = 0; i < 2*midlen; i++) {
372 printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]);
377 internal_sub(scratch + 2*midlen, scratch,
378 scratch + 2*midlen, 2*midlen);
380 printf("a1b0plusa0b1 = 0x");
381 for (i = 0; i < 2*midlen; i++) {
382 printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]);
388 * And now all we need to do is to add that middle coefficient
389 * back into the output. We may have to propagate a carry
390 * further up the output, but we can be sure it won't
391 * propagate right the way off the top.
393 carry = internal_add(c + 2*len - botlen - 2*midlen,
395 c + 2*len - botlen - 2*midlen, 2*midlen);
396 i = 2*len - botlen - 2*midlen - 1;
400 c[i] = (BignumInt)carry;
401 carry >>= BIGNUM_INT_BITS;
406 for (i = 0; i < 2*len; i++) {
407 printf("%0*x", BIGNUM_INT_BITS/4, c[i]);
416 const BignumInt *ap, *bp;
420 * Multiply in the ordinary O(N^2) way.
423 for (i = 0; i < 2 * len; i++)
426 for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) {
428 for (cp = cps, bp = b + len; cp--, bp-- > b ;) {
429 t = (MUL_WORD(*ap, *bp) + carry) + *cp;
431 carry = (BignumInt)(t >> BIGNUM_INT_BITS);
439 * Variant form of internal_mul used for the initial step of
440 * Montgomery reduction. Only bothers outputting 'len' words
441 * (everything above that is thrown away).
443 static void internal_mul_low(const BignumInt *a, const BignumInt *b,
444 BignumInt *c, int len, BignumInt *scratch)
446 if (len > KARATSUBA_THRESHOLD) {
450 * Karatsuba-aware version of internal_mul_low. As before, we
451 * express each input value as a shifted combination of two
457 * Then the full product is, as before,
459 * ab = a_1 b_1 D^2 + (a_1 b_0 + a_0 b_1) D + a_0 b_0
461 * Provided we choose D on the large side (so that a_0 and b_0
462 * are _at least_ as long as a_1 and b_1), we don't need the
463 * topmost term at all, and we only need half of the middle
464 * term. So there's no point in doing the proper Karatsuba
465 * optimisation which computes the middle term using the top
466 * one, because we'd take as long computing the top one as
467 * just computing the middle one directly.
469 * So instead, we do a much more obvious thing: we call the
470 * fully optimised internal_mul to compute a_0 b_0, and we
471 * recursively call ourself to compute the _bottom halves_ of
472 * a_1 b_0 and a_0 b_1, each of which we add into the result
473 * in the obvious way.
475 * In other words, there's no actual Karatsuba _optimisation_
476 * in this function; the only benefit in doing it this way is
477 * that we call internal_mul proper for a large part of the
478 * work, and _that_ can optimise its operation.
481 int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */
484 * Scratch space for the various bits and pieces we're going
485 * to be adding together: we need botlen*2 words for a_0 b_0
486 * (though we may end up throwing away its topmost word), and
487 * toplen words for each of a_1 b_0 and a_0 b_1. That adds up
492 internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen,
496 internal_mul_low(a, b + len - toplen, scratch + toplen, toplen,
500 internal_mul_low(a + len - toplen, b, scratch, toplen,
503 /* Copy the bottom half of the big coefficient into place */
504 for (i = 0; i < botlen; i++)
505 c[toplen + i] = scratch[2*toplen + botlen + i];
507 /* Add the two small coefficients, throwing away the returned carry */
508 internal_add(scratch, scratch + toplen, scratch, toplen);
510 /* And add that to the large coefficient, leaving the result in c. */
511 internal_add(scratch, scratch + 2*toplen + botlen - toplen,
518 const BignumInt *ap, *bp;
522 * Multiply in the ordinary O(N^2) way.
525 for (i = 0; i < len; i++)
528 for (cps = c + len, ap = a + len; ap-- > a; cps--) {
530 for (cp = cps, bp = b + len; bp--, cp-- > c ;) {
531 t = (MUL_WORD(*ap, *bp) + carry) + *cp;
533 carry = (BignumInt)(t >> BIGNUM_INT_BITS);
540 * Montgomery reduction. Expects x to be a big-endian array of 2*len
541 * BignumInts whose value satisfies 0 <= x < rn (where r = 2^(len *
542 * BIGNUM_INT_BITS) is the Montgomery base). Returns in the same array
543 * a value x' which is congruent to xr^{-1} mod n, and satisfies 0 <=
546 * 'n' and 'mninv' should be big-endian arrays of 'len' BignumInts
547 * each, containing respectively n and the multiplicative inverse of
550 * 'tmp' is an array of BignumInt used as scratch space, of length at
551 * least 3*len + mul_compute_scratch(len).
553 static void monty_reduce(BignumInt *x, const BignumInt *n,
554 const BignumInt *mninv, BignumInt *tmp, int len)
560 * Multiply x by (-n)^{-1} mod r. This gives us a value m such
561 * that mn is congruent to -x mod r. Hence, mn+x is an exact
562 * multiple of r, and is also (obviously) congruent to x mod n.
564 internal_mul_low(x + len, mninv, tmp, len, tmp + 3*len);
567 * Compute t = (mn+x)/r in ordinary, non-modular, integer
568 * arithmetic. By construction this is exact, and is congruent mod
569 * n to x * r^{-1}, i.e. the answer we want.
571 * The following multiply leaves that answer in the _most_
572 * significant half of the 'x' array, so then we must shift it
575 internal_mul(tmp, n, tmp+len, len, tmp + 3*len);
576 carry = internal_add(x, tmp+len, x, 2*len);
577 for (i = 0; i < len; i++)
578 x[len + i] = x[i], x[i] = 0;
581 * Reduce t mod n. This doesn't require a full-on division by n,
582 * but merely a test and single optional subtraction, since we can
583 * show that 0 <= t < 2n.
586 * + we computed m mod r, so 0 <= m < r.
587 * + so 0 <= mn < rn, obviously
588 * + hence we only need 0 <= x < rn to guarantee that 0 <= mn+x < 2rn
589 * + yielding 0 <= (mn+x)/r < 2n as required.
592 for (i = 0; i < len; i++)
593 if (x[len + i] != n[i])
596 if (carry || i >= len || x[len + i] > n[i])
597 internal_sub(x+len, n, x+len, len);
600 static void internal_add_shifted(BignumInt *number,
601 unsigned n, int shift)
603 int word = 1 + (shift / BIGNUM_INT_BITS);
604 int bshift = shift % BIGNUM_INT_BITS;
607 addend = (BignumDblInt)n << bshift;
610 addend += number[word];
611 number[word] = (BignumInt) addend & BIGNUM_INT_MASK;
612 addend >>= BIGNUM_INT_BITS;
619 * Input in first alen words of a and first mlen words of m.
620 * Output in first alen words of a
621 * (of which first alen-mlen words will be zero).
622 * The MSW of m MUST have its high bit set.
623 * Quotient is accumulated in the `quotient' array, which is a Bignum
624 * rather than the internal bigendian format. Quotient parts are shifted
625 * left by `qshift' before adding into quot.
627 static void internal_mod(BignumInt *a, int alen,
628 BignumInt *m, int mlen,
629 BignumInt *quot, int qshift)
636 assert(m0 >> (BIGNUM_INT_BITS-1) == 1);
642 for (i = 0; i <= alen - mlen; i++) {
644 unsigned int q, r, c, ai1;
658 /* Find q = h:a[i] / m0 */
663 * To illustrate it, suppose a BignumInt is 8 bits, and
664 * we are dividing (say) A1:23:45:67 by A1:B2:C3. Then
665 * our initial division will be 0xA123 / 0xA1, which
666 * will give a quotient of 0x100 and a divide overflow.
667 * However, the invariants in this division algorithm
668 * are not violated, since the full number A1:23:... is
669 * _less_ than the quotient prefix A1:B2:... and so the
670 * following correction loop would have sorted it out.
672 * In this situation we set q to be the largest
673 * quotient we _can_ stomach (0xFF, of course).
677 /* Macro doesn't want an array subscript expression passed
678 * into it (see definition), so use a temporary. */
679 BignumInt tmplo = a[i];
680 DIVMOD_WORD(q, r, h, tmplo, m0);
682 /* Refine our estimate of q by looking at
683 h:a[i]:a[i+1] / m0:m1 */
685 if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) {
688 r = (r + m0) & BIGNUM_INT_MASK; /* overflow? */
689 if (r >= (BignumDblInt) m0 &&
690 t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) q--;
694 /* Subtract q * m from a[i...] */
696 for (k = mlen - 1; k >= 0; k--) {
697 t = MUL_WORD(q, m[k]);
699 c = (unsigned)(t >> BIGNUM_INT_BITS);
700 if ((BignumInt) t > a[i + k])
702 a[i + k] -= (BignumInt) t;
705 /* Add back m in case of borrow */
708 for (k = mlen - 1; k >= 0; k--) {
711 a[i + k] = (BignumInt) t;
712 t = t >> BIGNUM_INT_BITS;
717 internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i));
722 * Compute (base ^ exp) % mod, the pedestrian way.
724 Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod)
726 BignumInt *a, *b, *n, *m, *scratch;
728 int mlen, scratchlen, i, j;
732 * The most significant word of mod needs to be non-zero. It
733 * should already be, but let's make sure.
735 assert(mod[mod[0]] != 0);
738 * Make sure the base is smaller than the modulus, by reducing
739 * it modulo the modulus if not.
741 base = bigmod(base_in, mod);
743 /* Allocate m of size mlen, copy mod to m */
744 /* We use big endian internally */
746 m = snewn(mlen, BignumInt);
747 for (j = 0; j < mlen; j++)
748 m[j] = mod[mod[0] - j];
750 /* Shift m left to make msb bit set */
751 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
752 if ((m[0] << mshift) & BIGNUM_TOP_BIT)
755 for (i = 0; i < mlen - 1; i++)
756 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
757 m[mlen - 1] = m[mlen - 1] << mshift;
760 /* Allocate n of size mlen, copy base to n */
761 n = snewn(mlen, BignumInt);
763 for (j = 0; j < i; j++)
765 for (j = 0; j < (int)base[0]; j++)
766 n[i + j] = base[base[0] - j];
768 /* Allocate a and b of size 2*mlen. Set a = 1 */
769 a = snewn(2 * mlen, BignumInt);
770 b = snewn(2 * mlen, BignumInt);
771 for (i = 0; i < 2 * mlen; i++)
775 /* Scratch space for multiplies */
776 scratchlen = mul_compute_scratch(mlen);
777 scratch = snewn(scratchlen, BignumInt);
779 /* Skip leading zero bits of exp. */
781 j = BIGNUM_INT_BITS-1;
782 while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
786 j = BIGNUM_INT_BITS-1;
790 /* Main computation */
791 while (i < (int)exp[0]) {
793 internal_mul(a + mlen, a + mlen, b, mlen, scratch);
794 internal_mod(b, mlen * 2, m, mlen, NULL, 0);
795 if ((exp[exp[0] - i] & (1 << j)) != 0) {
796 internal_mul(b + mlen, n, a, mlen, scratch);
797 internal_mod(a, mlen * 2, m, mlen, NULL, 0);
807 j = BIGNUM_INT_BITS-1;
810 /* Fixup result in case the modulus was shifted */
812 for (i = mlen - 1; i < 2 * mlen - 1; i++)
813 a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
814 a[2 * mlen - 1] = a[2 * mlen - 1] << mshift;
815 internal_mod(a, mlen * 2, m, mlen, NULL, 0);
816 for (i = 2 * mlen - 1; i >= mlen; i--)
817 a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
820 /* Copy result to buffer */
821 result = newbn(mod[0]);
822 for (i = 0; i < mlen; i++)
823 result[result[0] - i] = a[i + mlen];
824 while (result[0] > 1 && result[result[0]] == 0)
827 /* Free temporary arrays */
828 smemclr(a, 2 * mlen * sizeof(*a));
830 smemclr(scratch, scratchlen * sizeof(*scratch));
832 smemclr(b, 2 * mlen * sizeof(*b));
834 smemclr(m, mlen * sizeof(*m));
836 smemclr(n, mlen * sizeof(*n));
845 * Compute (base ^ exp) % mod. Uses the Montgomery multiplication
846 * technique where possible, falling back to modpow_simple otherwise.
848 Bignum modpow(Bignum base_in, Bignum exp, Bignum mod)
850 BignumInt *a, *b, *x, *n, *mninv, *scratch;
851 int len, scratchlen, i, j;
852 Bignum base, base2, r, rn, inv, result;
855 * The most significant word of mod needs to be non-zero. It
856 * should already be, but let's make sure.
858 assert(mod[mod[0]] != 0);
861 * mod had better be odd, or we can't do Montgomery multiplication
862 * using a power of two at all.
865 return modpow_simple(base_in, exp, mod);
868 * Make sure the base is smaller than the modulus, by reducing
869 * it modulo the modulus if not.
871 base = bigmod(base_in, mod);
874 * Compute the inverse of n mod r, for monty_reduce. (In fact we
875 * want the inverse of _minus_ n mod r, but we'll sort that out
879 r = bn_power_2(BIGNUM_INT_BITS * len);
880 inv = modinv(mod, r);
881 assert(inv); /* cannot fail, since mod is odd and r is a power of 2 */
884 * Multiply the base by r mod n, to get it into Montgomery
887 base2 = modmul(base, r, mod);
891 rn = bigmod(r, mod); /* r mod n, i.e. Montgomerified 1 */
893 freebn(r); /* won't need this any more */
896 * Set up internal arrays of the right lengths, in big-endian
897 * format, containing the base, the modulus, and the modulus's
900 n = snewn(len, BignumInt);
901 for (j = 0; j < len; j++)
902 n[len - 1 - j] = mod[j + 1];
904 mninv = snewn(len, BignumInt);
905 for (j = 0; j < len; j++)
906 mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0);
907 freebn(inv); /* we don't need this copy of it any more */
908 /* Now negate mninv mod r, so it's the inverse of -n rather than +n. */
909 x = snewn(len, BignumInt);
910 for (j = 0; j < len; j++)
912 internal_sub(x, mninv, mninv, len);
914 /* x = snewn(len, BignumInt); */ /* already done above */
915 for (j = 0; j < len; j++)
916 x[len - 1 - j] = (j < (int)base[0] ? base[j + 1] : 0);
917 freebn(base); /* we don't need this copy of it any more */
919 a = snewn(2*len, BignumInt);
920 b = snewn(2*len, BignumInt);
921 for (j = 0; j < len; j++)
922 a[2*len - 1 - j] = (j < (int)rn[0] ? rn[j + 1] : 0);
925 /* Scratch space for multiplies */
926 scratchlen = 3*len + mul_compute_scratch(len);
927 scratch = snewn(scratchlen, BignumInt);
929 /* Skip leading zero bits of exp. */
931 j = BIGNUM_INT_BITS-1;
932 while (i < (int)exp[0] && (exp[exp[0] - i] & (1 << j)) == 0) {
936 j = BIGNUM_INT_BITS-1;
940 /* Main computation */
941 while (i < (int)exp[0]) {
943 internal_mul(a + len, a + len, b, len, scratch);
944 monty_reduce(b, n, mninv, scratch, len);
945 if ((exp[exp[0] - i] & (1 << j)) != 0) {
946 internal_mul(b + len, x, a, len, scratch);
947 monty_reduce(a, n, mninv, scratch, len);
957 j = BIGNUM_INT_BITS-1;
961 * Final monty_reduce to get back from the adjusted Montgomery
964 monty_reduce(a, n, mninv, scratch, len);
966 /* Copy result to buffer */
967 result = newbn(mod[0]);
968 for (i = 0; i < len; i++)
969 result[result[0] - i] = a[i + len];
970 while (result[0] > 1 && result[result[0]] == 0)
973 /* Free temporary arrays */
974 smemclr(scratch, scratchlen * sizeof(*scratch));
976 smemclr(a, 2 * len * sizeof(*a));
978 smemclr(b, 2 * len * sizeof(*b));
980 smemclr(mninv, len * sizeof(*mninv));
982 smemclr(n, len * sizeof(*n));
984 smemclr(x, len * sizeof(*x));
991 * Compute (p * q) % mod.
992 * The most significant word of mod MUST be non-zero.
993 * We assume that the result array is the same size as the mod array.
995 Bignum modmul(Bignum p, Bignum q, Bignum mod)
997 BignumInt *a, *n, *m, *o, *scratch;
998 int mshift, scratchlen;
999 int pqlen, mlen, rlen, i, j;
1003 * The most significant word of mod needs to be non-zero. It
1004 * should already be, but let's make sure.
1006 assert(mod[mod[0]] != 0);
1008 /* Allocate m of size mlen, copy mod to m */
1009 /* We use big endian internally */
1011 m = snewn(mlen, BignumInt);
1012 for (j = 0; j < mlen; j++)
1013 m[j] = mod[mod[0] - j];
1015 /* Shift m left to make msb bit set */
1016 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
1017 if ((m[0] << mshift) & BIGNUM_TOP_BIT)
1020 for (i = 0; i < mlen - 1; i++)
1021 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
1022 m[mlen - 1] = m[mlen - 1] << mshift;
1025 pqlen = (p[0] > q[0] ? p[0] : q[0]);
1028 * Make sure that we're allowing enough space. The shifting below
1029 * will underflow the vectors we allocate if pqlen is too small.
1031 if (2*pqlen <= mlen)
1034 /* Allocate n of size pqlen, copy p to n */
1035 n = snewn(pqlen, BignumInt);
1037 for (j = 0; j < i; j++)
1039 for (j = 0; j < (int)p[0]; j++)
1040 n[i + j] = p[p[0] - j];
1042 /* Allocate o of size pqlen, copy q to o */
1043 o = snewn(pqlen, BignumInt);
1045 for (j = 0; j < i; j++)
1047 for (j = 0; j < (int)q[0]; j++)
1048 o[i + j] = q[q[0] - j];
1050 /* Allocate a of size 2*pqlen for result */
1051 a = snewn(2 * pqlen, BignumInt);
1053 /* Scratch space for multiplies */
1054 scratchlen = mul_compute_scratch(pqlen);
1055 scratch = snewn(scratchlen, BignumInt);
1057 /* Main computation */
1058 internal_mul(n, o, a, pqlen, scratch);
1059 internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
1061 /* Fixup result in case the modulus was shifted */
1063 for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++)
1064 a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift));
1065 a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift;
1066 internal_mod(a, pqlen * 2, m, mlen, NULL, 0);
1067 for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--)
1068 a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift));
1071 /* Copy result to buffer */
1072 rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2);
1073 result = newbn(rlen);
1074 for (i = 0; i < rlen; i++)
1075 result[result[0] - i] = a[i + 2 * pqlen - rlen];
1076 while (result[0] > 1 && result[result[0]] == 0)
1079 /* Free temporary arrays */
1080 smemclr(scratch, scratchlen * sizeof(*scratch));
1082 smemclr(a, 2 * pqlen * sizeof(*a));
1084 smemclr(m, mlen * sizeof(*m));
1086 smemclr(n, pqlen * sizeof(*n));
1088 smemclr(o, pqlen * sizeof(*o));
1096 * The most significant word of mod MUST be non-zero.
1097 * We assume that the result array is the same size as the mod array.
1098 * We optionally write out a quotient if `quotient' is non-NULL.
1099 * We can avoid writing out the result if `result' is NULL.
1101 static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient)
1105 int plen, mlen, i, j;
1108 * The most significant word of mod needs to be non-zero. It
1109 * should already be, but let's make sure.
1111 assert(mod[mod[0]] != 0);
1113 /* Allocate m of size mlen, copy mod to m */
1114 /* We use big endian internally */
1116 m = snewn(mlen, BignumInt);
1117 for (j = 0; j < mlen; j++)
1118 m[j] = mod[mod[0] - j];
1120 /* Shift m left to make msb bit set */
1121 for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++)
1122 if ((m[0] << mshift) & BIGNUM_TOP_BIT)
1125 for (i = 0; i < mlen - 1; i++)
1126 m[i] = (m[i] << mshift) | (m[i + 1] >> (BIGNUM_INT_BITS - mshift));
1127 m[mlen - 1] = m[mlen - 1] << mshift;
1131 /* Ensure plen > mlen */
1135 /* Allocate n of size plen, copy p to n */
1136 n = snewn(plen, BignumInt);
1137 for (j = 0; j < plen; j++)
1139 for (j = 1; j <= (int)p[0]; j++)
1142 /* Main computation */
1143 internal_mod(n, plen, m, mlen, quotient, mshift);
1145 /* Fixup result in case the modulus was shifted */
1147 for (i = plen - mlen - 1; i < plen - 1; i++)
1148 n[i] = (n[i] << mshift) | (n[i + 1] >> (BIGNUM_INT_BITS - mshift));
1149 n[plen - 1] = n[plen - 1] << mshift;
1150 internal_mod(n, plen, m, mlen, quotient, 0);
1151 for (i = plen - 1; i >= plen - mlen; i--)
1152 n[i] = (n[i] >> mshift) | (n[i - 1] << (BIGNUM_INT_BITS - mshift));
1155 /* Copy result to buffer */
1157 for (i = 1; i <= (int)result[0]; i++) {
1159 result[i] = j >= 0 ? n[j] : 0;
1163 /* Free temporary arrays */
1164 smemclr(m, mlen * sizeof(*m));
1166 smemclr(n, plen * sizeof(*n));
1171 * Decrement a number.
1173 void decbn(Bignum bn)
1176 while (i < (int)bn[0] && bn[i] == 0)
1177 bn[i++] = BIGNUM_INT_MASK;
1181 Bignum bignum_from_bytes(const unsigned char *data, int nbytes)
1186 assert(nbytes >= 0 && nbytes < INT_MAX/8);
1188 w = (nbytes + BIGNUM_INT_BYTES - 1) / BIGNUM_INT_BYTES; /* bytes->words */
1191 for (i = 1; i <= w; i++)
1193 for (i = nbytes; i--;) {
1194 unsigned char byte = *data++;
1195 result[1 + i / BIGNUM_INT_BYTES] |= byte << (8*i % BIGNUM_INT_BITS);
1198 while (result[0] > 1 && result[result[0]] == 0)
1204 * Read an SSH-1-format bignum from a data buffer. Return the number
1205 * of bytes consumed, or -1 if there wasn't enough data.
1207 int ssh1_read_bignum(const unsigned char *data, int len, Bignum * result)
1209 const unsigned char *p = data;
1217 for (i = 0; i < 2; i++)
1218 w = (w << 8) + *p++;
1219 b = (w + 7) / 8; /* bits -> bytes */
1224 if (!result) /* just return length */
1227 *result = bignum_from_bytes(p, b);
1229 return p + b - data;
1233 * Return the bit count of a bignum, for SSH-1 encoding.
1235 int bignum_bitcount(Bignum bn)
1237 int bitcount = bn[0] * BIGNUM_INT_BITS - 1;
1238 while (bitcount >= 0
1239 && (bn[bitcount / BIGNUM_INT_BITS + 1] >> (bitcount % BIGNUM_INT_BITS)) == 0) bitcount--;
1240 return bitcount + 1;
1244 * Return the byte length of a bignum when SSH-1 encoded.
1246 int ssh1_bignum_length(Bignum bn)
1248 return 2 + (bignum_bitcount(bn) + 7) / 8;
1252 * Return the byte length of a bignum when SSH-2 encoded.
1254 int ssh2_bignum_length(Bignum bn)
1256 return 4 + (bignum_bitcount(bn) + 8) / 8;
1260 * Return a byte from a bignum; 0 is least significant, etc.
1262 int bignum_byte(Bignum bn, int i)
1264 if (i < 0 || i >= (int)(BIGNUM_INT_BYTES * bn[0]))
1265 return 0; /* beyond the end */
1267 return (bn[i / BIGNUM_INT_BYTES + 1] >>
1268 ((i % BIGNUM_INT_BYTES)*8)) & 0xFF;
1272 * Return a bit from a bignum; 0 is least significant, etc.
1274 int bignum_bit(Bignum bn, int i)
1276 if (i < 0 || i >= (int)(BIGNUM_INT_BITS * bn[0]))
1277 return 0; /* beyond the end */
1279 return (bn[i / BIGNUM_INT_BITS + 1] >> (i % BIGNUM_INT_BITS)) & 1;
1283 * Set a bit in a bignum; 0 is least significant, etc.
1285 void bignum_set_bit(Bignum bn, int bitnum, int value)
1287 if (bitnum < 0 || bitnum >= (int)(BIGNUM_INT_BITS * bn[0]))
1288 abort(); /* beyond the end */
1290 int v = bitnum / BIGNUM_INT_BITS + 1;
1291 int mask = 1 << (bitnum % BIGNUM_INT_BITS);
1300 * Write a SSH-1-format bignum into a buffer. It is assumed the
1301 * buffer is big enough. Returns the number of bytes used.
1303 int ssh1_write_bignum(void *data, Bignum bn)
1305 unsigned char *p = data;
1306 int len = ssh1_bignum_length(bn);
1308 int bitc = bignum_bitcount(bn);
1310 *p++ = (bitc >> 8) & 0xFF;
1311 *p++ = (bitc) & 0xFF;
1312 for (i = len - 2; i--;)
1313 *p++ = bignum_byte(bn, i);
1318 * Compare two bignums. Returns like strcmp.
1320 int bignum_cmp(Bignum a, Bignum b)
1322 int amax = a[0], bmax = b[0];
1325 assert(amax == 0 || a[amax] != 0);
1326 assert(bmax == 0 || b[bmax] != 0);
1328 i = (amax > bmax ? amax : bmax);
1330 BignumInt aval = (i > amax ? 0 : a[i]);
1331 BignumInt bval = (i > bmax ? 0 : b[i]);
1342 * Right-shift one bignum to form another.
1344 Bignum bignum_rshift(Bignum a, int shift)
1347 int i, shiftw, shiftb, shiftbb, bits;
1352 bits = bignum_bitcount(a) - shift;
1353 ret = newbn((bits + BIGNUM_INT_BITS - 1) / BIGNUM_INT_BITS);
1356 shiftw = shift / BIGNUM_INT_BITS;
1357 shiftb = shift % BIGNUM_INT_BITS;
1358 shiftbb = BIGNUM_INT_BITS - shiftb;
1360 ai1 = a[shiftw + 1];
1361 for (i = 1; i <= (int)ret[0]; i++) {
1363 ai1 = (i + shiftw + 1 <= (int)a[0] ? a[i + shiftw + 1] : 0);
1364 ret[i] = ((ai >> shiftb) | (ai1 << shiftbb)) & BIGNUM_INT_MASK;
1372 * Non-modular multiplication and addition.
1374 Bignum bigmuladd(Bignum a, Bignum b, Bignum addend)
1376 int alen = a[0], blen = b[0];
1377 int mlen = (alen > blen ? alen : blen);
1378 int rlen, i, maxspot;
1380 BignumInt *workspace;
1383 /* mlen space for a, mlen space for b, 2*mlen for result,
1384 * plus scratch space for multiplication */
1385 wslen = mlen * 4 + mul_compute_scratch(mlen);
1386 workspace = snewn(wslen, BignumInt);
1387 for (i = 0; i < mlen; i++) {
1388 workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0);
1389 workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0);
1392 internal_mul(workspace + 0 * mlen, workspace + 1 * mlen,
1393 workspace + 2 * mlen, mlen, workspace + 4 * mlen);
1395 /* now just copy the result back */
1396 rlen = alen + blen + 1;
1397 if (addend && rlen <= (int)addend[0])
1398 rlen = addend[0] + 1;
1401 for (i = 1; i <= (int)ret[0]; i++) {
1402 ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0);
1408 /* now add in the addend, if any */
1410 BignumDblInt carry = 0;
1411 for (i = 1; i <= rlen; i++) {
1412 carry += (i <= (int)ret[0] ? ret[i] : 0);
1413 carry += (i <= (int)addend[0] ? addend[i] : 0);
1414 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
1415 carry >>= BIGNUM_INT_BITS;
1416 if (ret[i] != 0 && i > maxspot)
1422 smemclr(workspace, wslen * sizeof(*workspace));
1428 * Non-modular multiplication.
1430 Bignum bigmul(Bignum a, Bignum b)
1432 return bigmuladd(a, b, NULL);
1438 Bignum bigadd(Bignum a, Bignum b)
1440 int alen = a[0], blen = b[0];
1441 int rlen = (alen > blen ? alen : blen) + 1;
1450 for (i = 1; i <= rlen; i++) {
1451 carry += (i <= (int)a[0] ? a[i] : 0);
1452 carry += (i <= (int)b[0] ? b[i] : 0);
1453 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
1454 carry >>= BIGNUM_INT_BITS;
1455 if (ret[i] != 0 && i > maxspot)
1464 * Subtraction. Returns a-b, or NULL if the result would come out
1465 * negative (recall that this entire bignum module only handles
1466 * positive numbers).
1468 Bignum bigsub(Bignum a, Bignum b)
1470 int alen = a[0], blen = b[0];
1471 int rlen = (alen > blen ? alen : blen);
1480 for (i = 1; i <= rlen; i++) {
1481 carry += (i <= (int)a[0] ? a[i] : 0);
1482 carry += (i <= (int)b[0] ? b[i] ^ BIGNUM_INT_MASK : BIGNUM_INT_MASK);
1483 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
1484 carry >>= BIGNUM_INT_BITS;
1485 if (ret[i] != 0 && i > maxspot)
1499 * Create a bignum which is the bitmask covering another one. That
1500 * is, the smallest integer which is >= N and is also one less than
1503 Bignum bignum_bitmask(Bignum n)
1505 Bignum ret = copybn(n);
1510 while (n[i] == 0 && i > 0)
1513 return ret; /* input was zero */
1519 ret[i] = BIGNUM_INT_MASK;
1524 * Convert a (max 32-bit) long into a bignum.
1526 Bignum bignum_from_long(unsigned long nn)
1529 BignumDblInt n = nn;
1532 ret[1] = (BignumInt)(n & BIGNUM_INT_MASK);
1533 ret[2] = (BignumInt)((n >> BIGNUM_INT_BITS) & BIGNUM_INT_MASK);
1535 ret[0] = (ret[2] ? 2 : 1);
1540 * Add a long to a bignum.
1542 Bignum bignum_add_long(Bignum number, unsigned long addendx)
1544 Bignum ret = newbn(number[0] + 1);
1546 BignumDblInt carry = 0, addend = addendx;
1548 for (i = 1; i <= (int)ret[0]; i++) {
1549 carry += addend & BIGNUM_INT_MASK;
1550 carry += (i <= (int)number[0] ? number[i] : 0);
1551 addend >>= BIGNUM_INT_BITS;
1552 ret[i] = (BignumInt) carry & BIGNUM_INT_MASK;
1553 carry >>= BIGNUM_INT_BITS;
1562 * Compute the residue of a bignum, modulo a (max 16-bit) short.
1564 unsigned short bignum_mod_short(Bignum number, unsigned short modulus)
1566 BignumDblInt mod, r;
1571 for (i = number[0]; i > 0; i--)
1572 r = (r * (BIGNUM_TOP_BIT % mod) * 2 + number[i] % mod) % mod;
1573 return (unsigned short) r;
1577 void diagbn(char *prefix, Bignum md)
1579 int i, nibbles, morenibbles;
1580 static const char hex[] = "0123456789ABCDEF";
1582 debug(("%s0x", prefix ? prefix : ""));
1584 nibbles = (3 + bignum_bitcount(md)) / 4;
1587 morenibbles = 4 * md[0] - nibbles;
1588 for (i = 0; i < morenibbles; i++)
1590 for (i = nibbles; i--;)
1592 hex[(bignum_byte(md, i / 2) >> (4 * (i % 2))) & 0xF]));
1602 Bignum bigdiv(Bignum a, Bignum b)
1604 Bignum q = newbn(a[0]);
1605 bigdivmod(a, b, NULL, q);
1612 Bignum bigmod(Bignum a, Bignum b)
1614 Bignum r = newbn(b[0]);
1615 bigdivmod(a, b, r, NULL);
1620 * Greatest common divisor.
1622 Bignum biggcd(Bignum av, Bignum bv)
1624 Bignum a = copybn(av);
1625 Bignum b = copybn(bv);
1627 while (bignum_cmp(b, Zero) != 0) {
1628 Bignum t = newbn(b[0]);
1629 bigdivmod(a, b, t, NULL);
1630 while (t[0] > 1 && t[t[0]] == 0)
1642 * Modular inverse, using Euclid's extended algorithm.
1644 Bignum modinv(Bignum number, Bignum modulus)
1646 Bignum a = copybn(modulus);
1647 Bignum b = copybn(number);
1648 Bignum xp = copybn(Zero);
1649 Bignum x = copybn(One);
1652 assert(number[number[0]] != 0);
1653 assert(modulus[modulus[0]] != 0);
1655 while (bignum_cmp(b, One) != 0) {
1658 if (bignum_cmp(b, Zero) == 0) {
1660 * Found a common factor between the inputs, so we cannot
1661 * return a modular inverse at all.
1672 bigdivmod(a, b, t, q);
1673 while (t[0] > 1 && t[t[0]] == 0)
1680 x = bigmuladd(q, xp, t);
1690 /* now we know that sign * x == 1, and that x < modulus */
1692 /* set a new x to be modulus - x */
1693 Bignum newx = newbn(modulus[0]);
1694 BignumInt carry = 0;
1698 for (i = 1; i <= (int)newx[0]; i++) {
1699 BignumInt aword = (i <= (int)modulus[0] ? modulus[i] : 0);
1700 BignumInt bword = (i <= (int)x[0] ? x[i] : 0);
1701 newx[i] = aword - bword - carry;
1703 carry = carry ? (newx[i] >= bword) : (newx[i] > bword);
1717 * Render a bignum into decimal. Return a malloced string holding
1718 * the decimal representation.
1720 char *bignum_decimal(Bignum x)
1722 int ndigits, ndigit;
1726 BignumInt *workspace;
1729 * First, estimate the number of digits. Since log(10)/log(2)
1730 * is just greater than 93/28 (the joys of continued fraction
1731 * approximations...) we know that for every 93 bits, we need
1732 * at most 28 digits. This will tell us how much to malloc.
1734 * Formally: if x has i bits, that means x is strictly less
1735 * than 2^i. Since 2 is less than 10^(28/93), this is less than
1736 * 10^(28i/93). We need an integer power of ten, so we must
1737 * round up (rounding down might make it less than x again).
1738 * Therefore if we multiply the bit count by 28/93, rounding
1739 * up, we will have enough digits.
1741 * i=0 (i.e., x=0) is an irritating special case.
1743 i = bignum_bitcount(x);
1745 ndigits = 1; /* x = 0 */
1747 ndigits = (28 * i + 92) / 93; /* multiply by 28/93 and round up */
1748 ndigits++; /* allow for trailing \0 */
1749 ret = snewn(ndigits, char);
1752 * Now allocate some workspace to hold the binary form as we
1753 * repeatedly divide it by ten. Initialise this to the
1754 * big-endian form of the number.
1756 workspace = snewn(x[0], BignumInt);
1757 for (i = 0; i < (int)x[0]; i++)
1758 workspace[i] = x[x[0] - i];
1761 * Next, write the decimal number starting with the last digit.
1762 * We use ordinary short division, dividing 10 into the
1765 ndigit = ndigits - 1;
1770 for (i = 0; i < (int)x[0]; i++) {
1771 carry = (carry << BIGNUM_INT_BITS) + workspace[i];
1772 workspace[i] = (BignumInt) (carry / 10);
1777 ret[--ndigit] = (char) (carry + '0');
1781 * There's a chance we've fallen short of the start of the
1782 * string. Correct if so.
1785 memmove(ret, ret + ndigit, ndigits - ndigit);
1790 smemclr(workspace, x[0] * sizeof(*workspace));
1802 * gcc -Wall -g -O0 -DTESTBN -o testbn sshbn.c misc.c conf.c tree234.c unix/uxmisc.c -I. -I unix -I charset
1804 * Then feed to this program's standard input the output of
1805 * testdata/bignum.py .
1808 void modalfatalbox(char *p, ...)
1811 fprintf(stderr, "FATAL ERROR: ");
1813 vfprintf(stderr, p, ap);
1815 fputc('\n', stderr);
1819 #define fromxdigit(c) ( (c)>'9' ? ((c)&0xDF) - 'A' + 10 : (c) - '0' )
1821 int main(int argc, char **argv)
1825 int passes = 0, fails = 0;
1827 while ((buf = fgetline(stdin)) != NULL) {
1828 int maxlen = strlen(buf);
1829 unsigned char *data = snewn(maxlen, unsigned char);
1830 unsigned char *ptrs[5], *q;
1839 while (*bufp && !isspace((unsigned char)*bufp))
1848 while (*bufp && !isxdigit((unsigned char)*bufp))
1855 while (*bufp && isxdigit((unsigned char)*bufp))
1859 if (ptrnum >= lenof(ptrs))
1863 for (i = -((end - start) & 1); i < end-start; i += 2) {
1864 unsigned char val = (i < 0 ? 0 : fromxdigit(start[i]));
1865 val = val * 16 + fromxdigit(start[i+1]);
1872 if (!strcmp(buf, "mul")) {
1876 printf("%d: mul with %d parameters, expected 3\n", line, ptrnum);
1879 a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
1880 b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
1881 c = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
1884 if (bignum_cmp(c, p) == 0) {
1887 char *as = bignum_decimal(a);
1888 char *bs = bignum_decimal(b);
1889 char *cs = bignum_decimal(c);
1890 char *ps = bignum_decimal(p);
1892 printf("%d: fail: %s * %s gave %s expected %s\n",
1893 line, as, bs, ps, cs);
1905 } else if (!strcmp(buf, "modmul")) {
1906 Bignum a, b, m, c, p;
1909 printf("%d: modmul with %d parameters, expected 4\n",
1913 a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
1914 b = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
1915 m = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
1916 c = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);
1917 p = modmul(a, b, m);
1919 if (bignum_cmp(c, p) == 0) {
1922 char *as = bignum_decimal(a);
1923 char *bs = bignum_decimal(b);
1924 char *ms = bignum_decimal(m);
1925 char *cs = bignum_decimal(c);
1926 char *ps = bignum_decimal(p);
1928 printf("%d: fail: %s * %s mod %s gave %s expected %s\n",
1929 line, as, bs, ms, ps, cs);
1943 } else if (!strcmp(buf, "pow")) {
1944 Bignum base, expt, modulus, expected, answer;
1947 printf("%d: mul with %d parameters, expected 4\n", line, ptrnum);
1951 base = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]);
1952 expt = bignum_from_bytes(ptrs[1], ptrs[2]-ptrs[1]);
1953 modulus = bignum_from_bytes(ptrs[2], ptrs[3]-ptrs[2]);
1954 expected = bignum_from_bytes(ptrs[3], ptrs[4]-ptrs[3]);
1955 answer = modpow(base, expt, modulus);
1957 if (bignum_cmp(expected, answer) == 0) {
1960 char *as = bignum_decimal(base);
1961 char *bs = bignum_decimal(expt);
1962 char *cs = bignum_decimal(modulus);
1963 char *ds = bignum_decimal(answer);
1964 char *ps = bignum_decimal(expected);
1966 printf("%d: fail: %s ^ %s mod %s gave %s expected %s\n",
1967 line, as, bs, cs, ds, ps);
1982 printf("%d: unrecognised test keyword: '%s'\n", line, buf);
1990 printf("passed %d failed %d total %d\n", passes, fails, passes+fails);