X-Git-Url: https://git.distorted.org.uk/~mdw/sgt/putty/blobdiff_plain/f84f1e4687ac1d4cda81b0cf8cd5a5092b84235e..8d90b8b27bf086da6245030459ab3e5977313eb0:/sshbn.c diff --git a/sshbn.c b/sshbn.c index bfc34fb8..ecdb90e8 100644 --- a/sshbn.c +++ b/sshbn.c @@ -148,7 +148,7 @@ void freebn(Bignum b) /* * Burn the evidence, just in case. */ - memset(b, 0, sizeof(b[0]) * (b[0] + 1)); + smemclr(b, sizeof(b[0]) * (b[0] + 1)); sfree(b); } @@ -201,15 +201,28 @@ static void internal_sub(const BignumInt *a, const BignumInt *b, * Compute c = a * b. * Input is in the first len words of a and b. * Result is returned in the first 2*len words of c. + * + * 'scratch' must point to an array of BignumInt of size at least + * mul_compute_scratch(len). (This covers the needs of internal_mul + * and all its recursive calls to itself.) */ #define KARATSUBA_THRESHOLD 50 +static int mul_compute_scratch(int len) +{ + int ret = 0; + while (len > KARATSUBA_THRESHOLD) { + int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */ + int midlen = botlen + 1; + ret += 4*midlen; + len = midlen; + } + return ret; +} static void internal_mul(const BignumInt *a, const BignumInt *b, - BignumInt *c, int len) + BignumInt *c, int len, BignumInt *scratch) { - int i, j; - BignumDblInt t; - if (len > KARATSUBA_THRESHOLD) { + int i; /* * Karatsuba divide-and-conquer algorithm. Cut each input in @@ -245,7 +258,6 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */ int midlen = botlen + 1; - BignumInt *scratch; BignumDblInt carry; #ifdef KARA_DEBUG int i; @@ -273,7 +285,7 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, #endif /* a_1 b_1 */ - internal_mul(a, b, c, toplen); + internal_mul(a, b, c, toplen, scratch); #ifdef KARA_DEBUG printf("a1b1 = 0x"); for (i = 0; i < 2*toplen; i++) { @@ -283,7 +295,7 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, #endif /* a_0 b_0 */ - internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen); + internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch); #ifdef KARA_DEBUG printf("a0b0 = 0x"); for (i = 0; i < 2*botlen; i++) { @@ -292,23 +304,14 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, printf("\n"); #endif - /* - * We must allocate scratch space for the central coefficient, - * and also for the two input values that we multiply when - * computing it. Since either or both may carry into the - * (botlen+1)th word, we must use a slightly longer length - * 'midlen'. - */ - scratch = snewn(4 * midlen, BignumInt); - /* Zero padding. midlen exceeds toplen by at most 2, so just * zero the first two words of each input and the rest will be * copied over. */ scratch[0] = scratch[1] = scratch[midlen] = scratch[midlen+1] = 0; - for (j = 0; j < toplen; j++) { - scratch[midlen - toplen + j] = a[j]; /* a_1 */ - scratch[2*midlen - toplen + j] = b[j]; /* b_1 */ + for (i = 0; i < toplen; i++) { + scratch[midlen - toplen + i] = a[i]; /* a_1 */ + scratch[2*midlen - toplen + i] = b[i]; /* b_1 */ } /* compute a_1 + a_0 */ @@ -334,7 +337,8 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, /* * Now we can do the third multiplication. */ - internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen); + internal_mul(scratch, scratch + midlen, scratch + 2*midlen, midlen, + scratch + 4*midlen); #ifdef KARA_DEBUG printf("a1plusa0timesb1plusb0 = 0x"); for (i = 0; i < 2*midlen; i++) { @@ -349,8 +353,8 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, * product to obtain the middle one. */ scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0; - for (j = 0; j < 2*toplen; j++) - scratch[2*midlen - 2*toplen + j] = c[j]; + for (i = 0; i < 2*toplen; i++) + scratch[2*midlen - 2*toplen + i] = c[i]; scratch[1] = internal_add(scratch+2, c + 2*toplen, scratch+2, 2*botlen); #ifdef KARA_DEBUG @@ -380,13 +384,13 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, carry = internal_add(c + 2*len - botlen - 2*midlen, scratch + 2*midlen, c + 2*len - botlen - 2*midlen, 2*midlen); - j = 2*len - botlen - 2*midlen - 1; + i = 2*len - botlen - 2*midlen - 1; while (carry) { - assert(j >= 0); - carry += c[j]; - c[j] = (BignumInt)carry; + assert(i >= 0); + carry += c[i]; + c[i] = (BignumInt)carry; carry >>= BIGNUM_INT_BITS; - j--; + i--; } #ifdef KARA_DEBUG printf("ab = 0x"); @@ -396,29 +400,28 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, printf("\n"); #endif - /* Free scratch. */ - for (j = 0; j < 4 * midlen; j++) - scratch[j] = 0; - sfree(scratch); - } else { + int i; + BignumInt carry; + BignumDblInt t; + const BignumInt *ap, *bp; + BignumInt *cp, *cps; /* * Multiply in the ordinary O(N^2) way. */ - for (j = 0; j < 2 * len; j++) - c[j] = 0; + for (i = 0; i < 2 * len; i++) + c[i] = 0; - for (i = len - 1; i >= 0; i--) { - t = 0; - for (j = len - 1; j >= 0; j--) { - t += MUL_WORD(a[i], (BignumDblInt) b[j]); - t += (BignumDblInt) c[i + j + 1]; - c[i + j + 1] = (BignumInt) t; - t = t >> BIGNUM_INT_BITS; + for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) { + carry = 0; + for (cp = cps, bp = b + len; cp--, bp-- > b ;) { + t = (MUL_WORD(*ap, *bp) + carry) + *cp; + *cp = (BignumInt) t; + carry = (BignumInt)(t >> BIGNUM_INT_BITS); } - c[i] = (BignumInt) t; + *cp = carry; } } } @@ -429,12 +432,10 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, * (everything above that is thrown away). */ static void internal_mul_low(const BignumInt *a, const BignumInt *b, - BignumInt *c, int len) + BignumInt *c, int len, BignumInt *scratch) { - int i, j; - BignumDblInt t; - if (len > KARATSUBA_THRESHOLD) { + int i; /* * Karatsuba-aware version of internal_mul_low. As before, we @@ -469,29 +470,30 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, */ int toplen = len/2, botlen = len - toplen; /* botlen is the bigger */ - BignumInt *scratch; /* - * Allocate scratch space for the various bits and pieces - * we're going to be adding together. We need botlen*2 words - * for a_0 b_0 (though we may end up throwing away its topmost - * word), and toplen words for each of a_1 b_0 and a_0 b_1. - * That adds up to exactly 2*len. + * Scratch space for the various bits and pieces we're going + * to be adding together: we need botlen*2 words for a_0 b_0 + * (though we may end up throwing away its topmost word), and + * toplen words for each of a_1 b_0 and a_0 b_1. That adds up + * to exactly 2*len. */ - scratch = snewn(len*2, BignumInt); /* a_0 b_0 */ - internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen); + internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen, + scratch + 2*len); /* a_1 b_0 */ - internal_mul_low(a, b + len - toplen, scratch + toplen, toplen); + internal_mul_low(a, b + len - toplen, scratch + toplen, toplen, + scratch + 2*len); /* a_0 b_1 */ - internal_mul_low(a + len - toplen, b, scratch, toplen); + internal_mul_low(a + len - toplen, b, scratch, toplen, + scratch + 2*len); /* Copy the bottom half of the big coefficient into place */ - for (j = 0; j < botlen; j++) - c[toplen + j] = scratch[2*toplen + botlen + j]; + for (i = 0; i < botlen; i++) + c[toplen + i] = scratch[2*toplen + botlen + i]; /* Add the two small coefficients, throwing away the returned carry */ internal_add(scratch, scratch + toplen, scratch, toplen); @@ -500,26 +502,28 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, internal_add(scratch, scratch + 2*toplen + botlen - toplen, c, toplen); - /* Free scratch. */ - for (j = 0; j < len*2; j++) - scratch[j] = 0; - sfree(scratch); - } else { + int i; + BignumInt carry; + BignumDblInt t; + const BignumInt *ap, *bp; + BignumInt *cp, *cps; - for (j = 0; j < len; j++) - c[j] = 0; + /* + * Multiply in the ordinary O(N^2) way. + */ - for (i = len - 1; i >= 0; i--) { - t = 0; - for (j = len - 1; j >= len - i - 1; j--) { - t += MUL_WORD(a[i], (BignumDblInt) b[j]); - t += (BignumDblInt) c[i + j + 1 - len]; - c[i + j + 1 - len] = (BignumInt) t; - t = t >> BIGNUM_INT_BITS; + for (i = 0; i < len; i++) + c[i] = 0; + + for (cps = c + len, ap = a + len; ap-- > a; cps--) { + carry = 0; + for (cp = cps, bp = b + len; bp--, cp-- > c ;) { + t = (MUL_WORD(*ap, *bp) + carry) + *cp; + *cp = (BignumInt) t; + carry = (BignumInt)(t >> BIGNUM_INT_BITS); } } - } } @@ -534,8 +538,8 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, * each, containing respectively n and the multiplicative inverse of * -n mod r. * - * 'tmp' is an array of at least '3*len' BignumInts used as scratch - * space. + * 'tmp' is an array of BignumInt used as scratch space, of length at + * least 3*len + mul_compute_scratch(len). */ static void monty_reduce(BignumInt *x, const BignumInt *n, const BignumInt *mninv, BignumInt *tmp, int len) @@ -548,7 +552,7 @@ static void monty_reduce(BignumInt *x, const BignumInt *n, * that mn is congruent to -x mod r. Hence, mn+x is an exact * multiple of r, and is also (obviously) congruent to x mod n. */ - internal_mul_low(x + len, mninv, tmp, len); + internal_mul_low(x + len, mninv, tmp, len, tmp + 3*len); /* * Compute t = (mn+x)/r in ordinary, non-modular, integer @@ -559,7 +563,7 @@ static void monty_reduce(BignumInt *x, const BignumInt *n, * significant half of the 'x' array, so then we must shift it * down. */ - internal_mul(tmp, n, tmp+len, len); + internal_mul(tmp, n, tmp+len, len, tmp + 3*len); carry = internal_add(x, tmp+len, x, 2*len); for (i = 0; i < len; i++) x[len + i] = x[i], x[i] = 0; @@ -709,9 +713,9 @@ static void internal_mod(BignumInt *a, int alen, */ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) { - BignumInt *a, *b, *n, *m; + BignumInt *a, *b, *n, *m, *scratch; int mshift; - int mlen, i, j; + int mlen, scratchlen, i, j; Bignum base, result; /* @@ -758,6 +762,10 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) a[i] = 0; a[2 * mlen - 1] = 1; + /* Scratch space for multiplies */ + scratchlen = mul_compute_scratch(mlen); + scratch = snewn(scratchlen, BignumInt); + /* Skip leading zero bits of exp. */ i = 0; j = BIGNUM_INT_BITS-1; @@ -772,10 +780,10 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) /* Main computation */ while (i < (int)exp[0]) { while (j >= 0) { - internal_mul(a + mlen, a + mlen, b, mlen); + 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) { - internal_mul(b + mlen, n, a, mlen); + internal_mul(b + mlen, n, a, mlen, scratch); internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { BignumInt *t; @@ -807,17 +815,15 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) 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 < 2 * mlen; i++) - b[i] = 0; + smemclr(scratch, scratchlen * sizeof(*scratch)); + sfree(scratch); + 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); @@ -831,8 +837,8 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) */ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) { - BignumInt *a, *b, *x, *n, *mninv, *tmp; - int len, i, j; + BignumInt *a, *b, *x, *n, *mninv, *scratch; + int len, scratchlen, i, j; Bignum base, base2, r, rn, inv, result; /* @@ -886,7 +892,7 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) mninv = snewn(len, BignumInt); for (j = 0; j < len; j++) - mninv[len - 1 - j] = (j < inv[0] ? inv[j + 1] : 0); + mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0); freebn(inv); /* we don't need this copy of it any more */ /* Now negate mninv mod r, so it's the inverse of -n rather than +n. */ x = snewn(len, BignumInt); @@ -896,16 +902,18 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) /* x = snewn(len, BignumInt); */ /* already done above */ for (j = 0; j < len; j++) - x[len - 1 - j] = (j < base[0] ? base[j + 1] : 0); + x[len - 1 - j] = (j < (int)base[0] ? base[j + 1] : 0); freebn(base); /* we don't need this copy of it any more */ a = snewn(2*len, BignumInt); b = snewn(2*len, BignumInt); for (j = 0; j < len; j++) - a[2*len - 1 - j] = (j < rn[0] ? rn[j + 1] : 0); + a[2*len - 1 - j] = (j < (int)rn[0] ? rn[j + 1] : 0); freebn(rn); - tmp = snewn(3*len, BignumInt); + /* Scratch space for multiplies */ + scratchlen = 3*len + mul_compute_scratch(len); + scratch = snewn(scratchlen, BignumInt); /* Skip leading zero bits of exp. */ i = 0; @@ -921,11 +929,11 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) /* Main computation */ while (i < (int)exp[0]) { while (j >= 0) { - internal_mul(a + len, a + len, b, len); - monty_reduce(b, n, mninv, tmp, len); + internal_mul(a + len, a + len, b, len, scratch); + monty_reduce(b, n, mninv, scratch, len); if ((exp[exp[0] - i] & (1 << j)) != 0) { - internal_mul(b + len, x, a, len); - monty_reduce(a, n, mninv, tmp, len); + internal_mul(b + len, x, a, len, scratch); + monty_reduce(a, n, mninv, scratch, len); } else { BignumInt *t; t = a; @@ -942,7 +950,7 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) * Final monty_reduce to get back from the adjusted Montgomery * representation. */ - monty_reduce(a, n, mninv, tmp, len); + monty_reduce(a, n, mninv, scratch, len); /* Copy result to buffer */ result = newbn(mod[0]); @@ -952,23 +960,17 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) result[0]--; /* Free temporary arrays */ - for (i = 0; i < 3 * len; i++) - tmp[i] = 0; - sfree(tmp); - for (i = 0; i < 2 * len; i++) - a[i] = 0; + smemclr(scratch, scratchlen * sizeof(*scratch)); + sfree(scratch); + 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; @@ -981,8 +983,8 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) */ Bignum modmul(Bignum p, Bignum q, Bignum mod) { - BignumInt *a, *n, *m, *o; - int mshift; + BignumInt *a, *n, *m, *o, *scratch; + int mshift, scratchlen; int pqlen, mlen, rlen, i, j; Bignum result; @@ -1005,6 +1007,13 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) 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]; @@ -1024,8 +1033,12 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Allocate a of size 2*pqlen for result */ a = snewn(2 * pqlen, BignumInt); + /* Scratch space for multiplies */ + scratchlen = mul_compute_scratch(pqlen); + scratch = snewn(scratchlen, BignumInt); + /* Main computation */ - internal_mul(n, o, a, pqlen); + internal_mul(n, o, a, pqlen, scratch); internal_mod(a, pqlen * 2, m, mlen, NULL, 0); /* Fixup result in case the modulus was shifted */ @@ -1047,17 +1060,15 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) result[0]--; /* Free temporary arrays */ - for (i = 0; i < 2 * pqlen; i++) - a[i] = 0; + smemclr(scratch, scratchlen * sizeof(*scratch)); + sfree(scratch); + 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; @@ -1127,11 +1138,9 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) } /* 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); } @@ -1335,18 +1344,21 @@ 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; + int wslen; BignumInt *workspace; Bignum ret; - /* mlen space for a, mlen space for b, 2*mlen for result */ - workspace = snewn(mlen * 4, BignumInt); + /* mlen space for a, mlen space for b, 2*mlen for result, + * plus scratch space for multiplication */ + wslen = mlen * 4 + mul_compute_scratch(mlen); + workspace = snewn(wslen, BignumInt); for (i = 0; i < mlen; i++) { workspace[0 * mlen + i] = (mlen - i <= (int)a[0] ? a[mlen - i] : 0); workspace[1 * mlen + i] = (mlen - i <= (int)b[0] ? b[mlen - i] : 0); } internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, - workspace + 2 * mlen, mlen); + workspace + 2 * mlen, mlen, workspace + 4 * mlen); /* now just copy the result back */ rlen = alen + blen + 1; @@ -1375,6 +1387,7 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) } ret[0] = maxspot; + smemclr(workspace, wslen * sizeof(*workspace)); sfree(workspace); return ret; } @@ -1725,6 +1738,7 @@ char *bignum_decimal(Bignum x) /* * Done. */ + smemclr(workspace, x[0] * sizeof(*workspace)); sfree(workspace); return ret; } @@ -1736,7 +1750,7 @@ char *bignum_decimal(Bignum x) #include /* - * 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 . @@ -1810,7 +1824,7 @@ int main(int argc, char **argv) Bignum a, b, c, p; if (ptrnum != 3) { - printf("%d: mul with %d parameters, expected 3\n", line); + printf("%d: mul with %d parameters, expected 3\n", line, ptrnum); exit(1); } a = bignum_from_bytes(ptrs[0], ptrs[1]-ptrs[0]); @@ -1839,11 +1853,49 @@ 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 3\n", line); + printf("%d: mul with %d parameters, expected 4\n", line, ptrnum); exit(1); }