X-Git-Url: https://git.distorted.org.uk/u/mdw/putty/blobdiff_plain/aca5132bdf53bf0d7983c09b3b95c8bbec559580..c40be1ada3f1f69a36d0f6f149ee23b0389b78d2:/sshbn.c diff --git a/sshbn.c b/sshbn.c index da249781..2d81ee4c 100644 --- a/sshbn.c +++ b/sshbn.c @@ -161,7 +161,7 @@ Bignum bn_power_2(int n) /* * Internal addition. Sets c = a - b, where 'a', 'b' and 'c' are all - * big-endian arrays of 'len' BignumInts. Returns a BignumInt carried + * little-endian arrays of 'len' BignumInts. Returns a BignumInt carried * off the top. */ static BignumInt internal_add(const BignumInt *a, const BignumInt *b, @@ -170,7 +170,7 @@ static BignumInt internal_add(const BignumInt *a, const BignumInt *b, int i; BignumDblInt carry = 0; - for (i = len-1; i >= 0; i--) { + for (i = 0; i < len; i++) { carry += (BignumDblInt)a[i] + b[i]; c[i] = (BignumInt)carry; carry >>= BIGNUM_INT_BITS; @@ -181,7 +181,7 @@ static BignumInt internal_add(const BignumInt *a, const BignumInt *b, /* * Internal subtraction. Sets c = a - b, where 'a', 'b' and 'c' are - * all big-endian arrays of 'len' BignumInts. Any borrow from the top + * all little-endian arrays of 'len' BignumInts. Any borrow from the top * is ignored. */ static void internal_sub(const BignumInt *a, const BignumInt *b, @@ -190,7 +190,7 @@ static void internal_sub(const BignumInt *a, const BignumInt *b, int i; BignumDblInt carry = 1; - for (i = len-1; i >= 0; i--) { + for (i = 0; i < len; i++) { carry += (BignumDblInt)a[i] + (b[i] ^ BIGNUM_INT_MASK); c[i] = (BignumInt)carry; carry >>= BIGNUM_INT_BITS; @@ -270,63 +270,64 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, printf("a1,a0 = 0x"); for (i = 0; i < len; i++) { if (i == toplen) printf(", 0x"); - printf("%0*x", BIGNUM_INT_BITS/4, a[i]); + printf("%0*x", BIGNUM_INT_BITS/4, a[len - 1 - i]); } printf("\n"); printf("b1,b0 = 0x"); for (i = 0; i < len; i++) { if (i == toplen) printf(", 0x"); - printf("%0*x", BIGNUM_INT_BITS/4, b[i]); + printf("%0*x", BIGNUM_INT_BITS/4, b[len - 1 - i]); } printf("\n"); #endif /* a_1 b_1 */ - internal_mul(a, b, c, toplen, scratch); + internal_mul(a + botlen, b + botlen, c + 2*botlen, toplen, scratch); #ifdef KARA_DEBUG printf("a1b1 = 0x"); for (i = 0; i < 2*toplen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, c[i]); + printf("%0*x", BIGNUM_INT_BITS/4, c[2*len - 1 - i]); } printf("\n"); #endif /* a_0 b_0 */ - internal_mul(a + toplen, b + toplen, c + 2*toplen, botlen, scratch); + internal_mul(a, b, c, botlen, scratch); #ifdef KARA_DEBUG printf("a0b0 = 0x"); for (i = 0; i < 2*botlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, c[2*toplen+i]); + printf("%0*x", BIGNUM_INT_BITS/4, c[2*botlen - 1 - i]); } printf("\n"); #endif - /* 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; + /* Zero padding. botlen exceeds toplen by at most 1, and we'll set + * the extra carry explicitly below, so we only need to zero at most + * one of the top words here. + */ + scratch[midlen - 2] = scratch[2*midlen - 2] = 0; for (i = 0; i < toplen; i++) { - scratch[midlen - toplen + i] = a[i]; /* a_1 */ - scratch[2*midlen - toplen + i] = b[i]; /* b_1 */ + scratch[i] = a[i + botlen]; /* a_1 */ + scratch[midlen + i] = b[i + botlen]; /* b_1 */ } /* compute a_1 + a_0 */ - scratch[0] = internal_add(scratch+1, a+toplen, scratch+1, botlen); + scratch[midlen - 1] = internal_add(scratch, a, scratch, botlen); #ifdef KARA_DEBUG printf("a1plusa0 = 0x"); for (i = 0; i < midlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]); + printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen - 1 - i]); } printf("\n"); #endif /* compute b_1 + b_0 */ - scratch[midlen] = internal_add(scratch+midlen+1, b+toplen, - scratch+midlen+1, botlen); + scratch[2*midlen - 1] = internal_add(scratch+midlen, b, + scratch+midlen, botlen); #ifdef KARA_DEBUG printf("b1plusb0 = 0x"); for (i = 0; i < midlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, scratch[midlen+i]); + printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen - 1 - i]); } printf("\n"); #endif @@ -339,7 +340,7 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, #ifdef KARA_DEBUG printf("a1plusa0timesb1plusb0 = 0x"); for (i = 0; i < 2*midlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]); + printf("%0*x", BIGNUM_INT_BITS/4, scratch[4*midlen - 1 - i]); } printf("\n"); #endif @@ -349,25 +350,24 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, * sum of the outer two coefficients, to subtract from that * product to obtain the middle one. */ - scratch[0] = scratch[1] = scratch[2] = scratch[3] = 0; + scratch[2*botlen - 2] = scratch[2*botlen - 1] = 0; 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); + scratch[i] = c[2*botlen + i]; + scratch[2*botlen] = internal_add(scratch, c, scratch, 2*botlen); + scratch[2*botlen + 1] = 0; #ifdef KARA_DEBUG printf("a1b1plusa0b0 = 0x"); for (i = 0; i < 2*midlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, scratch[i]); + printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen - 1 - i]); } printf("\n"); #endif - internal_sub(scratch + 2*midlen, scratch, - scratch + 2*midlen, 2*midlen); + internal_sub(scratch + 2*midlen, scratch, scratch, 2*midlen); #ifdef KARA_DEBUG printf("a1b0plusa0b1 = 0x"); for (i = 0; i < 2*midlen; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, scratch[2*midlen+i]); + printf("%0*x", BIGNUM_INT_BITS/4, scratch[4*midlen - 1 - i]); } printf("\n"); #endif @@ -378,21 +378,19 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, * further up the output, but we can be sure it won't * propagate right the way off the top. */ - carry = internal_add(c + 2*len - botlen - 2*midlen, - scratch + 2*midlen, - c + 2*len - botlen - 2*midlen, 2*midlen); - i = 2*len - botlen - 2*midlen - 1; + carry = internal_add(c + botlen, scratch, c + botlen, 2*midlen); + i = botlen + 2*midlen; while (carry) { - assert(i >= 0); + assert(i <= 2*len); carry += c[i]; c[i] = (BignumInt)carry; carry >>= BIGNUM_INT_BITS; - i--; + i++; } #ifdef KARA_DEBUG printf("ab = 0x"); for (i = 0; i < 2*len; i++) { - printf("%0*x", BIGNUM_INT_BITS/4, c[i]); + printf("%0*x", BIGNUM_INT_BITS/4, c[2*len - i]); } printf("\n"); #endif @@ -401,7 +399,7 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, int i; BignumInt carry; BignumDblInt t; - const BignumInt *ap, *bp; + const BignumInt *ap, *alim = a + len, *bp, *blim = b + len; BignumInt *cp, *cps; /* @@ -411,9 +409,9 @@ static void internal_mul(const BignumInt *a, const BignumInt *b, for (i = 0; i < 2 * len; i++) c[i] = 0; - for (cps = c + 2*len, ap = a + len; ap-- > a; cps--) { + for (cps = c, ap = a; ap < alim; ap++, cps++) { carry = 0; - for (cp = cps, bp = b + len; cp--, bp-- > b ;) { + for (cp = cps, bp = b, i = blim - bp; i--; bp++, cp++) { t = (MUL_WORD(*ap, *bp) + carry) + *cp; *cp = (BignumInt) t; carry = (BignumInt)(t >> BIGNUM_INT_BITS); @@ -477,34 +475,32 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, */ /* a_0 b_0 */ - internal_mul(a + toplen, b + toplen, scratch + 2*toplen, botlen, - scratch + 2*len); + internal_mul(a, b, 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 + botlen, b, scratch + toplen, toplen, scratch + 2*len); /* a_0 b_1 */ - internal_mul_low(a + len - toplen, b, scratch, toplen, - scratch + 2*len); + internal_mul_low(a, b + botlen, scratch, toplen, scratch + 2*len); /* Copy the bottom half of the big coefficient into place */ for (i = 0; i < botlen; i++) - c[toplen + i] = scratch[2*toplen + botlen + i]; + c[i] = scratch[2*toplen + i]; /* Add the two small coefficients, throwing away the returned carry */ internal_add(scratch, scratch + toplen, scratch, toplen); /* And add that to the large coefficient, leaving the result in c. */ - internal_add(scratch, scratch + 2*toplen + botlen - toplen, - c, toplen); + internal_add(scratch, scratch + 2*toplen + botlen, + c + botlen, toplen); } else { int i; BignumInt carry; BignumDblInt t; - const BignumInt *ap, *bp; - BignumInt *cp, *cps; + const BignumInt *ap, *alim = a + len, *bp; + BignumInt *cp, *cps, *clim = c + len; /* * Multiply in the ordinary O(N^2) way. @@ -513,9 +509,9 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, for (i = 0; i < len; i++) c[i] = 0; - for (cps = c + len, ap = a + len; ap-- > a; cps--) { + for (cps = c, ap = a; ap < alim; ap++, cps++) { carry = 0; - for (cp = cps, bp = b + len; bp--, cp-- > c ;) { + for (cp = cps, bp = b, i = clim - cp; i--; bp++, cp++) { t = (MUL_WORD(*ap, *bp) + carry) + *cp; *cp = (BignumInt) t; carry = (BignumInt)(t >> BIGNUM_INT_BITS); @@ -525,13 +521,13 @@ static void internal_mul_low(const BignumInt *a, const BignumInt *b, } /* - * Montgomery reduction. Expects x to be a big-endian array of 2*len + * Montgomery reduction. Expects x to be a little-endian array of 2*len * BignumInts whose value satisfies 0 <= x < rn (where r = 2^(len * * BIGNUM_INT_BITS) is the Montgomery base). Returns in the same array * a value x' which is congruent to xr^{-1} mod n, and satisfies 0 <= * x' < n. * - * 'n' and 'mninv' should be big-endian arrays of 'len' BignumInts + * 'n' and 'mninv' should be little-endian arrays of 'len' BignumInts * each, containing respectively n and the multiplicative inverse of * -n mod r. * @@ -549,7 +545,7 @@ 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, tmp + 3*len); + internal_mul_low(x, mninv, tmp, len, tmp + 3*len); /* * Compute t = (mn+x)/r in ordinary, non-modular, integer @@ -563,7 +559,7 @@ static void monty_reduce(BignumInt *x, const BignumInt *n, 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; + x[i] = x[len + i], x[len + i] = 0; /* * Reduce t mod n. This doesn't require a full-on division by n, @@ -577,12 +573,12 @@ static void monty_reduce(BignumInt *x, const BignumInt *n, * + yielding 0 <= (mn+x)/r < 2n as required. */ if (!carry) { - for (i = 0; i < len; i++) - if (x[len + i] != n[i]) + for (i = len; i-- > 0; ) + if (x[i] != n[i]) break; } - if (carry || i >= len || x[len + i] > n[i]) - internal_sub(x+len, n, x+len, len); + if (carry || i < 0 || x[i] > n[i]) + internal_sub(x, n, x, len); } static void internal_add_shifted(BignumInt *number, @@ -606,11 +602,10 @@ static void internal_add_shifted(BignumInt *number, * Compute a = a % m. * Input in first alen words of a and first mlen words of m. * Output in first alen words of a - * (of which first alen-mlen words will be zero). + * (of which last alen-mlen words will be zero). * The MSW of m MUST have its high bit set. - * Quotient is accumulated in the `quotient' array, which is a Bignum - * rather than the internal bigendian format. Quotient parts are shifted - * left by `qshift' before adding into quot. + * Quotient is accumulated in the `quotient' array. Quotient parts + * are shifted left by `qshift' before adding into quot. */ static void internal_mod(BignumInt *a, int alen, BignumInt *m, int mlen, @@ -618,29 +613,22 @@ static void internal_mod(BignumInt *a, int alen, { BignumInt m0, m1; unsigned int h; - int i, k; + int i, j, k; - m0 = m[0]; + m0 = m[mlen - 1]; if (mlen > 1) - m1 = m[1]; + m1 = m[mlen - 2]; else m1 = 0; - for (i = 0; i <= alen - mlen; i++) { + for (i = alen, h = 0; i-- >= mlen; ) { BignumDblInt t; unsigned int q, r, c, ai1; - if (i == 0) { - h = 0; - } else { - h = a[i - 1]; - a[i - 1] = 0; - } - - if (i == alen - 1) - ai1 = 0; - else - ai1 = a[i + 1]; + if (i) + ai1 = a[i - 1]; + else + ai1 = 0; /* Find q = h:a[i] / m0 */ if (h >= m0) { @@ -667,7 +655,7 @@ static void internal_mod(BignumInt *a, int alen, DIVMOD_WORD(q, r, h, tmplo, m0); /* Refine our estimate of q by looking at - h:a[i]:a[i+1] / m0:m1 */ + h:a[i]:a[i-1] / m0:m1 */ t = MUL_WORD(m1, q); if (t > ((BignumDblInt) r << BIGNUM_INT_BITS) + ai1) { q--; @@ -678,33 +666,65 @@ static void internal_mod(BignumInt *a, int alen, } } + j = i + 1 - mlen; + /* Subtract q * m from a[i...] */ c = 0; - for (k = mlen - 1; k >= 0; k--) { + for (k = 0; k < mlen; k++) { t = MUL_WORD(q, m[k]); t += c; c = (unsigned)(t >> BIGNUM_INT_BITS); - if ((BignumInt) t > a[i + k]) + if ((BignumInt) t > a[j + k]) c++; - a[i + k] -= (BignumInt) t; + a[j + k] -= (BignumInt) t; } /* Add back m in case of borrow */ if (c != h) { t = 0; - for (k = mlen - 1; k >= 0; k--) { + for (k = 0; k < mlen; k++) { t += m[k]; - t += a[i + k]; - a[i + k] = (BignumInt) t; + t += a[j + k]; + a[j + k] = (BignumInt) t; t = t >> BIGNUM_INT_BITS; } q--; } + if (quot) - internal_add_shifted(quot, q, qshift + BIGNUM_INT_BITS * (alen - mlen - i)); + internal_add_shifted(quot, q, + qshift + BIGNUM_INT_BITS * (i + 1 - mlen)); + + if (i >= mlen) { + h = a[i]; + a[i] = 0; + } } } +static void shift_left(BignumInt *x, int xlen, int shift) +{ + int i; + + if (!shift) + return; + for (i = xlen; --i > 0; ) + x[i] = (x[i] << shift) | (x[i - 1] >> (BIGNUM_INT_BITS - shift)); + x[0] = x[0] << shift; +} + +static void shift_right(BignumInt *x, int xlen, int shift) +{ + int i; + + if (!shift || !xlen) + return; + xlen--; + for (i = 0; i < xlen; i++) + x[i] = (x[i] >> shift) | (x[i + 1] << (BIGNUM_INT_BITS - shift)); + x[i] = x[i] >> shift; +} + /* * Compute (base ^ exp) % mod, the pedestrian way. */ @@ -728,36 +748,31 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) base = bigmod(base_in, mod); /* Allocate m of size mlen, copy mod to m */ - /* We use big endian internally */ mlen = mod[0]; m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) - m[j] = mod[mod[0] - j]; + m[j] = mod[j + 1]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) - if ((m[0] << mshift) & BIGNUM_TOP_BIT) + if ((m[mlen - 1] << mshift) & BIGNUM_TOP_BIT) break; - if (mshift) { - 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; - } + if (mshift) + shift_left(m, mlen, mshift); /* Allocate n of size mlen, copy base to n */ n = snewn(mlen, BignumInt); - i = mlen - base[0]; - for (j = 0; j < i; j++) - n[j] = 0; - for (j = 0; j < (int)base[0]; j++) - n[i + j] = base[base[0] - j]; + for (i = 0; i < (int)base[0]; i++) + n[i] = base[i + 1]; + for (; i < mlen; i++) + n[i] = 0; /* Allocate a and b of size 2*mlen. Set a = 1 */ a = snewn(2 * mlen, BignumInt); b = snewn(2 * mlen, BignumInt); - for (i = 0; i < 2 * mlen; i++) + a[0] = 1; + for (i = 1; i < 2 * mlen; i++) a[i] = 0; - a[2 * mlen - 1] = 1; /* Scratch space for multiplies */ scratchlen = mul_compute_scratch(mlen); @@ -777,10 +792,10 @@ 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, scratch); + internal_mul(a, a, 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, scratch); + internal_mul(b, n, a, mlen, scratch); internal_mod(a, mlen * 2, m, mlen, NULL, 0); } else { BignumInt *t; @@ -796,18 +811,15 @@ Bignum modpow_simple(Bignum base_in, Bignum exp, Bignum mod) /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = mlen - 1; i < 2 * mlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); - a[2 * mlen - 1] = a[2 * mlen - 1] << mshift; - internal_mod(a, mlen * 2, m, mlen, NULL, 0); - for (i = 2 * mlen - 1; i >= mlen; i--) - a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); + shift_left(a, mlen + 1, mshift); + internal_mod(a, mlen + 1, m, mlen, NULL, 0); + shift_right(a, mlen, mshift); } /* Copy result to buffer */ result = newbn(mod[0]); for (i = 0; i < mlen; i++) - result[result[0] - i] = a[i + mlen]; + result[i + 1] = a[i]; while (result[0] > 1 && result[result[0]] == 0) result[0]--; @@ -884,17 +896,16 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) freebn(r); /* won't need this any more */ /* - * Set up internal arrays of the right lengths, in big-endian - * format, containing the base, the modulus, and the modulus's - * inverse. + * Set up internal arrays of the right lengths containing the base, + * the modulus, and the modulus's inverse. */ n = snewn(len, BignumInt); for (j = 0; j < len; j++) - n[len - 1 - j] = mod[j + 1]; + n[j] = mod[j + 1]; mninv = snewn(len, BignumInt); for (j = 0; j < len; j++) - mninv[len - 1 - j] = (j < (int)inv[0] ? inv[j + 1] : 0); + mninv[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); @@ -904,13 +915,13 @@ 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 < (int)base[0] ? base[j + 1] : 0); + x[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 < (int)rn[0] ? rn[j + 1] : 0); + a[j] = (j < (int)rn[0] ? rn[j + 1] : 0); freebn(rn); /* Scratch space for multiplies */ @@ -931,10 +942,10 @@ 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, scratch); + internal_mul(a, a, 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, scratch); + internal_mul(b, x, a, len, scratch); monty_reduce(a, n, mninv, scratch, len); } else { BignumInt *t; @@ -957,7 +968,7 @@ Bignum modpow(Bignum base_in, Bignum exp, Bignum mod) /* Copy result to buffer */ result = newbn(mod[0]); for (i = 0; i < len; i++) - result[result[0] - i] = a[i + len]; + result[i + 1] = a[i]; while (result[0] > 1 && result[result[0]] == 0) result[0]--; @@ -997,21 +1008,17 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) Bignum result; /* Allocate m of size mlen, copy mod to m */ - /* We use big endian internally */ mlen = mod[0]; m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) - m[j] = mod[mod[0] - j]; + m[j] = mod[j + 1]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) - if ((m[0] << mshift) & BIGNUM_TOP_BIT) + if ((m[mlen - 1] << mshift) & BIGNUM_TOP_BIT) break; - if (mshift) { - 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; - } + if (mshift) + shift_left(m, mlen, mshift); pqlen = (p[0] > q[0] ? p[0] : q[0]); @@ -1023,19 +1030,17 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Allocate n of size pqlen, copy p to n */ n = snewn(pqlen, BignumInt); - i = pqlen - p[0]; - for (j = 0; j < i; j++) - n[j] = 0; - for (j = 0; j < (int)p[0]; j++) - n[i + j] = p[p[0] - j]; + for (i = 0; i < (int)p[0]; i++) + n[i] = p[i + 1]; + for (; i < pqlen; i++) + n[i] = 0; /* Allocate o of size pqlen, copy q to o */ o = snewn(pqlen, BignumInt); - i = pqlen - q[0]; - for (j = 0; j < i; j++) - o[j] = 0; - for (j = 0; j < (int)q[0]; j++) - o[i + j] = q[q[0] - j]; + for (i = 0; i < (int)q[0]; i++) + o[i] = q[i + 1]; + for (; i < pqlen; i++) + o[i] = 0; /* Allocate a of size 2*pqlen for result */ a = snewn(2 * pqlen, BignumInt); @@ -1050,19 +1055,16 @@ Bignum modmul(Bignum p, Bignum q, Bignum mod) /* Fixup result in case the modulus was shifted */ if (mshift) { - for (i = 2 * pqlen - mlen - 1; i < 2 * pqlen - 1; i++) - a[i] = (a[i] << mshift) | (a[i + 1] >> (BIGNUM_INT_BITS - mshift)); - a[2 * pqlen - 1] = a[2 * pqlen - 1] << mshift; - internal_mod(a, pqlen * 2, m, mlen, NULL, 0); - for (i = 2 * pqlen - 1; i >= 2 * pqlen - mlen; i--) - a[i] = (a[i] >> mshift) | (a[i - 1] << (BIGNUM_INT_BITS - mshift)); + shift_left(a, mlen + 1, mshift); + internal_mod(a, mlen + 1, m, mlen, NULL, 0); + shift_right(a, mlen, mshift); } /* Copy result to buffer */ rlen = (mlen < pqlen * 2 ? mlen : pqlen * 2); result = newbn(rlen); for (i = 0; i < rlen; i++) - result[result[0] - i] = a[i + 2 * pqlen - rlen]; + result[i + 1] = a[i]; while (result[0] > 1 && result[result[0]] == 0) result[0]--; @@ -1100,21 +1102,17 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) int plen, mlen, i, j; /* Allocate m of size mlen, copy mod to m */ - /* We use big endian internally */ mlen = mod[0]; m = snewn(mlen, BignumInt); for (j = 0; j < mlen; j++) - m[j] = mod[mod[0] - j]; + m[j] = mod[j + 1]; /* Shift m left to make msb bit set */ for (mshift = 0; mshift < BIGNUM_INT_BITS-1; mshift++) - if ((m[0] << mshift) & BIGNUM_TOP_BIT) + if ((m[mlen - 1] << mshift) & BIGNUM_TOP_BIT) break; - if (mshift) { - 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; - } + if (mshift) + shift_left(m, mlen, mshift); plen = p[0]; /* Ensure plen > mlen */ @@ -1123,30 +1121,26 @@ static void bigdivmod(Bignum p, Bignum mod, Bignum result, Bignum quotient) /* 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 <= (int)p[0]; j++) - n[plen - j] = p[j]; + for (i = 0; i < (int)p[0]; i++) + n[i] = p[i + 1]; + for (; i < plen; i++) + n[i] = 0; /* 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; + shift_left(n, mlen + 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)); + shift_right(n, mlen, mshift); } /* Copy result to buffer */ if (result) { - for (i = 1; i <= (int)result[0]; i++) { - int j = plen - i; - result[i] = j >= 0 ? n[j] : 0; - } + for (i = 0; i < (int)result[0]; i++) + result[i + 1] = i < plen ? n[i] : 0; + bn_restore_invariant(result); } /* Free temporary arrays */ @@ -1367,8 +1361,8 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) 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); + workspace[0 * mlen + i] = i < (int)a[0] ? a[i + 1] : 0; + workspace[1 * mlen + i] = i < (int)b[0] ? b[i + 1] : 0; } internal_mul(workspace + 0 * mlen, workspace + 1 * mlen, @@ -1380,10 +1374,10 @@ Bignum bigmuladd(Bignum a, Bignum b, Bignum addend) rlen = addend[0] + 1; ret = newbn(rlen); maxspot = 0; - for (i = 1; i <= (int)ret[0]; i++) { - ret[i] = (i <= 2 * mlen ? workspace[4 * mlen - i] : 0); - if (ret[i] != 0) - maxspot = i; + for (i = 0; i < (int)ret[0]; i++) { + ret[i + 1] = (i < 2 * mlen ? workspace[2 * mlen + i] : 0); + if (ret[i + 1] != 0) + maxspot = i + 1; } ret[0] = maxspot;