| /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| * All rights reserved. |
| * |
| * This package is an SSL implementation written |
| * by Eric Young (eay@cryptsoft.com). |
| * The implementation was written so as to conform with Netscapes SSL. |
| * |
| * This library is free for commercial and non-commercial use as long as |
| * the following conditions are aheared to. The following conditions |
| * apply to all code found in this distribution, be it the RC4, RSA, |
| * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| * included with this distribution is covered by the same copyright terms |
| * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| * |
| * Copyright remains Eric Young's, and as such any Copyright notices in |
| * the code are not to be removed. |
| * If this package is used in a product, Eric Young should be given attribution |
| * as the author of the parts of the library used. |
| * This can be in the form of a textual message at program startup or |
| * in documentation (online or textual) provided with the package. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * 3. All advertising materials mentioning features or use of this software |
| * must display the following acknowledgement: |
| * "This product includes cryptographic software written by |
| * Eric Young (eay@cryptsoft.com)" |
| * The word 'cryptographic' can be left out if the rouines from the library |
| * being used are not cryptographic related :-). |
| * 4. If you include any Windows specific code (or a derivative thereof) from |
| * the apps directory (application code) you must include an acknowledgement: |
| * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| * |
| * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| * |
| * The licence and distribution terms for any publically available version or |
| * derivative of this code cannot be changed. i.e. this code cannot simply be |
| * copied and put under another distribution licence |
| * [including the GNU Public Licence.] */ |
| |
| #include <openssl/bn.h> |
| |
| #include <assert.h> |
| |
| #include "internal.h" |
| |
| |
| /* Generic implementations of most operations are needed for: |
| * - Configurations without inline assembly. |
| * - Architectures other than x86 or x86_64. |
| * - Windows x84_64; x86_64-gcc.c does not build on MSVC. */ |
| #if defined(OPENSSL_NO_ASM) || \ |
| (!defined(OPENSSL_X86_64) && !defined(OPENSSL_X86)) || \ |
| (defined(OPENSSL_X86_64) && defined(OPENSSL_WINDOWS)) |
| |
| #if defined(OPENSSL_WINDOWS) |
| #define alloca _alloca |
| #else |
| #include <alloca.h> |
| #endif |
| |
| #ifdef BN_LLONG |
| #define mul_add(r, a, w, c) \ |
| { \ |
| BN_ULLONG t; \ |
| t = (BN_ULLONG)w * (a) + (r) + (c); \ |
| (r) = Lw(t); \ |
| (c) = Hw(t); \ |
| } |
| |
| #define mul(r, a, w, c) \ |
| { \ |
| BN_ULLONG t; \ |
| t = (BN_ULLONG)w * (a) + (c); \ |
| (r) = Lw(t); \ |
| (c) = Hw(t); \ |
| } |
| |
| #define sqr(r0, r1, a) \ |
| { \ |
| BN_ULLONG t; \ |
| t = (BN_ULLONG)(a) * (a); \ |
| (r0) = Lw(t); \ |
| (r1) = Hw(t); \ |
| } |
| |
| #elif defined(BN_UMULT_LOHI) |
| #define mul_add(r, a, w, c) \ |
| { \ |
| BN_ULONG high, low, ret, tmp = (a); \ |
| ret = (r); \ |
| BN_UMULT_LOHI(low, high, w, tmp); \ |
| ret += (c); \ |
| (c) = (ret < (c)) ? 1 : 0; \ |
| (c) += high; \ |
| ret += low; \ |
| (c) += (ret < low) ? 1 : 0; \ |
| (r) = ret; \ |
| } |
| |
| #define mul(r, a, w, c) \ |
| { \ |
| BN_ULONG high, low, ret, ta = (a); \ |
| BN_UMULT_LOHI(low, high, w, ta); \ |
| ret = low + (c); \ |
| (c) = high; \ |
| (c) += (ret < low) ? 1 : 0; \ |
| (r) = ret; \ |
| } |
| |
| #define sqr(r0, r1, a) \ |
| { \ |
| BN_ULONG tmp = (a); \ |
| BN_UMULT_LOHI(r0, r1, tmp, tmp); \ |
| } |
| |
| #else |
| |
| /************************************************************* |
| * No long long type |
| */ |
| |
| #define LBITS(a) ((a) & BN_MASK2l) |
| #define HBITS(a) (((a) >> BN_BITS4) & BN_MASK2l) |
| #define L2HBITS(a) (((a) << BN_BITS4) & BN_MASK2) |
| |
| #define LLBITS(a) ((a) & BN_MASKl) |
| #define LHBITS(a) (((a) >> BN_BITS2) & BN_MASKl) |
| #define LL2HBITS(a) ((BN_ULLONG)((a) & BN_MASKl) << BN_BITS2) |
| |
| #define mul64(l, h, bl, bh) \ |
| { \ |
| BN_ULONG m, m1, lt, ht; \ |
| \ |
| lt = l; \ |
| ht = h; \ |
| m = (bh) * (lt); \ |
| lt = (bl) * (lt); \ |
| m1 = (bl) * (ht); \ |
| ht = (bh) * (ht); \ |
| m = (m + m1) & BN_MASK2; \ |
| if (m < m1) \ |
| ht += L2HBITS((BN_ULONG)1); \ |
| ht += HBITS(m); \ |
| m1 = L2HBITS(m); \ |
| lt = (lt + m1) & BN_MASK2; \ |
| if (lt < m1) \ |
| ht++; \ |
| (l) = lt; \ |
| (h) = ht; \ |
| } |
| |
| #define sqr64(lo, ho, in) \ |
| { \ |
| BN_ULONG l, h, m; \ |
| \ |
| h = (in); \ |
| l = LBITS(h); \ |
| h = HBITS(h); \ |
| m = (l) * (h); \ |
| l *= l; \ |
| h *= h; \ |
| h += (m & BN_MASK2h1) >> (BN_BITS4 - 1); \ |
| m = (m & BN_MASK2l) << (BN_BITS4 + 1); \ |
| l = (l + m) & BN_MASK2; \ |
| if (l < m) \ |
| h++; \ |
| (lo) = l; \ |
| (ho) = h; \ |
| } |
| |
| #define mul_add(r, a, bl, bh, c) \ |
| { \ |
| BN_ULONG l, h; \ |
| \ |
| h = (a); \ |
| l = LBITS(h); \ |
| h = HBITS(h); \ |
| mul64(l, h, (bl), (bh)); \ |
| \ |
| /* non-multiply part */ \ |
| l = (l + (c)) & BN_MASK2; \ |
| if (l < (c)) \ |
| h++; \ |
| (c) = (r); \ |
| l = (l + (c)) & BN_MASK2; \ |
| if (l < (c)) \ |
| h++; \ |
| (c) = h & BN_MASK2; \ |
| (r) = l; \ |
| } |
| |
| #define mul(r, a, bl, bh, c) \ |
| { \ |
| BN_ULONG l, h; \ |
| \ |
| h = (a); \ |
| l = LBITS(h); \ |
| h = HBITS(h); \ |
| mul64(l, h, (bl), (bh)); \ |
| \ |
| /* non-multiply part */ \ |
| l += (c); \ |
| if ((l & BN_MASK2) < (c)) \ |
| h++; \ |
| (c) = h & BN_MASK2; \ |
| (r) = l & BN_MASK2; \ |
| } |
| #endif /* !BN_LLONG */ |
| |
| #if defined(BN_LLONG) || defined(BN_UMULT_HIGH) |
| |
| BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, |
| BN_ULONG w) { |
| BN_ULONG c1 = 0; |
| |
| assert(num >= 0); |
| if (num <= 0) { |
| return c1; |
| } |
| |
| while (num & ~3) { |
| mul_add(rp[0], ap[0], w, c1); |
| mul_add(rp[1], ap[1], w, c1); |
| mul_add(rp[2], ap[2], w, c1); |
| mul_add(rp[3], ap[3], w, c1); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| |
| while (num) { |
| mul_add(rp[0], ap[0], w, c1); |
| ap++; |
| rp++; |
| num--; |
| } |
| |
| return c1; |
| } |
| |
| BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) { |
| BN_ULONG c1 = 0; |
| |
| assert(num >= 0); |
| if (num <= 0) { |
| return c1; |
| } |
| |
| while (num & ~3) { |
| mul(rp[0], ap[0], w, c1); |
| mul(rp[1], ap[1], w, c1); |
| mul(rp[2], ap[2], w, c1); |
| mul(rp[3], ap[3], w, c1); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| while (num) { |
| mul(rp[0], ap[0], w, c1); |
| ap++; |
| rp++; |
| num--; |
| } |
| return c1; |
| } |
| |
| void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) { |
| assert(n >= 0); |
| if (n <= 0) { |
| return; |
| } |
| |
| while (n & ~3) { |
| sqr(r[0], r[1], a[0]); |
| sqr(r[2], r[3], a[1]); |
| sqr(r[4], r[5], a[2]); |
| sqr(r[6], r[7], a[3]); |
| a += 4; |
| r += 8; |
| n -= 4; |
| } |
| while (n) { |
| sqr(r[0], r[1], a[0]); |
| a++; |
| r += 2; |
| n--; |
| } |
| } |
| |
| #else /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */ |
| |
| BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, |
| BN_ULONG w) { |
| BN_ULONG c = 0; |
| BN_ULONG bl, bh; |
| |
| assert(num >= 0); |
| if (num <= 0) { |
| return (BN_ULONG)0; |
| } |
| |
| bl = LBITS(w); |
| bh = HBITS(w); |
| |
| while (num & ~3) { |
| mul_add(rp[0], ap[0], bl, bh, c); |
| mul_add(rp[1], ap[1], bl, bh, c); |
| mul_add(rp[2], ap[2], bl, bh, c); |
| mul_add(rp[3], ap[3], bl, bh, c); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| while (num) { |
| mul_add(rp[0], ap[0], bl, bh, c); |
| ap++; |
| rp++; |
| num--; |
| } |
| return c; |
| } |
| |
| BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w) { |
| BN_ULONG carry = 0; |
| BN_ULONG bl, bh; |
| |
| assert(num >= 0); |
| if (num <= 0) { |
| return (BN_ULONG)0; |
| } |
| |
| bl = LBITS(w); |
| bh = HBITS(w); |
| |
| while (num & ~3) { |
| mul(rp[0], ap[0], bl, bh, carry); |
| mul(rp[1], ap[1], bl, bh, carry); |
| mul(rp[2], ap[2], bl, bh, carry); |
| mul(rp[3], ap[3], bl, bh, carry); |
| ap += 4; |
| rp += 4; |
| num -= 4; |
| } |
| while (num) { |
| mul(rp[0], ap[0], bl, bh, carry); |
| ap++; |
| rp++; |
| num--; |
| } |
| return carry; |
| } |
| |
| void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n) { |
| assert(n >= 0); |
| if (n <= 0) { |
| return; |
| } |
| |
| while (n & ~3) { |
| sqr64(r[0], r[1], a[0]); |
| sqr64(r[2], r[3], a[1]); |
| sqr64(r[4], r[5], a[2]); |
| sqr64(r[6], r[7], a[3]); |
| a += 4; |
| r += 8; |
| n -= 4; |
| } |
| while (n) { |
| sqr64(r[0], r[1], a[0]); |
| a++; |
| r += 2; |
| n--; |
| } |
| } |
| |
| #endif /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */ |
| |
| #if defined(BN_LLONG) |
| |
| BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) { |
| return (BN_ULONG)(((((BN_ULLONG)h) << BN_BITS2) | l) / (BN_ULLONG)d); |
| } |
| |
| #else |
| |
| /* Divide h,l by d and return the result. */ |
| BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d) { |
| BN_ULONG dh, dl, q, ret = 0, th, tl, t; |
| int i, count = 2; |
| |
| if (d == 0) { |
| return BN_MASK2; |
| } |
| |
| i = BN_num_bits_word(d); |
| assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i)); |
| |
| i = BN_BITS2 - i; |
| if (h >= d) { |
| h -= d; |
| } |
| |
| if (i) { |
| d <<= i; |
| h = (h << i) | (l >> (BN_BITS2 - i)); |
| l <<= i; |
| } |
| dh = (d & BN_MASK2h) >> BN_BITS4; |
| dl = (d & BN_MASK2l); |
| for (;;) { |
| if ((h >> BN_BITS4) == dh) { |
| q = BN_MASK2l; |
| } else { |
| q = h / dh; |
| } |
| |
| th = q * dh; |
| tl = dl * q; |
| for (;;) { |
| t = h - th; |
| if ((t & BN_MASK2h) || |
| ((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) { |
| break; |
| } |
| q--; |
| th -= dh; |
| tl -= dl; |
| } |
| t = (tl >> BN_BITS4); |
| tl = (tl << BN_BITS4) & BN_MASK2h; |
| th += t; |
| |
| if (l < tl) { |
| th++; |
| } |
| l -= tl; |
| if (h < th) { |
| h += d; |
| q--; |
| } |
| h -= th; |
| |
| if (--count == 0) { |
| break; |
| } |
| |
| ret = q << BN_BITS4; |
| h = ((h << BN_BITS4) | (l >> BN_BITS4)) & BN_MASK2; |
| l = (l & BN_MASK2l) << BN_BITS4; |
| } |
| |
| ret |= q; |
| return ret; |
| } |
| |
| #endif /* !defined(BN_LLONG) */ |
| |
| #ifdef BN_LLONG |
| BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) { |
| BN_ULLONG ll = 0; |
| |
| assert(n >= 0); |
| if (n <= 0) { |
| return (BN_ULONG)0; |
| } |
| |
| while (n & ~3) { |
| ll += (BN_ULLONG)a[0] + b[0]; |
| r[0] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG)a[1] + b[1]; |
| r[1] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG)a[2] + b[2]; |
| r[2] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| ll += (BN_ULLONG)a[3] + b[3]; |
| r[3] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| while (n) { |
| ll += (BN_ULLONG)a[0] + b[0]; |
| r[0] = (BN_ULONG)ll & BN_MASK2; |
| ll >>= BN_BITS2; |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return (BN_ULONG)ll; |
| } |
| |
| #else /* !BN_LLONG */ |
| |
| BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) { |
| BN_ULONG c, l, t; |
| |
| assert(n >= 0); |
| if (n <= 0) { |
| return (BN_ULONG)0; |
| } |
| |
| c = 0; |
| while (n & ~3) { |
| t = a[0]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[0]) & BN_MASK2; |
| c += (l < t); |
| r[0] = l; |
| t = a[1]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[1]) & BN_MASK2; |
| c += (l < t); |
| r[1] = l; |
| t = a[2]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[2]) & BN_MASK2; |
| c += (l < t); |
| r[2] = l; |
| t = a[3]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[3]) & BN_MASK2; |
| c += (l < t); |
| r[3] = l; |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| while (n) { |
| t = a[0]; |
| t = (t + c) & BN_MASK2; |
| c = (t < c); |
| l = (t + b[0]) & BN_MASK2; |
| c += (l < t); |
| r[0] = l; |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return (BN_ULONG)c; |
| } |
| |
| #endif /* !BN_LLONG */ |
| |
| BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, |
| int n) { |
| BN_ULONG t1, t2; |
| int c = 0; |
| |
| assert(n >= 0); |
| if (n <= 0) { |
| return (BN_ULONG)0; |
| } |
| |
| while (n & ~3) { |
| t1 = a[0]; |
| t2 = b[0]; |
| r[0] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) { |
| c = (t1 < t2); |
| } |
| t1 = a[1]; |
| t2 = b[1]; |
| r[1] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) { |
| c = (t1 < t2); |
| } |
| t1 = a[2]; |
| t2 = b[2]; |
| r[2] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) { |
| c = (t1 < t2); |
| } |
| t1 = a[3]; |
| t2 = b[3]; |
| r[3] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) { |
| c = (t1 < t2); |
| } |
| a += 4; |
| b += 4; |
| r += 4; |
| n -= 4; |
| } |
| while (n) { |
| t1 = a[0]; |
| t2 = b[0]; |
| r[0] = (t1 - t2 - c) & BN_MASK2; |
| if (t1 != t2) { |
| c = (t1 < t2); |
| } |
| a++; |
| b++; |
| r++; |
| n--; |
| } |
| return c; |
| } |
| |
| /* mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0) */ |
| /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */ |
| /* sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0) */ |
| /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */ |
| |
| #ifdef BN_LLONG |
| |
| /* Keep in mind that additions to multiplication result can not overflow, |
| * because its high half cannot be all-ones. */ |
| #define mul_add_c(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)(a) * (b); \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define mul_add_c2(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)(a) * (b); \ |
| BN_ULLONG tt = t + c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(tt); \ |
| hi = (BN_ULONG)Hw(tt); \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define sqr_add_c(a, i, c0, c1, c2) \ |
| do { \ |
| BN_ULONG hi; \ |
| BN_ULLONG t = (BN_ULLONG)a[i] * a[i]; \ |
| t += c0; /* no carry */ \ |
| c0 = (BN_ULONG)Lw(t); \ |
| hi = (BN_ULONG)Hw(t); \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) |
| |
| #elif defined(BN_UMULT_LOHI) |
| |
| /* Keep in mind that additions to hi can not overflow, because the high word of |
| * a multiplication result cannot be all-ones. */ |
| #define mul_add_c(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG ta = (a), tb = (b); \ |
| BN_ULONG lo, hi; \ |
| BN_UMULT_LOHI(lo, hi, ta, tb); \ |
| c0 += lo; \ |
| hi += (c0 < lo) ? 1 : 0; \ |
| c1 += hi; \ |
| c2 += (c1 < hi) ? 1 : 0; \ |
| } while (0) |
| |
| #define mul_add_c2(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG ta = (a), tb = (b); \ |
| BN_ULONG lo, hi, tt; \ |
| BN_UMULT_LOHI(lo, hi, ta, tb); \ |
| c0 += lo; \ |
| tt = hi + ((c0 < lo) ? 1 : 0); \ |
| c1 += tt; \ |
| c2 += (c1 < tt) ? 1 : 0; \ |
| c0 += lo; \ |
| hi += (c0 < lo) ? 1 : 0; \ |
| c1 += hi; \ |
| c2 += (c1 < hi) ? 1 : 0; \ |
| } while (0) |
| |
| #define sqr_add_c(a, i, c0, c1, c2) \ |
| do { \ |
| BN_ULONG ta = (a)[i]; \ |
| BN_ULONG lo, hi; \ |
| BN_UMULT_LOHI(lo, hi, ta, ta); \ |
| c0 += lo; \ |
| hi += (c0 < lo) ? 1 : 0; \ |
| c1 += hi; \ |
| c2 += (c1 < hi) ? 1 : 0; \ |
| } while (0) |
| |
| #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) |
| |
| #else /* !BN_LLONG */ |
| |
| /* Keep in mind that additions to hi can not overflow, because |
| * the high word of a multiplication result cannot be all-ones. */ |
| |
| #define mul_add_c(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG lo = LBITS(a), hi = HBITS(a); \ |
| BN_ULONG bl = LBITS(b), bh = HBITS(b); \ |
| mul64(lo, hi, bl, bh); \ |
| c0 = (c0 + lo) & BN_MASK2; \ |
| if (c0 < lo) \ |
| hi++; \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define mul_add_c2(a, b, c0, c1, c2) \ |
| do { \ |
| BN_ULONG tt; \ |
| BN_ULONG lo = LBITS(a), hi = HBITS(a); \ |
| BN_ULONG bl = LBITS(b), bh = HBITS(b); \ |
| mul64(lo, hi, bl, bh); \ |
| tt = hi; \ |
| c0 = (c0 + lo) & BN_MASK2; \ |
| if (c0 < lo) \ |
| tt++; \ |
| c1 = (c1 + tt) & BN_MASK2; \ |
| if (c1 < tt) \ |
| c2++; \ |
| c0 = (c0 + lo) & BN_MASK2; \ |
| if (c0 < lo) \ |
| hi++; \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define sqr_add_c(a, i, c0, c1, c2) \ |
| do { \ |
| BN_ULONG lo, hi; \ |
| sqr64(lo, hi, (a)[i]); \ |
| c0 = (c0 + lo) & BN_MASK2; \ |
| if (c0 < lo) \ |
| hi++; \ |
| c1 = (c1 + hi) & BN_MASK2; \ |
| if (c1 < hi) \ |
| c2++; \ |
| } while (0) |
| |
| #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2) |
| #endif /* !BN_LLONG */ |
| |
| void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| mul_add_c(a[0], b[0], c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[1], c2, c3, c1); |
| mul_add_c(a[1], b[0], c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[0], c3, c1, c2); |
| mul_add_c(a[1], b[1], c3, c1, c2); |
| mul_add_c(a[0], b[2], c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| mul_add_c(a[0], b[3], c1, c2, c3); |
| mul_add_c(a[1], b[2], c1, c2, c3); |
| mul_add_c(a[2], b[1], c1, c2, c3); |
| mul_add_c(a[3], b[0], c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| mul_add_c(a[4], b[0], c2, c3, c1); |
| mul_add_c(a[3], b[1], c2, c3, c1); |
| mul_add_c(a[2], b[2], c2, c3, c1); |
| mul_add_c(a[1], b[3], c2, c3, c1); |
| mul_add_c(a[0], b[4], c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| mul_add_c(a[0], b[5], c3, c1, c2); |
| mul_add_c(a[1], b[4], c3, c1, c2); |
| mul_add_c(a[2], b[3], c3, c1, c2); |
| mul_add_c(a[3], b[2], c3, c1, c2); |
| mul_add_c(a[4], b[1], c3, c1, c2); |
| mul_add_c(a[5], b[0], c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| mul_add_c(a[6], b[0], c1, c2, c3); |
| mul_add_c(a[5], b[1], c1, c2, c3); |
| mul_add_c(a[4], b[2], c1, c2, c3); |
| mul_add_c(a[3], b[3], c1, c2, c3); |
| mul_add_c(a[2], b[4], c1, c2, c3); |
| mul_add_c(a[1], b[5], c1, c2, c3); |
| mul_add_c(a[0], b[6], c1, c2, c3); |
| r[6] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[7], c2, c3, c1); |
| mul_add_c(a[1], b[6], c2, c3, c1); |
| mul_add_c(a[2], b[5], c2, c3, c1); |
| mul_add_c(a[3], b[4], c2, c3, c1); |
| mul_add_c(a[4], b[3], c2, c3, c1); |
| mul_add_c(a[5], b[2], c2, c3, c1); |
| mul_add_c(a[6], b[1], c2, c3, c1); |
| mul_add_c(a[7], b[0], c2, c3, c1); |
| r[7] = c2; |
| c2 = 0; |
| mul_add_c(a[7], b[1], c3, c1, c2); |
| mul_add_c(a[6], b[2], c3, c1, c2); |
| mul_add_c(a[5], b[3], c3, c1, c2); |
| mul_add_c(a[4], b[4], c3, c1, c2); |
| mul_add_c(a[3], b[5], c3, c1, c2); |
| mul_add_c(a[2], b[6], c3, c1, c2); |
| mul_add_c(a[1], b[7], c3, c1, c2); |
| r[8] = c3; |
| c3 = 0; |
| mul_add_c(a[2], b[7], c1, c2, c3); |
| mul_add_c(a[3], b[6], c1, c2, c3); |
| mul_add_c(a[4], b[5], c1, c2, c3); |
| mul_add_c(a[5], b[4], c1, c2, c3); |
| mul_add_c(a[6], b[3], c1, c2, c3); |
| mul_add_c(a[7], b[2], c1, c2, c3); |
| r[9] = c1; |
| c1 = 0; |
| mul_add_c(a[7], b[3], c2, c3, c1); |
| mul_add_c(a[6], b[4], c2, c3, c1); |
| mul_add_c(a[5], b[5], c2, c3, c1); |
| mul_add_c(a[4], b[6], c2, c3, c1); |
| mul_add_c(a[3], b[7], c2, c3, c1); |
| r[10] = c2; |
| c2 = 0; |
| mul_add_c(a[4], b[7], c3, c1, c2); |
| mul_add_c(a[5], b[6], c3, c1, c2); |
| mul_add_c(a[6], b[5], c3, c1, c2); |
| mul_add_c(a[7], b[4], c3, c1, c2); |
| r[11] = c3; |
| c3 = 0; |
| mul_add_c(a[7], b[5], c1, c2, c3); |
| mul_add_c(a[6], b[6], c1, c2, c3); |
| mul_add_c(a[5], b[7], c1, c2, c3); |
| r[12] = c1; |
| c1 = 0; |
| mul_add_c(a[6], b[7], c2, c3, c1); |
| mul_add_c(a[7], b[6], c2, c3, c1); |
| r[13] = c2; |
| c2 = 0; |
| mul_add_c(a[7], b[7], c3, c1, c2); |
| r[14] = c3; |
| r[15] = c1; |
| } |
| |
| void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b) { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| mul_add_c(a[0], b[0], c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| mul_add_c(a[0], b[1], c2, c3, c1); |
| mul_add_c(a[1], b[0], c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[0], c3, c1, c2); |
| mul_add_c(a[1], b[1], c3, c1, c2); |
| mul_add_c(a[0], b[2], c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| mul_add_c(a[0], b[3], c1, c2, c3); |
| mul_add_c(a[1], b[2], c1, c2, c3); |
| mul_add_c(a[2], b[1], c1, c2, c3); |
| mul_add_c(a[3], b[0], c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| mul_add_c(a[3], b[1], c2, c3, c1); |
| mul_add_c(a[2], b[2], c2, c3, c1); |
| mul_add_c(a[1], b[3], c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| mul_add_c(a[2], b[3], c3, c1, c2); |
| mul_add_c(a[3], b[2], c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| mul_add_c(a[3], b[3], c1, c2, c3); |
| r[6] = c1; |
| r[7] = c2; |
| } |
| |
| void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a) { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| sqr_add_c(a, 0, c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 1, 0, c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| sqr_add_c(a, 1, c3, c1, c2); |
| sqr_add_c2(a, 2, 0, c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 3, 0, c1, c2, c3); |
| sqr_add_c2(a, 2, 1, c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| sqr_add_c(a, 2, c2, c3, c1); |
| sqr_add_c2(a, 3, 1, c2, c3, c1); |
| sqr_add_c2(a, 4, 0, c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 5, 0, c3, c1, c2); |
| sqr_add_c2(a, 4, 1, c3, c1, c2); |
| sqr_add_c2(a, 3, 2, c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| sqr_add_c(a, 3, c1, c2, c3); |
| sqr_add_c2(a, 4, 2, c1, c2, c3); |
| sqr_add_c2(a, 5, 1, c1, c2, c3); |
| sqr_add_c2(a, 6, 0, c1, c2, c3); |
| r[6] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 7, 0, c2, c3, c1); |
| sqr_add_c2(a, 6, 1, c2, c3, c1); |
| sqr_add_c2(a, 5, 2, c2, c3, c1); |
| sqr_add_c2(a, 4, 3, c2, c3, c1); |
| r[7] = c2; |
| c2 = 0; |
| sqr_add_c(a, 4, c3, c1, c2); |
| sqr_add_c2(a, 5, 3, c3, c1, c2); |
| sqr_add_c2(a, 6, 2, c3, c1, c2); |
| sqr_add_c2(a, 7, 1, c3, c1, c2); |
| r[8] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 7, 2, c1, c2, c3); |
| sqr_add_c2(a, 6, 3, c1, c2, c3); |
| sqr_add_c2(a, 5, 4, c1, c2, c3); |
| r[9] = c1; |
| c1 = 0; |
| sqr_add_c(a, 5, c2, c3, c1); |
| sqr_add_c2(a, 6, 4, c2, c3, c1); |
| sqr_add_c2(a, 7, 3, c2, c3, c1); |
| r[10] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 7, 4, c3, c1, c2); |
| sqr_add_c2(a, 6, 5, c3, c1, c2); |
| r[11] = c3; |
| c3 = 0; |
| sqr_add_c(a, 6, c1, c2, c3); |
| sqr_add_c2(a, 7, 5, c1, c2, c3); |
| r[12] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 7, 6, c2, c3, c1); |
| r[13] = c2; |
| c2 = 0; |
| sqr_add_c(a, 7, c3, c1, c2); |
| r[14] = c3; |
| r[15] = c1; |
| } |
| |
| void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a) { |
| BN_ULONG c1, c2, c3; |
| |
| c1 = 0; |
| c2 = 0; |
| c3 = 0; |
| sqr_add_c(a, 0, c1, c2, c3); |
| r[0] = c1; |
| c1 = 0; |
| sqr_add_c2(a, 1, 0, c2, c3, c1); |
| r[1] = c2; |
| c2 = 0; |
| sqr_add_c(a, 1, c3, c1, c2); |
| sqr_add_c2(a, 2, 0, c3, c1, c2); |
| r[2] = c3; |
| c3 = 0; |
| sqr_add_c2(a, 3, 0, c1, c2, c3); |
| sqr_add_c2(a, 2, 1, c1, c2, c3); |
| r[3] = c1; |
| c1 = 0; |
| sqr_add_c(a, 2, c2, c3, c1); |
| sqr_add_c2(a, 3, 1, c2, c3, c1); |
| r[4] = c2; |
| c2 = 0; |
| sqr_add_c2(a, 3, 2, c3, c1, c2); |
| r[5] = c3; |
| c3 = 0; |
| sqr_add_c(a, 3, c1, c2, c3); |
| r[6] = c1; |
| r[7] = c2; |
| } |
| |
| #if defined(OPENSSL_NO_ASM) || (!defined(OPENSSL_ARM) && !defined(OPENSSL_X86_64)) |
| /* This is essentially reference implementation, which may or may not |
| * result in performance improvement. E.g. on IA-32 this routine was |
| * observed to give 40% faster rsa1024 private key operations and 10% |
| * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only |
| * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a |
| * reference implementation, one to be used as starting point for |
| * platform-specific assembler. Mentioned numbers apply to compiler |
| * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and |
| * can vary not only from platform to platform, but even for compiler |
| * versions. Assembler vs. assembler improvement coefficients can |
| * [and are known to] differ and are to be documented elsewhere. */ |
| int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, |
| const BN_ULONG *np, const BN_ULONG *n0p, int num) { |
| BN_ULONG c0, c1, ml, *tp, n0; |
| #ifdef mul64 |
| BN_ULONG mh; |
| #endif |
| volatile BN_ULONG *vp; |
| int i = 0, j; |
| |
| #if 0 /* template for platform-specific implementation */ |
| if (ap==bp) return bn_sqr_mont(rp,ap,np,n0p,num); |
| #endif |
| vp = tp = alloca((num + 2) * sizeof(BN_ULONG)); |
| |
| n0 = *n0p; |
| |
| c0 = 0; |
| ml = bp[0]; |
| #ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| for (j = 0; j < num; ++j) { |
| mul(tp[j], ap[j], ml, mh, c0); |
| } |
| #else |
| for (j = 0; j < num; ++j) { |
| mul(tp[j], ap[j], ml, c0); |
| } |
| #endif |
| |
| tp[num] = c0; |
| tp[num + 1] = 0; |
| goto enter; |
| |
| for (; i < num; i++) { |
| c0 = 0; |
| ml = bp[i]; |
| #ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| for (j = 0; j < num; ++j) { |
| mul_add(tp[j], ap[j], ml, mh, c0); |
| } |
| #else |
| for (j = 0; j < num; ++j) { |
| mul_add(tp[j], ap[j], ml, c0); |
| } |
| #endif |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num] = c1; |
| tp[num + 1] = (c1 < c0 ? 1 : 0); |
| enter: |
| c1 = tp[0]; |
| ml = (c1 * n0) & BN_MASK2; |
| c0 = 0; |
| #ifdef mul64 |
| mh = HBITS(ml); |
| ml = LBITS(ml); |
| mul_add(c1, np[0], ml, mh, c0); |
| #else |
| mul_add(c1, ml, np[0], c0); |
| #endif |
| for (j = 1; j < num; j++) { |
| c1 = tp[j]; |
| #ifdef mul64 |
| mul_add(c1, np[j], ml, mh, c0); |
| #else |
| mul_add(c1, ml, np[j], c0); |
| #endif |
| tp[j - 1] = c1 & BN_MASK2; |
| } |
| c1 = (tp[num] + c0) & BN_MASK2; |
| tp[num - 1] = c1; |
| tp[num] = tp[num + 1] + (c1 < c0 ? 1 : 0); |
| } |
| |
| if (tp[num] != 0 || tp[num - 1] >= np[num - 1]) { |
| c0 = bn_sub_words(rp, tp, np, num); |
| if (tp[num] != 0 || c0 == 0) { |
| for (i = 0; i < num + 2; i++) { |
| vp[i] = 0; |
| } |
| return 1; |
| } |
| } |
| for (i = 0; i < num; i++) { |
| rp[i] = tp[i], vp[i] = 0; |
| } |
| vp[num] = 0; |
| vp[num + 1] = 0; |
| return 1; |
| } |
| #endif |
| |
| #endif |
