/* 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" // This file has two other implementations: x86 assembly language in // asm/bn-586.pl and x86_64 inline assembly in asm/x86_64-gcc.c. #if defined(OPENSSL_NO_ASM) || \ !(defined(OPENSSL_X86) || \ (defined(OPENSSL_X86_64) && (defined(__GNUC__) || defined(__clang__)))) #ifdef BN_ULLONG #define mul_add(r, a, w, c) \ do { \ BN_ULLONG t; \ t = (BN_ULLONG)(w) * (a) + (r) + (c); \ (r) = Lw(t); \ (c) = Hw(t); \ } while (0) #define mul(r, a, w, c) \ do { \ BN_ULLONG t; \ t = (BN_ULLONG)(w) * (a) + (c); \ (r) = Lw(t); \ (c) = Hw(t); \ } while (0) #define sqr(r0, r1, a) \ do { \ BN_ULLONG t; \ t = (BN_ULLONG)(a) * (a); \ (r0) = Lw(t); \ (r1) = Hw(t); \ } while (0) #else #define mul_add(r, a, w, c) \ do { \ 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; \ } while (0) #define mul(r, a, w, c) \ do { \ 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; \ } while (0) #define sqr(r0, r1, a) \ do { \ BN_ULONG tmp = (a); \ BN_UMULT_LOHI(r0, r1, tmp, tmp); \ } while (0) #endif // !BN_ULLONG BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num, BN_ULONG w) { BN_ULONG c1 = 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, size_t num, BN_ULONG w) { BN_ULONG c1 = 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, size_t n) { 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--; } } #ifdef BN_ULLONG BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, size_t n) { BN_ULLONG ll = 0; if (n == 0) { return 0; } while (n & ~3) { ll += (BN_ULLONG)a[0] + b[0]; r[0] = (BN_ULONG)ll; ll >>= BN_BITS2; ll += (BN_ULLONG)a[1] + b[1]; r[1] = (BN_ULONG)ll; ll >>= BN_BITS2; ll += (BN_ULLONG)a[2] + b[2]; r[2] = (BN_ULONG)ll; ll >>= BN_BITS2; ll += (BN_ULLONG)a[3] + b[3]; r[3] = (BN_ULONG)ll; 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; ll >>= BN_BITS2; a++; b++; r++; n--; } return (BN_ULONG)ll; } #else // !BN_ULLONG BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, size_t n) { BN_ULONG c, l, t; if (n == 0) { return (BN_ULONG)0; } c = 0; while (n & ~3) { t = a[0]; t += c; c = (t < c); l = t + b[0]; c += (l < t); r[0] = l; t = a[1]; t += c; c = (t < c); l = t + b[1]; c += (l < t); r[1] = l; t = a[2]; t += c; c = (t < c); l = t + b[2]; c += (l < t); r[2] = l; t = a[3]; t += c; c = (t < c); l = t + b[3]; c += (l < t); r[3] = l; a += 4; b += 4; r += 4; n -= 4; } while (n) { t = a[0]; t += c; c = (t < c); l = t + b[0]; c += (l < t); r[0] = l; a++; b++; r++; n--; } return (BN_ULONG)c; } #endif // !BN_ULLONG BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, size_t n) { BN_ULONG t1, t2; int c = 0; if (n == 0) { return (BN_ULONG)0; } while (n & ~3) { t1 = a[0]; t2 = b[0]; r[0] = t1 - t2 - c; if (t1 != t2) { c = (t1 < t2); } t1 = a[1]; t2 = b[1]; r[1] = t1 - t2 - c; if (t1 != t2) { c = (t1 < t2); } t1 = a[2]; t2 = b[2]; r[2] = t1 - t2 - c; if (t1 != t2) { c = (t1 < t2); } t1 = a[3]; t2 = b[3]; r[3] = t1 - t2 - c; 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; 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_ULLONG // 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) += (hi); \ 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) += hi; \ if ((c1) < hi) { \ (c2)++; \ } \ t += (c0); /* no carry */ \ (c0) = (BN_ULONG)Lw(t); \ hi = (BN_ULONG)Hw(t); \ (c1) += hi; \ 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) += hi; \ 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) #else // 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) #endif // !BN_ULLONG void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]) { 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[8], const BN_ULONG a[4], const BN_ULONG b[4]) { 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[16], const BN_ULONG a[8]) { 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[8], const BN_ULONG a[4]) { 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; } #undef mul_add #undef mul #undef sqr #undef mul_add_c #undef mul_add_c2 #undef sqr_add_c #undef sqr_add_c2 #endif