/* crypto/bn/bn_lcl.h */ /* 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.] */ /* ==================================================================== * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved. * * 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 above 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 acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED 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 OpenSSL PROJECT OR * ITS 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. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #ifndef HEADER_BN_LCL_H #define HEADER_BN_LCL_H #include <openssl/bn.h> #ifdef __cplusplus extern "C" { #endif /* * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions * * * For window size 'w' (w >= 2) and a random 'b' bits exponent, * the number of multiplications is a constant plus on average * * 2^(w-1) + (b-w)/(w+1); * * here 2^(w-1) is for precomputing the table (we actually need * entries only for windows that have the lowest bit set), and * (b-w)/(w+1) is an approximation for the expected number of * w-bit windows, not counting the first one. * * Thus we should use * * w >= 6 if b > 671 * w = 5 if 671 > b > 239 * w = 4 if 239 > b > 79 * w = 3 if 79 > b > 23 * w <= 2 if 23 > b * * (with draws in between). Very small exponents are often selected * with low Hamming weight, so we use w = 1 for b <= 23. */ #if 1 #define BN_window_bits_for_exponent_size(b) \ ((b) > 671 ? 6 : \ (b) > 239 ? 5 : \ (b) > 79 ? 4 : \ (b) > 23 ? 3 : 1) #else /* Old SSLeay/OpenSSL table. * Maximum window size was 5, so this table differs for b==1024; * but it coincides for other interesting values (b==160, b==512). */ #define BN_window_bits_for_exponent_size(b) \ ((b) > 255 ? 5 : \ (b) > 127 ? 4 : \ (b) > 17 ? 3 : 1) #endif /* Pentium pro 16,16,16,32,64 */ /* Alpha 16,16,16,16.64 */ #define BN_MULL_SIZE_NORMAL (16) /* 32 */ #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */ #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */ #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */ #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */ #if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) /* * BN_UMULT_HIGH section. * * No, I'm not trying to overwhelm you when stating that the * product of N-bit numbers is 2*N bits wide:-) No, I don't expect * you to be impressed when I say that if the compiler doesn't * support 2*N integer type, then you have to replace every N*N * multiplication with 4 (N/2)*(N/2) accompanied by some shifts * and additions which unavoidably results in severe performance * penalties. Of course provided that the hardware is capable of * producing 2*N result... That's when you normally start * considering assembler implementation. However! It should be * pointed out that some CPUs (most notably Alpha, PowerPC and * upcoming IA-64 family:-) provide *separate* instruction * calculating the upper half of the product placing the result * into a general purpose register. Now *if* the compiler supports * inline assembler, then it's not impossible to implement the * "bignum" routines (and have the compiler optimize 'em) * exhibiting "native" performance in C. That's what BN_UMULT_HIGH * macro is about:-) * * <appro@fy.chalmers.se> */ # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) # if defined(__DECC) # include <c_asm.h> # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) # elif defined(__GNUC__) # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret; \ asm ("umulh %1,%2,%0" \ : "=r"(ret) \ : "r"(a), "r"(b)); \ ret; }) # endif /* compiler */ # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG) # if defined(__GNUC__) # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret; \ asm ("mulhdu %0,%1,%2" \ : "=r"(ret) \ : "r"(a), "r"(b)); \ ret; }) # endif /* compiler */ # endif /* cpu */ #endif /* NO_ASM */ /************************************************************* * Using the long long type */ #define Lw(t) (((BN_ULONG)(t))&BN_MASK2) #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) /* This is used for internal error checking and is not normally used */ #ifdef BN_DEBUG # include <assert.h> # define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax); #else # define bn_check_top(a) #endif /* This macro is to add extra stuff for development checking */ #ifdef BN_DEBUG #define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA)) #else #define bn_set_max(r) #endif /* These macros are used to 'take' a section of a bignum for read only use */ #define bn_set_low(r,a,n) \ { \ (r)->top=((a)->top > (n))?(n):(a)->top; \ (r)->d=(a)->d; \ (r)->neg=(a)->neg; \ (r)->flags|=BN_FLG_STATIC_DATA; \ bn_set_max(r); \ } #define bn_set_high(r,a,n) \ { \ if ((a)->top > (n)) \ { \ (r)->top=(a)->top-n; \ (r)->d= &((a)->d[n]); \ } \ else \ (r)->top=0; \ (r)->neg=(a)->neg; \ (r)->flags|=BN_FLG_STATIC_DATA; \ bn_set_max(r); \ } #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_HIGH) #define mul_add(r,a,w,c) { \ BN_ULONG high,low,ret,tmp=(a); \ ret = (r); \ high= BN_UMULT_HIGH(w,tmp); \ ret += (c); \ low = (w) * tmp; \ (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); \ low = (w) * ta; \ high= BN_UMULT_HIGH(w,ta); \ ret = low + (c); \ (c) = high; \ (c) += (ret<low)?1:0; \ (r) = ret; \ } #define sqr(r0,r1,a) { \ BN_ULONG tmp=(a); \ (r0) = tmp * tmp; \ (r1) = BN_UMULT_HIGH(tmp,tmp); \ } #else /************************************************************* * No long long type */ #define LBITS(a) ((a)&BN_MASK2l) #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l) #define L2HBITS(a) ((BN_ULONG)((a)&BN_MASK2l)<<BN_BITS4) #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(1L); \ 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 */ void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb); void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b); void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); void bn_sqr_comba8(BN_ULONG *r,BN_ULONG *a); void bn_sqr_comba4(BN_ULONG *r,BN_ULONG *a); int bn_cmp_words(BN_ULONG *a,BN_ULONG *b,int n); void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,BN_ULONG *t); void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int tn, int n,BN_ULONG *t); void bn_sqr_recursive(BN_ULONG *r,BN_ULONG *a, int n2, BN_ULONG *t); void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n); void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2, BN_ULONG *t); void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2, BN_ULONG *t); #ifdef __cplusplus } #endif #endif