/* * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved. * * Licensed under the OpenSSL license (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html */ #ifndef HEADER_BN_LCL_H # define HEADER_BN_LCL_H /* * The EDK2 build doesn't use bn_conf.h; it sets THIRTY_TWO_BIT or * SIXTY_FOUR_BIT in its own environment since it doesn't re-run our * Configure script and needs to support both 32-bit and 64-bit. */ # include # if !defined(OPENSSL_SYS_UEFI) # include "internal/bn_conf.h" # endif # include "internal/bn_int.h" /* * These preprocessor symbols control various aspects of the bignum headers * and library code. They're not defined by any "normal" configuration, as * they are intended for development and testing purposes. NB: defining all * three can be useful for debugging application code as well as openssl * itself. BN_DEBUG - turn on various debugging alterations to the bignum * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up * mismanagement of bignum internals. You must also define BN_DEBUG. */ /* #define BN_DEBUG */ /* #define BN_DEBUG_RAND */ # ifndef OPENSSL_SMALL_FOOTPRINT # define BN_MUL_COMBA # define BN_SQR_COMBA # define BN_RECURSION # endif /* * This next option uses the C libraries (2 word)/(1 word) function. If it is * not defined, I use my C version (which is slower). The reason for this * flag is that when the particular C compiler library routine is used, and * the library is linked with a different compiler, the library is missing. * This mostly happens when the library is built with gcc and then linked * using normal cc. This would be a common occurrence because gcc normally * produces code that is 2 times faster than system compilers for the big * number stuff. For machines with only one compiler (or shared libraries), * this should be on. Again this in only really a problem on machines using * "long long's", are 32bit, and are not using my assembler code. */ # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \ defined(OPENSSL_SYS_WIN32) || defined(linux) # define BN_DIV2W # endif /* * 64-bit processor with LP64 ABI */ # ifdef SIXTY_FOUR_BIT_LONG # define BN_ULLONG unsigned long long # define BN_BITS4 32 # define BN_MASK2 (0xffffffffffffffffL) # define BN_MASK2l (0xffffffffL) # define BN_MASK2h (0xffffffff00000000L) # define BN_MASK2h1 (0xffffffff80000000L) # define BN_DEC_CONV (10000000000000000000UL) # define BN_DEC_NUM 19 # define BN_DEC_FMT1 "%lu" # define BN_DEC_FMT2 "%019lu" # endif /* * 64-bit processor other than LP64 ABI */ # ifdef SIXTY_FOUR_BIT # undef BN_LLONG # undef BN_ULLONG # define BN_BITS4 32 # define BN_MASK2 (0xffffffffffffffffLL) # define BN_MASK2l (0xffffffffL) # define BN_MASK2h (0xffffffff00000000LL) # define BN_MASK2h1 (0xffffffff80000000LL) # define BN_DEC_CONV (10000000000000000000ULL) # define BN_DEC_NUM 19 # define BN_DEC_FMT1 "%llu" # define BN_DEC_FMT2 "%019llu" # endif # ifdef THIRTY_TWO_BIT # ifdef BN_LLONG # if defined(_WIN32) && !defined(__GNUC__) # define BN_ULLONG unsigned __int64 # else # define BN_ULLONG unsigned long long # endif # endif # define BN_BITS4 16 # define BN_MASK2 (0xffffffffL) # define BN_MASK2l (0xffff) # define BN_MASK2h1 (0xffff8000L) # define BN_MASK2h (0xffff0000L) # define BN_DEC_CONV (1000000000L) # define BN_DEC_NUM 9 # define BN_DEC_FMT1 "%u" # define BN_DEC_FMT2 "%09u" # endif /*- * Bignum consistency macros * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from * bignum data after direct manipulations on the data. There is also an * "internal" macro, bn_check_top(), for verifying that there are no leading * zeroes. Unfortunately, some auditing is required due to the fact that * bn_fix_top() has become an overabused duct-tape because bignum data is * occasionally passed around in an inconsistent state. So the following * changes have been made to sort this out; * - bn_fix_top()s implementation has been moved to bn_correct_top() * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and * bn_check_top() is as before. * - if BN_DEBUG *is* defined; * - bn_check_top() tries to pollute unused words even if the bignum 'top' is * consistent. (ed: only if BN_DEBUG_RAND is defined) * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything. * The idea is to have debug builds flag up inconsistent bignums when they * occur. If that occurs in a bn_fix_top(), we examine the code in question; if * the use of bn_fix_top() was appropriate (ie. it follows directly after code * that manipulates the bignum) it is converted to bn_correct_top(), and if it * was not appropriate, we convert it permanently to bn_check_top() and track * down the cause of the bug. Eventually, no internal code should be using the * bn_fix_top() macro. External applications and libraries should try this with * their own code too, both in terms of building against the openssl headers * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it * defined. This not only improves external code, it provides more test * coverage for openssl's own code. */ # ifdef BN_DEBUG /* * The new BN_FLG_FIXED_TOP flag marks vectors that were not treated with * bn_correct_top, in other words such vectors are permitted to have zeros * in most significant limbs. Such vectors are used internally to achieve * execution time invariance for critical operations with private keys. * It's BN_DEBUG-only flag, because user application is not supposed to * observe it anyway. Moreover, optimizing compiler would actually remove * all operations manipulating the bit in question in non-BN_DEBUG build. */ # define BN_FLG_FIXED_TOP 0x10000 # ifdef BN_DEBUG_RAND # define bn_pollute(a) \ do { \ const BIGNUM *_bnum1 = (a); \ if (_bnum1->top < _bnum1->dmax) { \ unsigned char _tmp_char; \ /* We cast away const without the compiler knowing, any \ * *genuinely* constant variables that aren't mutable \ * wouldn't be constructed with top!=dmax. */ \ BN_ULONG *_not_const; \ memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \ RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\ memset(_not_const + _bnum1->top, _tmp_char, \ sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \ } \ } while(0) # else # define bn_pollute(a) # endif # define bn_check_top(a) \ do { \ const BIGNUM *_bnum2 = (a); \ if (_bnum2 != NULL) { \ int _top = _bnum2->top; \ (void)ossl_assert((_top == 0 && !_bnum2->neg) || \ (_top && ((_bnum2->flags & BN_FLG_FIXED_TOP) \ || _bnum2->d[_top - 1] != 0))); \ bn_pollute(_bnum2); \ } \ } while(0) # define bn_fix_top(a) bn_check_top(a) # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2) # define bn_wcheck_size(bn, words) \ do { \ const BIGNUM *_bnum2 = (bn); \ assert((words) <= (_bnum2)->dmax && \ (words) >= (_bnum2)->top); \ /* avoid unused variable warning with NDEBUG */ \ (void)(_bnum2); \ } while(0) # else /* !BN_DEBUG */ # define BN_FLG_FIXED_TOP 0 # define bn_pollute(a) # define bn_check_top(a) # define bn_fix_top(a) bn_correct_top(a) # define bn_check_size(bn, bits) # define bn_wcheck_size(bn, words) # endif BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w); BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w); void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num); BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num); BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, int num); struct bignum_st { BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit * chunks. */ int top; /* Index of last used d +1. */ /* The next are internal book keeping for bn_expand. */ int dmax; /* Size of the d array. */ int neg; /* one if the number is negative */ int flags; }; /* Used for montgomery multiplication */ struct bn_mont_ctx_st { int ri; /* number of bits in R */ BIGNUM RR; /* used to convert to montgomery form, possibly zero-padded */ BIGNUM N; /* The modulus */ BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only * stored for bignum algorithm) */ BN_ULONG n0[2]; /* least significant word(s) of Ni; (type * changed with 0.9.9, was "BN_ULONG n0;" * before) */ int flags; }; /* * Used for reciprocal division/mod functions It cannot be shared between * threads */ struct bn_recp_ctx_st { BIGNUM N; /* the divisor */ BIGNUM Nr; /* the reciprocal */ int num_bits; int shift; int flags; }; /* Used for slow "generation" functions. */ struct bn_gencb_st { unsigned int ver; /* To handle binary (in)compatibility */ void *arg; /* callback-specific data */ union { /* if (ver==1) - handles old style callbacks */ void (*cb_1) (int, int, void *); /* if (ver==2) - new callback style */ int (*cb_2) (int, int, BN_GENCB *); } cb; }; /*- * 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. */ # define BN_window_bits_for_exponent_size(b) \ ((b) > 671 ? 6 : \ (b) > 239 ? 5 : \ (b) > 79 ? 4 : \ (b) > 23 ? 3 : 1) /* * BN_mod_exp_mont_consttime is based on the assumption that the L1 data cache * line width of the target processor is at least the following value. */ # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 ) # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1) /* * Window sizes optimized for fixed window size modular exponentiation * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are * defined for cache line sizes of 32 and 64, cache line sizes where * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be * used on processors that have a 128 byte or greater cache line size. */ # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64 # define BN_window_bits_for_ctime_exponent_size(b) \ ((b) > 937 ? 6 : \ (b) > 306 ? 5 : \ (b) > 89 ? 4 : \ (b) > 22 ? 3 : 1) # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6) # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32 # define BN_window_bits_for_ctime_exponent_size(b) \ ((b) > 306 ? 5 : \ (b) > 89 ? 4 : \ (b) > 22 ? 3 : 1) # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5) # 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 */ /* * 2011-02-22 SMS. In various places, a size_t variable or a type cast to * size_t was used to perform integer-only operations on pointers. This * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t * is still only 32 bits. What's needed in these cases is an integer type * with the same size as a pointer, which size_t is not certain to be. The * only fix here is VMS-specific. */ # if defined(OPENSSL_SYS_VMS) # if __INITIAL_POINTER_SIZE == 64 # define PTR_SIZE_INT long long # else /* __INITIAL_POINTER_SIZE == 64 */ # define PTR_SIZE_INT int # endif /* __INITIAL_POINTER_SIZE == 64 [else] */ # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */ # define PTR_SIZE_INT size_t # endif /* defined(OPENSSL_SYS_VMS) [else] */ # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC) /* * BN_UMULT_HIGH section. * 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 (e.g., * PowerPC, Alpha, and IA-64) 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:-) Note that more recent compilers do * support 2*64 integer type, which is also used here. */ # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \ (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)) # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64) # define BN_UMULT_LOHI(low,high,a,b) ({ \ __uint128_t ret=(__uint128_t)(a)*(b); \ (high)=ret>>64; (low)=ret; }) # elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) # if defined(__DECC) # include # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b)) # elif defined(__GNUC__) && __GNUC__>=2 # 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_PPC64) && defined(SIXTY_FOUR_BIT_LONG) # if defined(__GNUC__) && __GNUC__>=2 # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret; \ asm ("mulhdu %0,%1,%2" \ : "=r"(ret) \ : "r"(a), "r"(b)); \ ret; }) # endif /* compiler */ # elif (defined(__x86_64) || defined(__x86_64__)) && \ (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT)) # if defined(__GNUC__) && __GNUC__>=2 # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret,discard; \ asm ("mulq %3" \ : "=a"(discard),"=d"(ret) \ : "a"(a), "g"(b) \ : "cc"); \ ret; }) # define BN_UMULT_LOHI(low,high,a,b) \ asm ("mulq %3" \ : "=a"(low),"=d"(high) \ : "a"(a),"g"(b) \ : "cc"); # endif # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT) # if defined(_MSC_VER) && _MSC_VER>=1400 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b); unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b, unsigned __int64 *h); # pragma intrinsic(__umulh,_umul128) # define BN_UMULT_HIGH(a,b) __umulh((a),(b)) # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high))) # endif # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)) # if defined(__GNUC__) && __GNUC__>=2 # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret; \ asm ("dmultu %1,%2" \ : "=h"(ret) \ : "r"(a), "r"(b) : "l"); \ ret; }) # define BN_UMULT_LOHI(low,high,a,b) \ asm ("dmultu %2,%3" \ : "=l"(low),"=h"(high) \ : "r"(a), "r"(b)); # endif # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG) # if defined(__GNUC__) && __GNUC__>=2 # define BN_UMULT_HIGH(a,b) ({ \ register BN_ULONG ret; \ asm ("umulh %0,%1,%2" \ : "=r"(ret) \ : "r"(a), "r"(b)); \ ret; }) # endif # endif /* cpu */ # endif /* OPENSSL_NO_ASM */ # ifdef BN_DEBUG_RAND # define bn_clear_top2max(a) \ { \ int ind = (a)->dmax - (a)->top; \ BN_ULONG *ftl = &(a)->d[(a)->top-1]; \ for (; ind != 0; ind--) \ *(++ftl) = 0x0; \ } # else # define bn_clear_top2max(a) # endif # ifdef BN_LLONG /******************************************************************* * Using the long long type, has to be twice as wide as BN_ULONG... */ # define Lw(t) (((BN_ULONG)(t))&BN_MASK2) # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2) # 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>BN_BITS4)&BN_MASK2l) # define L2HBITS(a) (((a)<>BN_BITS2)&BN_MASKl) # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<>(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_RECP_CTX_init(BN_RECP_CTX *recp); void BN_MONT_CTX_init(BN_MONT_CTX *ctx); void bn_init(BIGNUM *a); 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, const BN_ULONG *a, int n, BN_ULONG *tmp); void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a); void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a); int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n); int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl); void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna, int dnb, BN_ULONG *t); void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna, int tnb, BN_ULONG *t); void bn_sqr_recursive(BN_ULONG *r, const 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); BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, int dl); int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np, const BN_ULONG *n0, int num); BIGNUM *int_bn_mod_inverse(BIGNUM *in, const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx, int *noinv); int bn_probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits) { if (bits > (INT_MAX - BN_BITS2 + 1)) return NULL; if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax) return a; return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2); } #endif