2 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 #ifndef HEADER_BN_LCL_H
11 # define HEADER_BN_LCL_H
14 * The EDK2 build doesn't use bn_conf.h; it sets THIRTY_TWO_BIT or
15 * SIXTY_FOUR_BIT in its own environment since it doesn't re-run our
16 * Configure script and needs to support both 32-bit and 64-bit.
18 # include <openssl/opensslconf.h>
20 # if !defined(OPENSSL_SYS_UEFI)
21 # include "internal/bn_conf.h"
24 # include "internal/bn_int.h"
31 * These preprocessor symbols control various aspects of the bignum headers
32 * and library code. They're not defined by any "normal" configuration, as
33 * they are intended for development and testing purposes. NB: defining all
34 * three can be useful for debugging application code as well as openssl
35 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
36 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
37 * mismanagement of bignum internals. You must also define BN_DEBUG.
39 /* #define BN_DEBUG */
40 /* #define BN_DEBUG_RAND */
42 # ifndef OPENSSL_SMALL_FOOTPRINT
49 * This next option uses the C libraries (2 word)/(1 word) function. If it is
50 * not defined, I use my C version (which is slower). The reason for this
51 * flag is that when the particular C compiler library routine is used, and
52 * the library is linked with a different compiler, the library is missing.
53 * This mostly happens when the library is built with gcc and then linked
54 * using normal cc. This would be a common occurrence because gcc normally
55 * produces code that is 2 times faster than system compilers for the big
56 * number stuff. For machines with only one compiler (or shared libraries),
57 * this should be on. Again this in only really a problem on machines using
58 * "long long's", are 32bit, and are not using my assembler code.
60 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
61 defined(OPENSSL_SYS_WIN32) || defined(linux)
66 * 64-bit processor with LP64 ABI
68 # ifdef SIXTY_FOUR_BIT_LONG
69 # define BN_ULLONG unsigned long long
71 # define BN_MASK2 (0xffffffffffffffffL)
72 # define BN_MASK2l (0xffffffffL)
73 # define BN_MASK2h (0xffffffff00000000L)
74 # define BN_MASK2h1 (0xffffffff80000000L)
75 # define BN_DEC_CONV (10000000000000000000UL)
76 # define BN_DEC_NUM 19
77 # define BN_DEC_FMT1 "%lu"
78 # define BN_DEC_FMT2 "%019lu"
82 * 64-bit processor other than LP64 ABI
84 # ifdef SIXTY_FOUR_BIT
88 # define BN_MASK2 (0xffffffffffffffffLL)
89 # define BN_MASK2l (0xffffffffL)
90 # define BN_MASK2h (0xffffffff00000000LL)
91 # define BN_MASK2h1 (0xffffffff80000000LL)
92 # define BN_DEC_CONV (10000000000000000000ULL)
93 # define BN_DEC_NUM 19
94 # define BN_DEC_FMT1 "%llu"
95 # define BN_DEC_FMT2 "%019llu"
98 # ifdef THIRTY_TWO_BIT
100 # if defined(_WIN32) && !defined(__GNUC__)
101 # define BN_ULLONG unsigned __int64
103 # define BN_ULLONG unsigned long long
107 # define BN_MASK2 (0xffffffffL)
108 # define BN_MASK2l (0xffff)
109 # define BN_MASK2h1 (0xffff8000L)
110 # define BN_MASK2h (0xffff0000L)
111 # define BN_DEC_CONV (1000000000L)
112 # define BN_DEC_NUM 9
113 # define BN_DEC_FMT1 "%u"
114 # define BN_DEC_FMT2 "%09u"
119 * Bignum consistency macros
120 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
121 * bignum data after direct manipulations on the data. There is also an
122 * "internal" macro, bn_check_top(), for verifying that there are no leading
123 * zeroes. Unfortunately, some auditing is required due to the fact that
124 * bn_fix_top() has become an overabused duct-tape because bignum data is
125 * occasionally passed around in an inconsistent state. So the following
126 * changes have been made to sort this out;
127 * - bn_fix_top()s implementation has been moved to bn_correct_top()
128 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
129 * bn_check_top() is as before.
130 * - if BN_DEBUG *is* defined;
131 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
132 * consistent. (ed: only if BN_DEBUG_RAND is defined)
133 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
134 * The idea is to have debug builds flag up inconsistent bignums when they
135 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
136 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
137 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
138 * was not appropriate, we convert it permanently to bn_check_top() and track
139 * down the cause of the bug. Eventually, no internal code should be using the
140 * bn_fix_top() macro. External applications and libraries should try this with
141 * their own code too, both in terms of building against the openssl headers
142 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
143 * defined. This not only improves external code, it provides more test
144 * coverage for openssl's own code.
149 # ifdef BN_DEBUG_RAND
150 # define bn_pollute(a) \
152 const BIGNUM *_bnum1 = (a); \
153 if (_bnum1->top < _bnum1->dmax) { \
154 unsigned char _tmp_char; \
155 /* We cast away const without the compiler knowing, any \
156 * *genuinely* constant variables that aren't mutable \
157 * wouldn't be constructed with top!=dmax. */ \
158 BN_ULONG *_not_const; \
159 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
160 RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
161 memset(_not_const + _bnum1->top, _tmp_char, \
162 sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
166 # define bn_pollute(a)
168 # define bn_check_top(a) \
170 const BIGNUM *_bnum2 = (a); \
171 if (_bnum2 != NULL) { \
172 OPENSSL_assert(((_bnum2->top == 0) && !_bnum2->neg) || \
173 (_bnum2->top && (_bnum2->d[_bnum2->top - 1] != 0))); \
174 bn_pollute(_bnum2); \
178 # define bn_fix_top(a) bn_check_top(a)
180 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
181 # define bn_wcheck_size(bn, words) \
183 const BIGNUM *_bnum2 = (bn); \
184 OPENSSL_assert((words) <= (_bnum2)->dmax && \
185 (words) >= (_bnum2)->top); \
186 /* avoid unused variable warning with NDEBUG */ \
190 # else /* !BN_DEBUG */
192 # define bn_pollute(a)
193 # define bn_check_top(a)
194 # define bn_fix_top(a) bn_correct_top(a)
195 # define bn_check_size(bn, bits)
196 # define bn_wcheck_size(bn, words)
200 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
202 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
203 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
204 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
205 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
207 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
211 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
213 int top; /* Index of last used d +1. */
214 /* The next are internal book keeping for bn_expand. */
215 int dmax; /* Size of the d array. */
216 int neg; /* one if the number is negative */
220 /* Used for montgomery multiplication */
221 struct bn_mont_ctx_st {
222 int ri; /* number of bits in R */
223 BIGNUM RR; /* used to convert to montgomery form */
224 BIGNUM N; /* The modulus */
225 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
226 * stored for bignum algorithm) */
227 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
228 * changed with 0.9.9, was "BN_ULONG n0;"
234 * Used for reciprocal division/mod functions It cannot be shared between
237 struct bn_recp_ctx_st {
238 BIGNUM N; /* the divisor */
239 BIGNUM Nr; /* the reciprocal */
245 /* Used for slow "generation" functions. */
247 unsigned int ver; /* To handle binary (in)compatibility */
248 void *arg; /* callback-specific data */
250 /* if (ver==1) - handles old style callbacks */
251 void (*cb_1) (int, int, void *);
252 /* if (ver==2) - new callback style */
253 int (*cb_2) (int, int, BN_GENCB *);
258 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
261 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
262 * the number of multiplications is a constant plus on average
264 * 2^(w-1) + (b-w)/(w+1);
266 * here 2^(w-1) is for precomputing the table (we actually need
267 * entries only for windows that have the lowest bit set), and
268 * (b-w)/(w+1) is an approximation for the expected number of
269 * w-bit windows, not counting the first one.
274 * w = 5 if 671 > b > 239
275 * w = 4 if 239 > b > 79
276 * w = 3 if 79 > b > 23
279 * (with draws in between). Very small exponents are often selected
280 * with low Hamming weight, so we use w = 1 for b <= 23.
282 # define BN_window_bits_for_exponent_size(b) \
289 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
290 * line width of the target processor is at least the following value.
292 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
293 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
296 * Window sizes optimized for fixed window size modular exponentiation
297 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
298 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
299 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
300 * defined for cache line sizes of 32 and 64, cache line sizes where
301 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
302 * used on processors that have a 128 byte or greater cache line size.
304 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
306 # define BN_window_bits_for_ctime_exponent_size(b) \
311 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
313 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
315 # define BN_window_bits_for_ctime_exponent_size(b) \
319 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
323 /* Pentium pro 16,16,16,32,64 */
324 /* Alpha 16,16,16,16.64 */
325 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
326 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
327 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
328 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
329 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
332 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
333 * size_t was used to perform integer-only operations on pointers. This
334 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
335 * is still only 32 bits. What's needed in these cases is an integer type
336 * with the same size as a pointer, which size_t is not certain to be. The
337 * only fix here is VMS-specific.
339 # if defined(OPENSSL_SYS_VMS)
340 # if __INITIAL_POINTER_SIZE == 64
341 # define PTR_SIZE_INT long long
342 # else /* __INITIAL_POINTER_SIZE == 64 */
343 # define PTR_SIZE_INT int
344 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
345 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
346 # define PTR_SIZE_INT size_t
347 # endif /* defined(OPENSSL_SYS_VMS) [else] */
349 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
351 * BN_UMULT_HIGH section.
353 * No, I'm not trying to overwhelm you when stating that the
354 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
355 * you to be impressed when I say that if the compiler doesn't
356 * support 2*N integer type, then you have to replace every N*N
357 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
358 * and additions which unavoidably results in severe performance
359 * penalties. Of course provided that the hardware is capable of
360 * producing 2*N result... That's when you normally start
361 * considering assembler implementation. However! It should be
362 * pointed out that some CPUs (most notably Alpha, PowerPC and
363 * upcoming IA-64 family:-) provide *separate* instruction
364 * calculating the upper half of the product placing the result
365 * into a general purpose register. Now *if* the compiler supports
366 * inline assembler, then it's not impossible to implement the
367 * "bignum" routines (and have the compiler optimize 'em)
368 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
371 * <appro@fy.chalmers.se>
373 # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
376 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
377 # elif defined(__GNUC__) && __GNUC__>=2
378 # define BN_UMULT_HIGH(a,b) ({ \
379 register BN_ULONG ret; \
380 asm ("umulh %1,%2,%0" \
384 # endif /* compiler */
385 # elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
386 # if defined(__GNUC__) && __GNUC__>=2
387 # define BN_UMULT_HIGH(a,b) ({ \
388 register BN_ULONG ret; \
389 asm ("mulhdu %0,%1,%2" \
393 # endif /* compiler */
394 # elif (defined(__x86_64) || defined(__x86_64__)) && \
395 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
396 # if defined(__GNUC__) && __GNUC__>=2
397 # define BN_UMULT_HIGH(a,b) ({ \
398 register BN_ULONG ret,discard; \
400 : "=a"(discard),"=d"(ret) \
404 # define BN_UMULT_LOHI(low,high,a,b) \
406 : "=a"(low),"=d"(high) \
410 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
411 # if defined(_MSC_VER) && _MSC_VER>=1400
412 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
413 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
414 unsigned __int64 *h);
415 # pragma intrinsic(__umulh,_umul128)
416 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
417 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
419 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
420 # if defined(__GNUC__) && __GNUC__>=2
421 # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16
422 /* "h" constraint is not an option on R6 and was removed in 4.4 */
423 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
424 # define BN_UMULT_LOHI(low,high,a,b) ({ \
425 __uint128_t ret=(__uint128_t)(a)*(b); \
426 (high)=ret>>64; (low)=ret; })
428 # define BN_UMULT_HIGH(a,b) ({ \
429 register BN_ULONG ret; \
430 asm ("dmultu %1,%2" \
432 : "r"(a), "r"(b) : "l"); \
434 # define BN_UMULT_LOHI(low,high,a,b)\
435 asm ("dmultu %2,%3" \
436 : "=l"(low),"=h"(high) \
440 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
441 # if defined(__GNUC__) && __GNUC__>=2
442 # define BN_UMULT_HIGH(a,b) ({ \
443 register BN_ULONG ret; \
444 asm ("umulh %0,%1,%2" \
450 # endif /* OPENSSL_NO_ASM */
452 # ifdef BN_DEBUG_RAND
453 # define bn_clear_top2max(a) \
455 int ind = (a)->dmax - (a)->top; \
456 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
457 for (; ind != 0; ind--) \
461 # define bn_clear_top2max(a)
465 /*******************************************************************
466 * Using the long long type, has to be twice as wide as BN_ULONG...
468 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
469 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
471 # define mul_add(r,a,w,c) { \
473 t=(BN_ULLONG)w * (a) + (r) + (c); \
478 # define mul(r,a,w,c) { \
480 t=(BN_ULLONG)w * (a) + (c); \
485 # define sqr(r0,r1,a) { \
487 t=(BN_ULLONG)(a)*(a); \
492 # elif defined(BN_UMULT_LOHI)
493 # define mul_add(r,a,w,c) { \
494 BN_ULONG high,low,ret,tmp=(a); \
496 BN_UMULT_LOHI(low,high,w,tmp); \
498 (c) = (ret<(c))?1:0; \
501 (c) += (ret<low)?1:0; \
505 # define mul(r,a,w,c) { \
506 BN_ULONG high,low,ret,ta=(a); \
507 BN_UMULT_LOHI(low,high,w,ta); \
510 (c) += (ret<low)?1:0; \
514 # define sqr(r0,r1,a) { \
516 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
519 # elif defined(BN_UMULT_HIGH)
520 # define mul_add(r,a,w,c) { \
521 BN_ULONG high,low,ret,tmp=(a); \
523 high= BN_UMULT_HIGH(w,tmp); \
526 (c) = (ret<(c))?1:0; \
529 (c) += (ret<low)?1:0; \
533 # define mul(r,a,w,c) { \
534 BN_ULONG high,low,ret,ta=(a); \
536 high= BN_UMULT_HIGH(w,ta); \
539 (c) += (ret<low)?1:0; \
543 # define sqr(r0,r1,a) { \
546 (r1) = BN_UMULT_HIGH(tmp,tmp); \
550 /*************************************************************
554 # define LBITS(a) ((a)&BN_MASK2l)
555 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
556 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
558 # define LLBITS(a) ((a)&BN_MASKl)
559 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
560 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
562 # define mul64(l,h,bl,bh) \
564 BN_ULONG m,m1,lt,ht; \
572 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
575 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
580 # define sqr64(lo,ho,in) \
590 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
591 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
592 l=(l+m)&BN_MASK2; if (l < m) h++; \
597 # define mul_add(r,a,bl,bh,c) { \
603 mul64(l,h,(bl),(bh)); \
605 /* non-multiply part */ \
606 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
608 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
613 # define mul(r,a,bl,bh,c) { \
619 mul64(l,h,(bl),(bh)); \
621 /* non-multiply part */ \
622 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
626 # endif /* !BN_LLONG */
628 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
629 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
631 void bn_init(BIGNUM *a);
632 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
633 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
634 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
635 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
636 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
637 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
638 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
639 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
640 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
641 int dna, int dnb, BN_ULONG *t);
642 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
643 int n, int tna, int tnb, BN_ULONG *t);
644 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
645 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
646 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
648 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
650 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
651 const BN_ULONG *np, const BN_ULONG *n0, int num);
653 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
654 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
657 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
658 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
660 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
662 if (bits > (INT_MAX - BN_BITS2 + 1))
665 if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
668 return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);