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"
27 * These preprocessor symbols control various aspects of the bignum headers
28 * and library code. They're not defined by any "normal" configuration, as
29 * they are intended for development and testing purposes. NB: defining all
30 * three can be useful for debugging application code as well as openssl
31 * itself. BN_DEBUG - turn on various debugging alterations to the bignum
32 * code BN_DEBUG_RAND - uses random poisoning of unused words to trip up
33 * mismanagement of bignum internals. You must also define BN_DEBUG.
35 /* #define BN_DEBUG */
36 /* #define BN_DEBUG_RAND */
38 # ifndef OPENSSL_SMALL_FOOTPRINT
45 * This next option uses the C libraries (2 word)/(1 word) function. If it is
46 * not defined, I use my C version (which is slower). The reason for this
47 * flag is that when the particular C compiler library routine is used, and
48 * the library is linked with a different compiler, the library is missing.
49 * This mostly happens when the library is built with gcc and then linked
50 * using normal cc. This would be a common occurrence because gcc normally
51 * produces code that is 2 times faster than system compilers for the big
52 * number stuff. For machines with only one compiler (or shared libraries),
53 * this should be on. Again this in only really a problem on machines using
54 * "long long's", are 32bit, and are not using my assembler code.
56 # if defined(OPENSSL_SYS_MSDOS) || defined(OPENSSL_SYS_WINDOWS) || \
57 defined(OPENSSL_SYS_WIN32) || defined(linux)
62 * 64-bit processor with LP64 ABI
64 # ifdef SIXTY_FOUR_BIT_LONG
65 # define BN_ULLONG unsigned long long
67 # define BN_MASK2 (0xffffffffffffffffL)
68 # define BN_MASK2l (0xffffffffL)
69 # define BN_MASK2h (0xffffffff00000000L)
70 # define BN_MASK2h1 (0xffffffff80000000L)
71 # define BN_DEC_CONV (10000000000000000000UL)
72 # define BN_DEC_NUM 19
73 # define BN_DEC_FMT1 "%lu"
74 # define BN_DEC_FMT2 "%019lu"
78 * 64-bit processor other than LP64 ABI
80 # ifdef SIXTY_FOUR_BIT
84 # define BN_MASK2 (0xffffffffffffffffLL)
85 # define BN_MASK2l (0xffffffffL)
86 # define BN_MASK2h (0xffffffff00000000LL)
87 # define BN_MASK2h1 (0xffffffff80000000LL)
88 # define BN_DEC_CONV (10000000000000000000ULL)
89 # define BN_DEC_NUM 19
90 # define BN_DEC_FMT1 "%llu"
91 # define BN_DEC_FMT2 "%019llu"
94 # ifdef THIRTY_TWO_BIT
96 # if defined(_WIN32) && !defined(__GNUC__)
97 # define BN_ULLONG unsigned __int64
99 # define BN_ULLONG unsigned long long
103 # define BN_MASK2 (0xffffffffL)
104 # define BN_MASK2l (0xffff)
105 # define BN_MASK2h1 (0xffff8000L)
106 # define BN_MASK2h (0xffff0000L)
107 # define BN_DEC_CONV (1000000000L)
108 # define BN_DEC_NUM 9
109 # define BN_DEC_FMT1 "%u"
110 # define BN_DEC_FMT2 "%09u"
115 * Bignum consistency macros
116 * There is one "API" macro, bn_fix_top(), for stripping leading zeroes from
117 * bignum data after direct manipulations on the data. There is also an
118 * "internal" macro, bn_check_top(), for verifying that there are no leading
119 * zeroes. Unfortunately, some auditing is required due to the fact that
120 * bn_fix_top() has become an overabused duct-tape because bignum data is
121 * occasionally passed around in an inconsistent state. So the following
122 * changes have been made to sort this out;
123 * - bn_fix_top()s implementation has been moved to bn_correct_top()
124 * - if BN_DEBUG isn't defined, bn_fix_top() maps to bn_correct_top(), and
125 * bn_check_top() is as before.
126 * - if BN_DEBUG *is* defined;
127 * - bn_check_top() tries to pollute unused words even if the bignum 'top' is
128 * consistent. (ed: only if BN_DEBUG_RAND is defined)
129 * - bn_fix_top() maps to bn_check_top() rather than "fixing" anything.
130 * The idea is to have debug builds flag up inconsistent bignums when they
131 * occur. If that occurs in a bn_fix_top(), we examine the code in question; if
132 * the use of bn_fix_top() was appropriate (ie. it follows directly after code
133 * that manipulates the bignum) it is converted to bn_correct_top(), and if it
134 * was not appropriate, we convert it permanently to bn_check_top() and track
135 * down the cause of the bug. Eventually, no internal code should be using the
136 * bn_fix_top() macro. External applications and libraries should try this with
137 * their own code too, both in terms of building against the openssl headers
138 * with BN_DEBUG defined *and* linking with a version of OpenSSL built with it
139 * defined. This not only improves external code, it provides more test
140 * coverage for openssl's own code.
145 # ifdef BN_DEBUG_RAND
146 # define bn_pollute(a) \
148 const BIGNUM *_bnum1 = (a); \
149 if (_bnum1->top < _bnum1->dmax) { \
150 unsigned char _tmp_char; \
151 /* We cast away const without the compiler knowing, any \
152 * *genuinely* constant variables that aren't mutable \
153 * wouldn't be constructed with top!=dmax. */ \
154 BN_ULONG *_not_const; \
155 memcpy(&_not_const, &_bnum1->d, sizeof(_not_const)); \
156 RAND_bytes(&_tmp_char, 1); /* Debug only - safe to ignore error return */\
157 memset(_not_const + _bnum1->top, _tmp_char, \
158 sizeof(*_not_const) * (_bnum1->dmax - _bnum1->top)); \
162 # define bn_pollute(a)
164 # define bn_check_top(a) \
166 const BIGNUM *_bnum2 = (a); \
167 if (_bnum2 != NULL) { \
168 assert(((_bnum2->top == 0) && !_bnum2->neg) || \
169 (_bnum2->top && (_bnum2->d[_bnum2->top - 1] != 0))); \
170 bn_pollute(_bnum2); \
174 # define bn_fix_top(a) bn_check_top(a)
176 # define bn_check_size(bn, bits) bn_wcheck_size(bn, ((bits+BN_BITS2-1))/BN_BITS2)
177 # define bn_wcheck_size(bn, words) \
179 const BIGNUM *_bnum2 = (bn); \
180 assert((words) <= (_bnum2)->dmax && \
181 (words) >= (_bnum2)->top); \
182 /* avoid unused variable warning with NDEBUG */ \
186 # else /* !BN_DEBUG */
188 # define bn_pollute(a)
189 # define bn_check_top(a)
190 # define bn_fix_top(a) bn_correct_top(a)
191 # define bn_check_size(bn, bits)
192 # define bn_wcheck_size(bn, words)
196 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num,
198 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w);
199 void bn_sqr_words(BN_ULONG *rp, const BN_ULONG *ap, int num);
200 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
201 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
203 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
207 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit
209 int top; /* Index of last used d +1. */
210 /* The next are internal book keeping for bn_expand. */
211 int dmax; /* Size of the d array. */
212 int neg; /* one if the number is negative */
216 /* Used for montgomery multiplication */
217 struct bn_mont_ctx_st {
218 int ri; /* number of bits in R */
219 BIGNUM RR; /* used to convert to montgomery form */
220 BIGNUM N; /* The modulus */
221 BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1 (Ni is only
222 * stored for bignum algorithm) */
223 BN_ULONG n0[2]; /* least significant word(s) of Ni; (type
224 * changed with 0.9.9, was "BN_ULONG n0;"
230 * Used for reciprocal division/mod functions It cannot be shared between
233 struct bn_recp_ctx_st {
234 BIGNUM N; /* the divisor */
235 BIGNUM Nr; /* the reciprocal */
241 /* Used for slow "generation" functions. */
243 unsigned int ver; /* To handle binary (in)compatibility */
244 void *arg; /* callback-specific data */
246 /* if (ver==1) - handles old style callbacks */
247 void (*cb_1) (int, int, void *);
248 /* if (ver==2) - new callback style */
249 int (*cb_2) (int, int, BN_GENCB *);
254 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
257 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
258 * the number of multiplications is a constant plus on average
260 * 2^(w-1) + (b-w)/(w+1);
262 * here 2^(w-1) is for precomputing the table (we actually need
263 * entries only for windows that have the lowest bit set), and
264 * (b-w)/(w+1) is an approximation for the expected number of
265 * w-bit windows, not counting the first one.
270 * w = 5 if 671 > b > 239
271 * w = 4 if 239 > b > 79
272 * w = 3 if 79 > b > 23
275 * (with draws in between). Very small exponents are often selected
276 * with low Hamming weight, so we use w = 1 for b <= 23.
278 # define BN_window_bits_for_exponent_size(b) \
285 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
286 * line width of the target processor is at least the following value.
288 # define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
289 # define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
292 * Window sizes optimized for fixed window size modular exponentiation
293 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
294 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
295 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
296 * defined for cache line sizes of 32 and 64, cache line sizes where
297 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
298 * used on processors that have a 128 byte or greater cache line size.
300 # if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
302 # define BN_window_bits_for_ctime_exponent_size(b) \
307 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
309 # elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
311 # define BN_window_bits_for_ctime_exponent_size(b) \
315 # define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
319 /* Pentium pro 16,16,16,32,64 */
320 /* Alpha 16,16,16,16.64 */
321 # define BN_MULL_SIZE_NORMAL (16)/* 32 */
322 # define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
323 # define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
324 # define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
325 # define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
328 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
329 * size_t was used to perform integer-only operations on pointers. This
330 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
331 * is still only 32 bits. What's needed in these cases is an integer type
332 * with the same size as a pointer, which size_t is not certain to be. The
333 * only fix here is VMS-specific.
335 # if defined(OPENSSL_SYS_VMS)
336 # if __INITIAL_POINTER_SIZE == 64
337 # define PTR_SIZE_INT long long
338 # else /* __INITIAL_POINTER_SIZE == 64 */
339 # define PTR_SIZE_INT int
340 # endif /* __INITIAL_POINTER_SIZE == 64 [else] */
341 # elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
342 # define PTR_SIZE_INT size_t
343 # endif /* defined(OPENSSL_SYS_VMS) [else] */
345 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
347 * BN_UMULT_HIGH section.
348 * If the compiler doesn't support 2*N integer type, then you have to
349 * replace every N*N multiplication with 4 (N/2)*(N/2) accompanied by some
350 * shifts and additions which unavoidably results in severe performance
351 * penalties. Of course provided that the hardware is capable of producing
352 * 2*N result... That's when you normally start considering assembler
353 * implementation. However! It should be pointed out that some CPUs (e.g.,
354 * PowerPC, Alpha, and IA-64) provide *separate* instruction calculating
355 * the upper half of the product placing the result into a general
356 * purpose register. Now *if* the compiler supports inline assembler,
357 * then it's not impossible to implement the "bignum" routines (and have
358 * the compiler optimize 'em) exhibiting "native" performance in C. That's
359 * what BN_UMULT_HIGH macro is about:-) Note that more recent compilers do
360 * support 2*64 integer type, which is also used here.
362 # if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 && \
363 (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
364 # define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
365 # define BN_UMULT_LOHI(low,high,a,b) ({ \
366 __uint128_t ret=(__uint128_t)(a)*(b); \
367 (high)=ret>>64; (low)=ret; })
368 # elif defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
371 # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
372 # elif defined(__GNUC__) && __GNUC__>=2
373 # define BN_UMULT_HIGH(a,b) ({ \
374 register BN_ULONG ret; \
375 asm ("umulh %1,%2,%0" \
379 # endif /* compiler */
380 # elif defined(_ARCH_PPC64) && defined(SIXTY_FOUR_BIT_LONG)
381 # if defined(__GNUC__) && __GNUC__>=2
382 # define BN_UMULT_HIGH(a,b) ({ \
383 register BN_ULONG ret; \
384 asm ("mulhdu %0,%1,%2" \
388 # endif /* compiler */
389 # elif (defined(__x86_64) || defined(__x86_64__)) && \
390 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
391 # if defined(__GNUC__) && __GNUC__>=2
392 # define BN_UMULT_HIGH(a,b) ({ \
393 register BN_ULONG ret,discard; \
395 : "=a"(discard),"=d"(ret) \
399 # define BN_UMULT_LOHI(low,high,a,b) \
401 : "=a"(low),"=d"(high) \
405 # elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
406 # if defined(_MSC_VER) && _MSC_VER>=1400
407 unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
408 unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
409 unsigned __int64 *h);
410 # pragma intrinsic(__umulh,_umul128)
411 # define BN_UMULT_HIGH(a,b) __umulh((a),(b))
412 # define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
414 # elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
415 # if defined(__GNUC__) && __GNUC__>=2
416 # define BN_UMULT_HIGH(a,b) ({ \
417 register BN_ULONG ret; \
418 asm ("dmultu %1,%2" \
420 : "r"(a), "r"(b) : "l"); \
422 # define BN_UMULT_LOHI(low,high,a,b) \
423 asm ("dmultu %2,%3" \
424 : "=l"(low),"=h"(high) \
427 # elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
428 # if defined(__GNUC__) && __GNUC__>=2
429 # define BN_UMULT_HIGH(a,b) ({ \
430 register BN_ULONG ret; \
431 asm ("umulh %0,%1,%2" \
437 # endif /* OPENSSL_NO_ASM */
439 # ifdef BN_DEBUG_RAND
440 # define bn_clear_top2max(a) \
442 int ind = (a)->dmax - (a)->top; \
443 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
444 for (; ind != 0; ind--) \
448 # define bn_clear_top2max(a)
452 /*******************************************************************
453 * Using the long long type, has to be twice as wide as BN_ULONG...
455 # define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
456 # define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
458 # define mul_add(r,a,w,c) { \
460 t=(BN_ULLONG)w * (a) + (r) + (c); \
465 # define mul(r,a,w,c) { \
467 t=(BN_ULLONG)w * (a) + (c); \
472 # define sqr(r0,r1,a) { \
474 t=(BN_ULLONG)(a)*(a); \
479 # elif defined(BN_UMULT_LOHI)
480 # define mul_add(r,a,w,c) { \
481 BN_ULONG high,low,ret,tmp=(a); \
483 BN_UMULT_LOHI(low,high,w,tmp); \
485 (c) = (ret<(c))?1:0; \
488 (c) += (ret<low)?1:0; \
492 # define mul(r,a,w,c) { \
493 BN_ULONG high,low,ret,ta=(a); \
494 BN_UMULT_LOHI(low,high,w,ta); \
497 (c) += (ret<low)?1:0; \
501 # define sqr(r0,r1,a) { \
503 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
506 # elif defined(BN_UMULT_HIGH)
507 # define mul_add(r,a,w,c) { \
508 BN_ULONG high,low,ret,tmp=(a); \
510 high= BN_UMULT_HIGH(w,tmp); \
513 (c) = (ret<(c))?1:0; \
516 (c) += (ret<low)?1:0; \
520 # define mul(r,a,w,c) { \
521 BN_ULONG high,low,ret,ta=(a); \
523 high= BN_UMULT_HIGH(w,ta); \
526 (c) += (ret<low)?1:0; \
530 # define sqr(r0,r1,a) { \
533 (r1) = BN_UMULT_HIGH(tmp,tmp); \
537 /*************************************************************
541 # define LBITS(a) ((a)&BN_MASK2l)
542 # define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
543 # define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
545 # define LLBITS(a) ((a)&BN_MASKl)
546 # define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
547 # define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
549 # define mul64(l,h,bl,bh) \
551 BN_ULONG m,m1,lt,ht; \
559 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
562 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
567 # define sqr64(lo,ho,in) \
577 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
578 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
579 l=(l+m)&BN_MASK2; if (l < m) h++; \
584 # define mul_add(r,a,bl,bh,c) { \
590 mul64(l,h,(bl),(bh)); \
592 /* non-multiply part */ \
593 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
595 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
600 # define mul(r,a,bl,bh,c) { \
606 mul64(l,h,(bl),(bh)); \
608 /* non-multiply part */ \
609 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
613 # endif /* !BN_LLONG */
615 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
616 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
618 void bn_init(BIGNUM *a);
619 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
620 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
621 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
622 void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
623 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
624 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
625 int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
626 int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
627 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
628 int dna, int dnb, BN_ULONG *t);
629 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
630 int n, int tna, int tnb, BN_ULONG *t);
631 void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
632 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
633 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
635 BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
637 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
638 const BN_ULONG *np, const BN_ULONG *n0, int num);
640 BIGNUM *int_bn_mod_inverse(BIGNUM *in,
641 const BIGNUM *a, const BIGNUM *n, BN_CTX *ctx,
644 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
645 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx);
647 static ossl_inline BIGNUM *bn_expand(BIGNUM *a, int bits)
649 if (bits > (INT_MAX - BN_BITS2 + 1))
652 if (((bits+BN_BITS2-1)/BN_BITS2) <= (a)->dmax)
655 return bn_expand2((a),(bits+BN_BITS2-1)/BN_BITS2);