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140 .IX Title "bn_internal 3"
141 .TH bn_internal 3 "0.9.6e" "2000-11-12" "OpenSSL"
144 bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
145 bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
146 bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
147 bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
148 bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
149 bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
150 bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- \s-1BIGNUM\s0
151 library internal functions
153 .IX Header "SYNOPSIS"
155 \& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
156 \& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
158 \& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
159 \& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
160 \& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
162 \& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
166 \& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
167 \& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
168 \& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
169 \& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
172 \& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
175 \& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
177 \& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
178 \& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
180 \& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
181 \& int tn, int n, BN_ULONG *tmp);
182 \& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
183 \& int n2, BN_ULONG *tmp);
184 \& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
185 \& int n2, BN_ULONG *tmp);
188 \& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
189 \& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
192 \& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
193 \& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
194 \& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
197 \& BIGNUM *bn_expand(BIGNUM *a, int bits);
198 \& BIGNUM *bn_wexpand(BIGNUM *a, int n);
199 \& BIGNUM *bn_expand2(BIGNUM *a, int n);
200 \& void bn_fix_top(BIGNUM *a);
203 \& void bn_check_top(BIGNUM *a);
204 \& void bn_print(BIGNUM *a);
205 \& void bn_dump(BN_ULONG *d, int n);
206 \& void bn_set_max(BIGNUM *a);
207 \& void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
208 \& void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
211 .IX Header "DESCRIPTION"
212 This page documents the internal functions used by the OpenSSL
213 \&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate
214 debugging and extending the library. They are \fInot\fR to be used by
216 .Sh "The \s-1BIGNUM\s0 structure"
217 .IX Subsection "The BIGNUM structure"
219 \& typedef struct bignum_st
221 \& int top; /* index of last used d (most significant word) */
222 \& BN_ULONG *d; /* pointer to an array of 'BITS2' bit chunks */
223 \& int max; /* size of the d array */
224 \& int neg; /* sign */
227 The big number is stored in \fBd\fR, a \fImalloc()\fRed array of \fB\s-1BN_ULONG\s0\fRs,
228 least significant first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
229 in size (\fB\s-1BITS2\s0\fR), depending on the 'number of bits' specified in
230 \&\f(CW\*(C`openssl/bn.h\*(C'\fR.
232 \&\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR
233 is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and
234 bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is
235 \&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR.
237 Various routines in this library require the use of temporary
238 \&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory
239 allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in
240 conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is
241 used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see
243 .Sh "Low-level arithmetic operations"
244 .IX Subsection "Low-level arithmetic operations"
245 These functions are implemented in C and for several platforms in
248 bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word
249 arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result
250 in \fBrp\fR, and returns the high word (carry).
252 bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR
253 word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places
254 the result in \fBrp\fR, and returns the high word (carry).
256 bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array
257 \&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR
258 word-wise, and places the low and high bytes of the result in \fBrp\fR.
260 bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR)
261 by \fBd\fR and returns the result.
263 bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
264 arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the
265 result in \fBrp\fR, and returns the high word (carry).
267 bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
268 arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the
269 result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0
272 bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
273 \&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
276 bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
277 \&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
280 bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
281 \&\fBb\fR and the 8 word array \fBr\fR.
283 bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
284 \&\fBb\fR and the 16 word array \fBr\fR.
286 The following functions are implemented in C:
288 bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR
289 and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and
292 bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR
293 word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word
294 array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR.
296 bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
297 arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of
298 \&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
300 bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBt\fR) operates on the \fBn2\fR
301 word arrays \fBa\fR and \fBb\fR and the 2*\fBn2\fR word arrays \fBr\fR and \fBt\fR.
302 \&\fBn2\fR must be a power of 2. It computes \fBa\fR*\fBb\fR and places the
305 bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBtn\fR, \fBn\fR, \fBtmp\fR) operates
306 on the \fBn\fR+\fBtn\fR word arrays \fBa\fR and \fBb\fR and the 4*\fBn\fR word arrays
307 \&\fBr\fR and \fBtmp\fR.
309 bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
310 \&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
313 bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
314 \&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
317 \&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
318 factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
319 words long, \fIbn_mul_recursive()\fR if they are larger than
320 \&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
321 size, and \fIbn_mul_part_recursive()\fR for others that are larger than
322 \&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
324 bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
325 \&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
327 The implementations use the following macros which, depending on the
328 architecture, may use \*(L"long long\*(R" C operations or inline assembler.
329 They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR.
331 mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
332 low word of the result in \fBr\fR and the high word in \fBc\fR.
334 mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
335 places the low word of the result in \fBr\fR and the high word in \fBc\fR.
337 sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
338 of the result in \fBr0\fR and the high word in \fBr1\fR.
340 .IX Subsection "Size changes"
341 \&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
342 number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
343 \&\fBn\fR word number. If the number has to be expanded, both macros
344 call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
345 data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
347 The \fIbn_fix_top()\fR macro reduces \fBa->top\fR to point to the most
348 significant non-zero word when \fBa\fR has shrunk.
350 .IX Subsection "Debugging"
351 \&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top
352 <= (a)\->max)\*(C'\fR. A violation will cause the program to abort.
354 \&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
355 (in reverse order, i.e. most significant word first) to stderr.
357 \&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size.
358 This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
359 \&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
361 If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
362 and \fIbn_set_max()\fR are defined as empty macros.
364 .IX Header "SEE ALSO"