Upgrade to OpenSSL 0.9.8h.
[dragonfly.git] / secure / lib / libcrypto / man / bn_internal.3
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129.\" ========================================================================
130.\"
131.IX Title "bn_internal 3"
aac4ff6f 132.TH bn_internal 3 "2008-09-06" "0.9.8h" "OpenSSL"
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133.SH "NAME"
134bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
135bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
136bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
137bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
138bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
139bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
74dab6c2 140bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM
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141library internal functions
142.SH "SYNOPSIS"
8b0cefbb 143.IX Header "SYNOPSIS"
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144.Vb 9
145\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
146\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
147\& BN_ULONG w);
148\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
149\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
150\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
151\& int num);
152\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
153\& int num);
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154.Ve
155.PP
156.Vb 4
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157\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
158\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
159\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
160\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
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161.Ve
162.PP
163.Vb 1
984263bc 164\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
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165.Ve
166.PP
167.Vb 11
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168\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
169\& int nb);
170\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
171\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
172\& int dna,int dnb,BN_ULONG *tmp);
173\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
174\& int n, int tna,int tnb, BN_ULONG *tmp);
175\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
176\& int n2, BN_ULONG *tmp);
177\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
178\& int n2, BN_ULONG *tmp);
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179.Ve
180.PP
181.Vb 2
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182\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
183\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
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184.Ve
185.PP
186.Vb 3
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187\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
188\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
189\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
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190.Ve
191.PP
192.Vb 4
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193\& BIGNUM *bn_expand(BIGNUM *a, int bits);
194\& BIGNUM *bn_wexpand(BIGNUM *a, int n);
195\& BIGNUM *bn_expand2(BIGNUM *a, int n);
196\& void bn_fix_top(BIGNUM *a);
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197.Ve
198.PP
199.Vb 6
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200\& void bn_check_top(BIGNUM *a);
201\& void bn_print(BIGNUM *a);
202\& void bn_dump(BN_ULONG *d, int n);
203\& void bn_set_max(BIGNUM *a);
204\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
205\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
206.Ve
207.SH "DESCRIPTION"
8b0cefbb 208.IX Header "DESCRIPTION"
984263bc 209This page documents the internal functions used by the OpenSSL
8b0cefbb 210\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate
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211debugging and extending the library. They are \fInot\fR to be used by
212applications.
213.Sh "The \s-1BIGNUM\s0 structure"
8b0cefbb 214.IX Subsection "The BIGNUM structure"
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215.Vb 7
216\& typedef struct bignum_st
217\& {
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218\& int top; /* number of words used in d */
219\& BN_ULONG *d; /* pointer to an array containing the integer value */
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220\& int max; /* size of the d array */
221\& int neg; /* sign */
222\& } BIGNUM;
223.Ve
8b0cefbb 224.PP
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225The integer value is stored in \fBd\fR, a \fImalloc()\fRed array of words (\fB\s-1BN_ULONG\s0\fR),
226least significant word first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
227in size, depending on the 'number of bits' (\fB\s-1BITS2\s0\fR) specified in
8b0cefbb 228\&\f(CW\*(C`openssl/bn.h\*(C'\fR.
984263bc 229.PP
8b0cefbb 230\&\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR
a561f9ff 231is the number of words being used, so for a value of 4, bn.d[0]=4 and
984263bc 232bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is
8b0cefbb 233\&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR.
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234.PP
235Various routines in this library require the use of temporary
8b0cefbb 236\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory
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237allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in
238conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is
239used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see
8b0cefbb 240\&\fIBN_CTX_start\fR\|(3).
984263bc 241.Sh "Low-level arithmetic operations"
8b0cefbb 242.IX Subsection "Low-level arithmetic operations"
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243These functions are implemented in C and for several platforms in
244assembly language:
245.PP
8b0cefbb 246bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word
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247arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result
248in \fBrp\fR, and returns the high word (carry).
249.PP
8b0cefbb 250bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR
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251word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places
252the result in \fBrp\fR, and returns the high word (carry).
253.PP
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254bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array
255\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR
aac4ff6f 256word\-wise, and places the low and high bytes of the result in \fBrp\fR.
984263bc 257.PP
8b0cefbb 258bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR)
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259by \fBd\fR and returns the result.
260.PP
8b0cefbb 261bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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262arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the
263result in \fBrp\fR, and returns the high word (carry).
264.PP
8b0cefbb 265bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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266arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the
267result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0
268otherwise).
269.PP
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270bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
271\&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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272result in \fBr\fR.
273.PP
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274bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
275\&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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276result in \fBr\fR.
277.PP
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278bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
279\&\fBb\fR and the 8 word array \fBr\fR.
984263bc 280.PP
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281bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
282\&\fBb\fR and the 16 word array \fBr\fR.
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283.PP
284The following functions are implemented in C:
285.PP
8b0cefbb 286bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR
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287and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and
288less than \fBb\fR.
289.PP
8b0cefbb 290bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR
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291word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word
292array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR.
293.PP
8b0cefbb 294bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
984263bc 295arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of
8b0cefbb 296\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 297.PP
8b0cefbb 298bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates
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299on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR
300(\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR
301word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes
8b0cefbb 302\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 303.PP
8b0cefbb 304bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR)
984263bc 305operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and
8b0cefbb 306\&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR.
984263bc 307.PP
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308bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
309\&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
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310and \fBb\fR.
311.PP
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312bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
313\&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
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314array \fBtmp\fR.
315.PP
8b0cefbb 316\&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
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317factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
318words long, \fIbn_mul_recursive()\fR if they are larger than
8b0cefbb 319\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
984263bc 320size, and \fIbn_mul_part_recursive()\fR for others that are larger than
8b0cefbb 321\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
984263bc 322.PP
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323bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
324\&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
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325.PP
326The implementations use the following macros which, depending on the
327architecture, may use \*(L"long long\*(R" C operations or inline assembler.
8b0cefbb 328They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR.
984263bc 329.PP
8b0cefbb 330mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
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331low word of the result in \fBr\fR and the high word in \fBc\fR.
332.PP
8b0cefbb 333mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
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334places the low word of the result in \fBr\fR and the high word in \fBc\fR.
335.PP
8b0cefbb 336sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
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337of the result in \fBr0\fR and the high word in \fBr1\fR.
338.Sh "Size changes"
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339.IX Subsection "Size changes"
340\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
984263bc 341number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
8b0cefbb 342\&\fBn\fR word number. If the number has to be expanded, both macros
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343call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
344data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
345.PP
8b0cefbb 346The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most
a561f9ff 347significant non-zero word plus one when \fBa\fR has shrunk.
984263bc 348.Sh "Debugging"
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349.IX Subsection "Debugging"
350\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top
351<= (a)\->max)\*(C'\fR. A violation will cause the program to abort.
984263bc 352.PP
8b0cefbb 353\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
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354(in reverse order, i.e. most significant word first) to stderr.
355.PP
8b0cefbb 356\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size.
984263bc 357This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
8b0cefbb 358\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
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359.PP
360If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
361and \fIbn_set_max()\fR are defined as empty macros.
362.SH "SEE ALSO"
74dab6c2 363.IX Header "SEE ALSO"
8b0cefbb 364\&\fIbn\fR\|(3)