Update build for OpenSSL-0.9.8j upgrade.
[dragonfly.git] / secure / lib / libcrypto / man / bn_internal.3
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132.\" ========================================================================
133.\"
134.IX Title "bn_internal 3"
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135.TH bn_internal 3 "2009-01-11" "0.9.8j" "OpenSSL"
136.\" For nroff, turn off justification. Always turn off hyphenation; it makes
137.\" way too many mistakes in technical documents.
138.if n .ad l
139.nh
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140.SH "NAME"
141bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
142bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
143bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
144bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
145bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
146bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
74dab6c2 147bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM
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148library internal functions
149.SH "SYNOPSIS"
8b0cefbb 150.IX Header "SYNOPSIS"
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151.Vb 9
152\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
153\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
154\& BN_ULONG w);
155\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
156\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
157\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
158\& int num);
159\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
160\& int num);
e257b235 161\&
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162\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
163\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
164\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
165\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
e257b235 166\&
984263bc 167\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
e257b235 168\&
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169\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
170\& int nb);
171\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
172\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
173\& int dna,int dnb,BN_ULONG *tmp);
174\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
175\& int n, int tna,int tnb, BN_ULONG *tmp);
176\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
177\& int n2, BN_ULONG *tmp);
178\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
179\& int n2, BN_ULONG *tmp);
e257b235 180\&
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181\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
182\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
e257b235 183\&
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184\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
185\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
186\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
e257b235 187\&
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188\& BIGNUM *bn_expand(BIGNUM *a, int bits);
189\& BIGNUM *bn_wexpand(BIGNUM *a, int n);
190\& BIGNUM *bn_expand2(BIGNUM *a, int n);
191\& void bn_fix_top(BIGNUM *a);
e257b235 192\&
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193\& void bn_check_top(BIGNUM *a);
194\& void bn_print(BIGNUM *a);
195\& void bn_dump(BN_ULONG *d, int n);
196\& void bn_set_max(BIGNUM *a);
197\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
198\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
199.Ve
200.SH "DESCRIPTION"
8b0cefbb 201.IX Header "DESCRIPTION"
984263bc 202This page documents the internal functions used by the OpenSSL
8b0cefbb 203\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate
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204debugging and extending the library. They are \fInot\fR to be used by
205applications.
206.Sh "The \s-1BIGNUM\s0 structure"
8b0cefbb 207.IX Subsection "The BIGNUM structure"
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208.Vb 7
209\& typedef struct bignum_st
210\& {
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211\& int top; /* number of words used in d */
212\& BN_ULONG *d; /* pointer to an array containing the integer value */
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213\& int max; /* size of the d array */
214\& int neg; /* sign */
215\& } BIGNUM;
216.Ve
8b0cefbb 217.PP
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218The integer value is stored in \fBd\fR, a \fImalloc()\fRed array of words (\fB\s-1BN_ULONG\s0\fR),
219least significant word first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
220in size, depending on the 'number of bits' (\fB\s-1BITS2\s0\fR) specified in
8b0cefbb 221\&\f(CW\*(C`openssl/bn.h\*(C'\fR.
984263bc 222.PP
8b0cefbb 223\&\fBmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR
a561f9ff 224is the number of words being used, so for a value of 4, bn.d[0]=4 and
984263bc 225bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is
8b0cefbb 226\&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR.
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227.PP
228Various routines in this library require the use of temporary
8b0cefbb 229\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory
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230allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in
231conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is
232used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see
8b0cefbb 233\&\fIBN_CTX_start\fR\|(3).
984263bc 234.Sh "Low-level arithmetic operations"
8b0cefbb 235.IX Subsection "Low-level arithmetic operations"
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236These functions are implemented in C and for several platforms in
237assembly language:
238.PP
8b0cefbb 239bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word
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240arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result
241in \fBrp\fR, and returns the high word (carry).
242.PP
8b0cefbb 243bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR
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244word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places
245the result in \fBrp\fR, and returns the high word (carry).
246.PP
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247bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array
248\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR
e257b235 249word-wise, and places the low and high bytes of the result in \fBrp\fR.
984263bc 250.PP
8b0cefbb 251bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR)
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252by \fBd\fR and returns the result.
253.PP
8b0cefbb 254bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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255arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the
256result in \fBrp\fR, and returns the high word (carry).
257.PP
8b0cefbb 258bn_sub_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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259arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR \- \fBbp\fR, places the
260result in \fBrp\fR, and returns the carry (1 if \fBbp\fR > \fBap\fR, 0
261otherwise).
262.PP
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263bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
264\&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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265result in \fBr\fR.
266.PP
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267bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
268\&\fBb\fR and the 16 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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269result in \fBr\fR.
270.PP
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271bn_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
272\&\fBb\fR and the 8 word array \fBr\fR.
984263bc 273.PP
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274bn_sqr_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.
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276.PP
277The following functions are implemented in C:
278.PP
8b0cefbb 279bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR
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280and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and
281less than \fBb\fR.
282.PP
8b0cefbb 283bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR
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284word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word
285array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR.
286.PP
8b0cefbb 287bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
984263bc 288arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of
8b0cefbb 289\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 290.PP
8b0cefbb 291bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates
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292on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR
293(\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR
294word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes
8b0cefbb 295\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 296.PP
8b0cefbb 297bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR)
984263bc 298operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and
8b0cefbb 299\&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR.
984263bc 300.PP
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301bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
302\&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
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303and \fBb\fR.
304.PP
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305bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
306\&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
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307array \fBtmp\fR.
308.PP
8b0cefbb 309\&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
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310factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
311words long, \fIbn_mul_recursive()\fR if they are larger than
8b0cefbb 312\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
984263bc 313size, and \fIbn_mul_part_recursive()\fR for others that are larger than
8b0cefbb 314\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
984263bc 315.PP
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316bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
317\&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
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318.PP
319The implementations use the following macros which, depending on the
320architecture, may use \*(L"long long\*(R" C operations or inline assembler.
8b0cefbb 321They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR.
984263bc 322.PP
8b0cefbb 323mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
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324low word of the result in \fBr\fR and the high word in \fBc\fR.
325.PP
8b0cefbb 326mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
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327places the low word of the result in \fBr\fR and the high word in \fBc\fR.
328.PP
8b0cefbb 329sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
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330of the result in \fBr0\fR and the high word in \fBr1\fR.
331.Sh "Size changes"
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332.IX Subsection "Size changes"
333\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
984263bc 334number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
8b0cefbb 335\&\fBn\fR word number. If the number has to be expanded, both macros
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336call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
337data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
338.PP
8b0cefbb 339The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most
a561f9ff 340significant non-zero word plus one when \fBa\fR has shrunk.
984263bc 341.Sh "Debugging"
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342.IX Subsection "Debugging"
343\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top
344<= (a)\->max)\*(C'\fR. A violation will cause the program to abort.
984263bc 345.PP
8b0cefbb 346\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
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347(in reverse order, i.e. most significant word first) to stderr.
348.PP
8b0cefbb 349\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBmax\fR of its current size.
984263bc 350This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
8b0cefbb 351\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
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352.PP
353If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
354and \fIbn_set_max()\fR are defined as empty macros.
355.SH "SEE ALSO"
74dab6c2 356.IX Header "SEE ALSO"
8b0cefbb 357\&\fIbn\fR\|(3)