Update files for OpenSSL-1.0.0f import.
[dragonfly.git] / secure / lib / libcrypto / man / bn_internal.3
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124.\" ========================================================================
125.\"
126.IX Title "bn_internal 3"
e3261593 127.TH bn_internal 3 "2012-01-04" "1.0.0f" "OpenSSL"
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128.\" For nroff, turn off justification. Always turn off hyphenation; it makes
129.\" way too many mistakes in technical documents.
130.if n .ad l
131.nh
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132.SH "NAME"
133bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words,
134bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8,
135bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal,
136bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive,
137bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive,
138bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top,
74dab6c2 139bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low \- BIGNUM
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140library internal functions
141.SH "SYNOPSIS"
8b0cefbb 142.IX Header "SYNOPSIS"
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143.Vb 1
144\& #include <openssl/bn.h>
145\&
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146\& BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
147\& BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num,
148\& BN_ULONG w);
149\& void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num);
150\& BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d);
151\& BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
152\& int num);
153\& BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,
154\& int num);
e257b235 155\&
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156\& void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
157\& void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
158\& void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a);
159\& void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a);
e257b235 160\&
984263bc 161\& int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n);
e257b235 162\&
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163\& void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
164\& int nb);
165\& void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
166\& void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
167\& int dna,int dnb,BN_ULONG *tmp);
168\& void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
169\& int n, int tna,int tnb, BN_ULONG *tmp);
170\& void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
171\& int n2, BN_ULONG *tmp);
172\& void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l,
173\& int n2, BN_ULONG *tmp);
e257b235 174\&
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175\& void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
176\& void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp);
e257b235 177\&
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178\& void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
179\& void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c);
180\& void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a);
e257b235 181\&
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182\& BIGNUM *bn_expand(BIGNUM *a, int bits);
183\& BIGNUM *bn_wexpand(BIGNUM *a, int n);
184\& BIGNUM *bn_expand2(BIGNUM *a, int n);
185\& void bn_fix_top(BIGNUM *a);
e257b235 186\&
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187\& void bn_check_top(BIGNUM *a);
188\& void bn_print(BIGNUM *a);
189\& void bn_dump(BN_ULONG *d, int n);
190\& void bn_set_max(BIGNUM *a);
191\& void bn_set_high(BIGNUM *r, BIGNUM *a, int n);
192\& void bn_set_low(BIGNUM *r, BIGNUM *a, int n);
193.Ve
194.SH "DESCRIPTION"
8b0cefbb 195.IX Header "DESCRIPTION"
984263bc 196This page documents the internal functions used by the OpenSSL
8b0cefbb 197\&\fB\s-1BIGNUM\s0\fR implementation. They are described here to facilitate
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198debugging and extending the library. They are \fInot\fR to be used by
199applications.
01185282 200.SS "The \s-1BIGNUM\s0 structure"
8b0cefbb 201.IX Subsection "The BIGNUM structure"
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202.Vb 1
203\& typedef struct bignum_st BIGNUM;
204\&
205\& struct bignum_st
984263bc 206\& {
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207\& BN_ULONG *d; /* Pointer to an array of \*(AqBN_BITS2\*(Aq bit chunks. */
208\& int top; /* Index of last used d +1. */
209\& /* The next are internal book keeping for bn_expand. */
210\& int dmax; /* Size of the d array. */
211\& int neg; /* one if the number is negative */
212\& int flags;
213\& };
984263bc 214.Ve
8b0cefbb 215.PP
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216The integer value is stored in \fBd\fR, a \fImalloc()\fRed array of words (\fB\s-1BN_ULONG\s0\fR),
217least significant word first. A \fB\s-1BN_ULONG\s0\fR can be either 16, 32 or 64 bits
218in size, depending on the 'number of bits' (\fB\s-1BITS2\s0\fR) specified in
8b0cefbb 219\&\f(CW\*(C`openssl/bn.h\*(C'\fR.
984263bc 220.PP
01185282 221\&\fBdmax\fR is the size of the \fBd\fR array that has been allocated. \fBtop\fR
a561f9ff 222is the number of words being used, so for a value of 4, bn.d[0]=4 and
984263bc 223bn.top=1. \fBneg\fR is 1 if the number is negative. When a \fB\s-1BIGNUM\s0\fR is
8b0cefbb 224\&\fB0\fR, the \fBd\fR field can be \fB\s-1NULL\s0\fR and \fBtop\fR == \fB0\fR.
984263bc 225.PP
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226\&\fBflags\fR is a bit field of flags which are defined in \f(CW\*(C`openssl/bn.h\*(C'\fR. The
227flags begin with \fB\s-1BN_FLG_\s0\fR. The macros BN_set_flags(b,n) and
228BN_get_flags(b,n) exist to enable or fetch flag(s) \fBn\fR from \fB\s-1BIGNUM\s0\fR
229structure \fBb\fR.
230.PP
984263bc 231Various routines in this library require the use of temporary
8b0cefbb 232\&\fB\s-1BIGNUM\s0\fR variables during their execution. Since dynamic memory
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233allocation to create \fB\s-1BIGNUM\s0\fRs is rather expensive when used in
234conjunction with repeated subroutine calls, the \fB\s-1BN_CTX\s0\fR structure is
235used. This structure contains \fB\s-1BN_CTX_NUM\s0\fR \fB\s-1BIGNUM\s0\fRs, see
8b0cefbb 236\&\fIBN_CTX_start\fR\|(3).
01185282 237.SS "Low-level arithmetic operations"
8b0cefbb 238.IX Subsection "Low-level arithmetic operations"
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239These functions are implemented in C and for several platforms in
240assembly language:
241.PP
8b0cefbb 242bn_mul_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR word
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243arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR, places the result
244in \fBrp\fR, and returns the high word (carry).
245.PP
8b0cefbb 246bn_mul_add_words(\fBrp\fR, \fBap\fR, \fBnum\fR, \fBw\fR) operates on the \fBnum\fR
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247word arrays \fBrp\fR and \fBap\fR. It computes \fBap\fR * \fBw\fR + \fBrp\fR, places
248the result in \fBrp\fR, and returns the high word (carry).
249.PP
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250bn_sqr_words(\fBrp\fR, \fBap\fR, \fBn\fR) operates on the \fBnum\fR word array
251\&\fBap\fR and the 2*\fBnum\fR word array \fBap\fR. It computes \fBap\fR * \fBap\fR
e257b235 252word-wise, and places the low and high bytes of the result in \fBrp\fR.
984263bc 253.PP
8b0cefbb 254bn_div_words(\fBh\fR, \fBl\fR, \fBd\fR) divides the two word number (\fBh\fR,\fBl\fR)
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255by \fBd\fR and returns the result.
256.PP
8b0cefbb 257bn_add_words(\fBrp\fR, \fBap\fR, \fBbp\fR, \fBnum\fR) operates on the \fBnum\fR word
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258arrays \fBap\fR, \fBbp\fR and \fBrp\fR. It computes \fBap\fR + \fBbp\fR, places the
259result in \fBrp\fR, and returns the high word (carry).
260.PP
8b0cefbb 261bn_sub_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 carry (1 if \fBbp\fR > \fBap\fR, 0
264otherwise).
265.PP
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266bn_mul_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
267\&\fBb\fR and the 8 word array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the
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268result in \fBr\fR.
269.PP
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270bn_mul_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
271\&\fBb\fR and the 16 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_sqr_comba4(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 4 word arrays \fBa\fR and
275\&\fBb\fR and the 8 word array \fBr\fR.
984263bc 276.PP
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277bn_sqr_comba8(\fBr\fR, \fBa\fR, \fBb\fR) operates on the 8 word arrays \fBa\fR and
278\&\fBb\fR and the 16 word array \fBr\fR.
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279.PP
280The following functions are implemented in C:
281.PP
8b0cefbb 282bn_cmp_words(\fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word arrays \fBa\fR
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283and \fBb\fR. It returns 1, 0 and \-1 if \fBa\fR is greater than, equal and
284less than \fBb\fR.
285.PP
8b0cefbb 286bn_mul_normal(\fBr\fR, \fBa\fR, \fBna\fR, \fBb\fR, \fBnb\fR) operates on the \fBna\fR
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287word array \fBa\fR, the \fBnb\fR word array \fBb\fR and the \fBna\fR+\fBnb\fR word
288array \fBr\fR. It computes \fBa\fR*\fBb\fR and places the result in \fBr\fR.
289.PP
8b0cefbb 290bn_mul_low_normal(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR) operates on the \fBn\fR word
984263bc 291arrays \fBr\fR, \fBa\fR and \fBb\fR. It computes the \fBn\fR low words of
8b0cefbb 292\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 293.PP
8b0cefbb 294bn_mul_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBdna\fR, \fBdnb\fR, \fBt\fR) operates
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295on the word arrays \fBa\fR and \fBb\fR of length \fBn2\fR+\fBdna\fR and \fBn2\fR+\fBdnb\fR
296(\fBdna\fR and \fBdnb\fR are currently allowed to be 0 or negative) and the 2*\fBn2\fR
297word arrays \fBr\fR and \fBt\fR. \fBn2\fR must be a power of 2. It computes
8b0cefbb 298\&\fBa\fR*\fBb\fR and places the result in \fBr\fR.
984263bc 299.PP
8b0cefbb 300bn_mul_part_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn\fR, \fBtna\fR, \fBtnb\fR, \fBtmp\fR)
984263bc 301operates on the word arrays \fBa\fR and \fBb\fR of length \fBn\fR+\fBtna\fR and
8b0cefbb 302\&\fBn\fR+\fBtnb\fR and the 4*\fBn\fR word arrays \fBr\fR and \fBtmp\fR.
984263bc 303.PP
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304bn_mul_low_recursive(\fBr\fR, \fBa\fR, \fBb\fR, \fBn2\fR, \fBtmp\fR) operates on the
305\&\fBn2\fR word arrays \fBr\fR and \fBtmp\fR and the \fBn2\fR/2 word arrays \fBa\fR
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306and \fBb\fR.
307.PP
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308bn_mul_high(\fBr\fR, \fBa\fR, \fBb\fR, \fBl\fR, \fBn2\fR, \fBtmp\fR) operates on the
309\&\fBn2\fR word arrays \fBr\fR, \fBa\fR, \fBb\fR and \fBl\fR (?) and the 3*\fBn2\fR word
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310array \fBtmp\fR.
311.PP
8b0cefbb 312\&\fIBN_mul()\fR calls \fIbn_mul_normal()\fR, or an optimized implementation if the
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313factors have the same size: \fIbn_mul_comba8()\fR is used if they are 8
314words long, \fIbn_mul_recursive()\fR if they are larger than
8b0cefbb 315\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR and the size is an exact multiple of the word
984263bc 316size, and \fIbn_mul_part_recursive()\fR for others that are larger than
8b0cefbb 317\&\fB\s-1BN_MULL_SIZE_NORMAL\s0\fR.
984263bc 318.PP
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319bn_sqr_normal(\fBr\fR, \fBa\fR, \fBn\fR, \fBtmp\fR) operates on the \fBn\fR word array
320\&\fBa\fR and the 2*\fBn\fR word arrays \fBtmp\fR and \fBr\fR.
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321.PP
322The implementations use the following macros which, depending on the
323architecture, may use \*(L"long long\*(R" C operations or inline assembler.
8b0cefbb 324They are defined in \f(CW\*(C`bn_lcl.h\*(C'\fR.
984263bc 325.PP
8b0cefbb 326mul(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBc\fR and places the
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327low word of the result in \fBr\fR and the high word in \fBc\fR.
328.PP
8b0cefbb 329mul_add(\fBr\fR, \fBa\fR, \fBw\fR, \fBc\fR) computes \fBw\fR*\fBa\fR+\fBr\fR+\fBc\fR and
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330places the low word of the result in \fBr\fR and the high word in \fBc\fR.
331.PP
8b0cefbb 332sqr(\fBr0\fR, \fBr1\fR, \fBa\fR) computes \fBa\fR*\fBa\fR and places the low word
984263bc 333of the result in \fBr0\fR and the high word in \fBr1\fR.
01185282 334.SS "Size changes"
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335.IX Subsection "Size changes"
336\&\fIbn_expand()\fR ensures that \fBb\fR has enough space for a \fBbits\fR bit
984263bc 337number. \fIbn_wexpand()\fR ensures that \fBb\fR has enough space for an
8b0cefbb 338\&\fBn\fR word number. If the number has to be expanded, both macros
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339call \fIbn_expand2()\fR, which allocates a new \fBd\fR array and copies the
340data. They return \fB\s-1NULL\s0\fR on error, \fBb\fR otherwise.
341.PP
8b0cefbb 342The \fIbn_fix_top()\fR macro reduces \fBa\->top\fR to point to the most
a561f9ff 343significant non-zero word plus one when \fBa\fR has shrunk.
01185282 344.SS "Debugging"
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345.IX Subsection "Debugging"
346\&\fIbn_check_top()\fR verifies that \f(CW\*(C`((a)\->top >= 0 && (a)\->top
01185282 347<= (a)\->dmax)\*(C'\fR. A violation will cause the program to abort.
984263bc 348.PP
8b0cefbb 349\&\fIbn_print()\fR prints \fBa\fR to stderr. \fIbn_dump()\fR prints \fBn\fR words at \fBd\fR
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350(in reverse order, i.e. most significant word first) to stderr.
351.PP
01185282 352\&\fIbn_set_max()\fR makes \fBa\fR a static number with a \fBdmax\fR of its current size.
984263bc 353This is used by \fIbn_set_low()\fR and \fIbn_set_high()\fR to make \fBr\fR a read-only
8b0cefbb 354\&\fB\s-1BIGNUM\s0\fR that contains the \fBn\fR low or high words of \fBa\fR.
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355.PP
356If \fB\s-1BN_DEBUG\s0\fR is not defined, \fIbn_check_top()\fR, \fIbn_print()\fR, \fIbn_dump()\fR
357and \fIbn_set_max()\fR are defined as empty macros.
358.SH "SEE ALSO"
74dab6c2 359.IX Header "SEE ALSO"
8b0cefbb 360\&\fIbn\fR\|(3)