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[dragonfly.git] / secure / lib / libcrypto / man / bn.3
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1.rn '' }`
2''' $RCSfile$$Revision$$Date$
3'''
4''' $Log$
5'''
6.de Sh
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7.br
8.if t .Sp
9.ne 5
10.PP
11\fB\\$1\fR
12.PP
13..
74dab6c2 14.de Sp
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15.if t .sp .5v
16.if n .sp
17..
74dab6c2 18.de Ip
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19.br
20.ie \\n(.$>=3 .ne \\$3
21.el .ne 3
22.IP "\\$1" \\$2
23..
74dab6c2 24.de Vb
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25.ft CW
26.nf
27.ne \\$1
28..
74dab6c2 29.de Ve
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30.ft R
31
32.fi
33..
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34'''
35'''
36''' Set up \*(-- to give an unbreakable dash;
37''' string Tr holds user defined translation string.
38''' Bell System Logo is used as a dummy character.
39'''
984263bc 40.tr \(*W-|\(bv\*(Tr
984263bc 41.ie n \{\
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42.ds -- \(*W-
43.ds PI pi
44.if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
45.if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch
46.ds L" ""
47.ds R" ""
48''' \*(M", \*(S", \*(N" and \*(T" are the equivalent of
49''' \*(L" and \*(R", except that they are used on ".xx" lines,
50''' such as .IP and .SH, which do another additional levels of
51''' double-quote interpretation
52.ds M" """
53.ds S" """
54.ds N" """""
55.ds T" """""
56.ds L' '
57.ds R' '
58.ds M' '
59.ds S' '
60.ds N' '
61.ds T' '
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62'br\}
63.el\{\
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64.ds -- \(em\|
65.tr \*(Tr
66.ds L" ``
67.ds R" ''
68.ds M" ``
69.ds S" ''
70.ds N" ``
71.ds T" ''
72.ds L' `
73.ds R' '
74.ds M' `
75.ds S' '
76.ds N' `
77.ds T' '
78.ds PI \(*p
984263bc 79'br\}
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80.\" If the F register is turned on, we'll generate
81.\" index entries out stderr for the following things:
82.\" TH Title
83.\" SH Header
84.\" Sh Subsection
85.\" Ip Item
86.\" X<> Xref (embedded
87.\" Of course, you have to process the output yourself
88.\" in some meaninful fashion.
89.if \nF \{
90.de IX
91.tm Index:\\$1\t\\n%\t"\\$2"
984263bc 92..
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93.nr % 0
94.rr F
984263bc 95.\}
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96.TH bn 3 "0.9.7d" "2/Sep/2004" "OpenSSL"
97.UC
98.if n .hy 0
984263bc 99.if n .na
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100.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
101.de CQ \" put $1 in typewriter font
102.ft CW
103'if n "\c
104'if t \\&\\$1\c
105'if n \\&\\$1\c
106'if n \&"
107\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
108'.ft R
109..
110.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
111. \" AM - accent mark definitions
984263bc 112.bd B 3
74dab6c2 113. \" fudge factors for nroff and troff
984263bc 114.if n \{\
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115. ds #H 0
116. ds #V .8m
117. ds #F .3m
118. ds #[ \f1
119. ds #] \fP
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120.\}
121.if t \{\
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122. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
123. ds #V .6m
124. ds #F 0
125. ds #[ \&
126. ds #] \&
984263bc 127.\}
74dab6c2 128. \" simple accents for nroff and troff
984263bc 129.if n \{\
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130. ds ' \&
131. ds ` \&
132. ds ^ \&
133. ds , \&
134. ds ~ ~
135. ds ? ?
136. ds ! !
137. ds /
138. ds q
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139.\}
140.if t \{\
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141. ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u"
142. ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u'
143. ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u'
144. ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u'
145. ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u'
146. ds ? \s-2c\h'-\w'c'u*7/10'\u\h'\*(#H'\zi\d\s+2\h'\w'c'u*8/10'
147. ds ! \s-2\(or\s+2\h'-\w'\(or'u'\v'-.8m'.\v'.8m'
148. ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u'
149. ds q o\h'-\w'o'u*8/10'\s-4\v'.4m'\z\(*i\v'-.4m'\s+4\h'\w'o'u*8/10'
984263bc 150.\}
74dab6c2 151. \" troff and (daisy-wheel) nroff accents
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152.ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V'
153.ds 8 \h'\*(#H'\(*b\h'-\*(#H'
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154.ds v \\k:\h'-(\\n(.wu*9/10-\*(#H)'\v'-\*(#V'\*(#[\s-4v\s0\v'\*(#V'\h'|\\n:u'\*(#]
155.ds _ \\k:\h'-(\\n(.wu*9/10-\*(#H+(\*(#F*2/3))'\v'-.4m'\z\(hy\v'.4m'\h'|\\n:u'
156.ds . \\k:\h'-(\\n(.wu*8/10)'\v'\*(#V*4/10'\z.\v'-\*(#V*4/10'\h'|\\n:u'
157.ds 3 \*(#[\v'.2m'\s-2\&3\s0\v'-.2m'\*(#]
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158.ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#]
159.ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H'
160.ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u'
161.ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#]
162.ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#]
163.ds ae a\h'-(\w'a'u*4/10)'e
164.ds Ae A\h'-(\w'A'u*4/10)'E
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165.ds oe o\h'-(\w'o'u*4/10)'e
166.ds Oe O\h'-(\w'O'u*4/10)'E
167. \" corrections for vroff
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168.if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u'
169.if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u'
74dab6c2 170. \" for low resolution devices (crt and lpr)
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171.if \n(.H>23 .if \n(.V>19 \
172\{\
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173. ds : e
174. ds 8 ss
175. ds v \h'-1'\o'\(aa\(ga'
176. ds _ \h'-1'^
177. ds . \h'-1'.
178. ds 3 3
179. ds o a
180. ds d- d\h'-1'\(ga
181. ds D- D\h'-1'\(hy
182. ds th \o'bp'
183. ds Th \o'LP'
184. ds ae ae
185. ds Ae AE
186. ds oe oe
187. ds Oe OE
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188.\}
189.rm #[ #] #H #V #F C
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190.SH "NAME"
191bn \- multiprecision integer arithmetics
192.SH "SYNOPSIS"
74dab6c2 193.PP
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194.Vb 1
195\& #include <openssl/bn.h>
196.Ve
197.Vb 5
198\& BIGNUM *BN_new(void);
199\& void BN_free(BIGNUM *a);
200\& void BN_init(BIGNUM *);
201\& void BN_clear(BIGNUM *a);
202\& void BN_clear_free(BIGNUM *a);
203.Ve
204.Vb 3
205\& BN_CTX *BN_CTX_new(void);
206\& void BN_CTX_init(BN_CTX *c);
207\& void BN_CTX_free(BN_CTX *c);
208.Ve
209.Vb 2
210\& BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
211\& BIGNUM *BN_dup(const BIGNUM *a);
212.Ve
213.Vb 1
214\& BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);
215.Ve
216.Vb 3
217\& int BN_num_bytes(const BIGNUM *a);
218\& int BN_num_bits(const BIGNUM *a);
219\& int BN_num_bits_word(BN_ULONG w);
220.Ve
221.Vb 19
222\& int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
223\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
224\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
225\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
226\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
227\& BN_CTX *ctx);
228\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
229\& int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
230\& int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
231\& BN_CTX *ctx);
232\& int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
233\& BN_CTX *ctx);
234\& int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
235\& BN_CTX *ctx);
236\& int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
237\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
238\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
239\& const BIGNUM *m, BN_CTX *ctx);
240\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
241.Ve
242.Vb 5
243\& int BN_add_word(BIGNUM *a, BN_ULONG w);
244\& int BN_sub_word(BIGNUM *a, BN_ULONG w);
245\& int BN_mul_word(BIGNUM *a, BN_ULONG w);
246\& BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
247\& BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
248.Ve
249.Vb 6
250\& int BN_cmp(BIGNUM *a, BIGNUM *b);
251\& int BN_ucmp(BIGNUM *a, BIGNUM *b);
252\& int BN_is_zero(BIGNUM *a);
253\& int BN_is_one(BIGNUM *a);
254\& int BN_is_word(BIGNUM *a, BN_ULONG w);
255\& int BN_is_odd(BIGNUM *a);
256.Ve
257.Vb 5
258\& int BN_zero(BIGNUM *a);
259\& int BN_one(BIGNUM *a);
260\& const BIGNUM *BN_value_one(void);
261\& int BN_set_word(BIGNUM *a, unsigned long w);
262\& unsigned long BN_get_word(BIGNUM *a);
263.Ve
264.Vb 4
265\& int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
266\& int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
267\& int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
268\& int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
269.Ve
270.Vb 4
271\& BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
272\& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
273\& int BN_is_prime(const BIGNUM *p, int nchecks,
274\& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
275.Ve
276.Vb 8
277\& int BN_set_bit(BIGNUM *a, int n);
278\& int BN_clear_bit(BIGNUM *a, int n);
279\& int BN_is_bit_set(const BIGNUM *a, int n);
280\& int BN_mask_bits(BIGNUM *a, int n);
281\& int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
282\& int BN_lshift1(BIGNUM *r, BIGNUM *a);
283\& int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
284\& int BN_rshift1(BIGNUM *r, BIGNUM *a);
285.Ve
286.Vb 10
287\& int BN_bn2bin(const BIGNUM *a, unsigned char *to);
288\& BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
289\& char *BN_bn2hex(const BIGNUM *a);
290\& char *BN_bn2dec(const BIGNUM *a);
291\& int BN_hex2bn(BIGNUM **a, const char *str);
292\& int BN_dec2bn(BIGNUM **a, const char *str);
293\& int BN_print(BIO *fp, const BIGNUM *a);
294\& int BN_print_fp(FILE *fp, const BIGNUM *a);
295\& int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
296\& BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
297.Ve
298.Vb 2
299\& BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
300\& BN_CTX *ctx);
301.Ve
302.Vb 6
303\& BN_RECP_CTX *BN_RECP_CTX_new(void);
304\& void BN_RECP_CTX_init(BN_RECP_CTX *recp);
305\& void BN_RECP_CTX_free(BN_RECP_CTX *recp);
306\& int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
307\& int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
308\& BN_RECP_CTX *recp, BN_CTX *ctx);
309.Ve
310.Vb 11
311\& BN_MONT_CTX *BN_MONT_CTX_new(void);
312\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
313\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
314\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
315\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
316\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
317\& BN_MONT_CTX *mont, BN_CTX *ctx);
318\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
319\& BN_CTX *ctx);
320\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
321\& BN_CTX *ctx);
322.Ve
323.SH "DESCRIPTION"
984263bc 324This library performs arithmetic operations on integers of arbitrary
74dab6c2 325size. It was written for use in public key cryptography, such as RSA
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326and Diffie-Hellman.
327.PP
328It uses dynamic memory allocation for storing its data structures.
329That means that there is no limit on the size of the numbers
330manipulated by these functions, but return values must always be
331checked in case a memory allocation error has occurred.
332.PP
74dab6c2 333The basic object in this library is a \fBBIGNUM\fR. It is used to hold a
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334single large integer. This type should be considered opaque and fields
335should not be modified or accessed directly.
336.PP
74dab6c2 337The creation of \fBBIGNUM\fR objects is described in BN_new(3);
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338BN_add(3) describes most of the arithmetic operations.
339Comparison is described in BN_cmp(3); BN_zero(3)
340describes certain assignments, BN_rand(3) the generation of
341random numbers, BN_generate_prime(3) deals with prime
342numbers and BN_set_bit(3) with bit operations. The conversion
74dab6c2 343of \fBBIGNUM\fRs to external formats is described in BN_bn2bin(3).
984263bc 344.SH "SEE ALSO"
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345bn_internal(3),
346dh(3), err(3), rand(3), rsa(3),
347BN_new(3), BN_CTX_new(3),
348BN_copy(3), BN_swap(3), BN_num_bytes(3),
349BN_add(3), BN_add_word(3),
350BN_cmp(3), BN_zero(3), BN_rand(3),
351BN_generate_prime(3), BN_set_bit(3),
352BN_bn2bin(3), BN_mod_inverse(3),
353BN_mod_mul_reciprocal(3),
354BN_mod_mul_montgomery(3)
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355
356.rn }` ''
357.IX Title "bn 3"
358.IX Name "bn - multiprecision integer arithmetics"
359
360.IX Header "NAME"
361
362.IX Header "SYNOPSIS"
363
364.IX Header "DESCRIPTION"
365
366.IX Header "SEE ALSO"
367