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1.\" $OpenBSD: BN_mod_mul_reciprocal.3,v 1.10 2018/03/27 17:35:50 schwarze Exp $
2.\" OpenSSL 6859cf74 Sep 25 13:33:28 2002 +0000
3.\"
4.\" This file was written by Ulf Moeller <ulf@openssl.org>.
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51.Dd $Mdocdate: March 27 2018 $
52.Dt BN_MOD_MUL_RECIPROCAL 3
53.Os
54.Sh NAME
55.Nm BN_mod_mul_reciprocal ,
56.Nm BN_RECP_CTX_new ,
57.Nm BN_RECP_CTX_init ,
58.Nm BN_RECP_CTX_free ,
59.Nm BN_RECP_CTX_set ,
60.Nm BN_div_recp
61.Nd modular multiplication using reciprocal
62.Sh SYNOPSIS
63.In openssl/bn.h
64.Ft int
65.Fo BN_mod_mul_reciprocal
66.Fa "BIGNUM *r"
67.Fa "BIGNUM *a"
68.Fa "BIGNUM *b"
69.Fa "BN_RECP_CTX *recp"
70.Fa "BN_CTX *ctx"
71.Fc
72.Ft BN_RECP_CTX *
73.Fo BN_RECP_CTX_new
74.Fa void
75.Fc
76.Ft void
77.Fo BN_RECP_CTX_init
78.Fa "BN_RECP_CTX *recp"
79.Fc
80.Ft void
81.Fo BN_RECP_CTX_free
82.Fa "BN_RECP_CTX *recp"
83.Fc
84.Ft int
85.Fo BN_RECP_CTX_set
86.Fa "BN_RECP_CTX *recp"
87.Fa "const BIGNUM *m"
88.Fa "BN_CTX *ctx"
89.Fc
90.Ft int
91.Fo BN_div_recp
92.Fa "BIGNUM *dv"
93.Fa "BIGNUM *rem"
94.Fa "BIGNUM *a"
95.Fa "BN_RECP_CTX *recp"
96.Fa "BN_CTX *ctx"
97.Fc
98.Sh DESCRIPTION
99.Fn BN_mod_mul_reciprocal
100can be used to perform an efficient
101.Xr BN_mod_mul 3
102operation when the operation will be performed repeatedly with the same
103modulus.
104It computes
105.Fa r Ns =( Ns Fa a Ns * Ns Fa b Ns )% Ns Fa m
106using
107.Fa recp Ns =1/ Ns Fa m ,
108which is set as described below.
109.Fa ctx
110is a previously allocated
111.Vt BN_CTX
112used for temporary variables.
113.Pp
114.Fn BN_RECP_CTX_new
115allocates and initializes a
116.Vt BN_RECP_CTX
117structure.
118.Pp
119.Fn BN_RECP_CTX_init
120initializes an existing uninitialized
121.Vt BN_RECP_CTX .
122It is deprecated and dangerous: see
123.Sx CAVEATS .
124.Pp
125.Fn BN_RECP_CTX_free
126frees the components of the
127.Vt BN_RECP_CTX ,
128and, if it was created by
129.Fn BN_RECP_CTX_new ,
130also the structure itself.
131If
132.Fa recp
133is a
134.Dv NULL
135pointer, no action occurs.
136.Pp
137.Fn BN_RECP_CTX_set
138stores
139.Fa m
140in
141.Fa recp
142and sets it up for computing
143.Pf 1/ Fa m
144and shifting it left by
145.Fn BN_num_bits m Ns +1
146to make it an integer.
147The result and the number of bits it was shifted left will later be
148stored in
149.Fa recp .
150.Pp
151.Fn BN_div_recp
152divides
153.Fa a
154by
155.Fa m
156using
157.Fa recp .
158It places the quotient in
159.Fa dv
160and the remainder in
161.Fa rem .
162.Pp
163The
164.Vt BN_RECP_CTX
165structure is defined as follows:
166.Bd -literal
167typedef struct bn_recp_ctx_st {
168 BIGNUM N; /* the divisor */
169 BIGNUM Nr; /* the reciprocal */
170 int num_bits;
171 int shift;
172 int flags;
173} BN_RECP_CTX;
174.Ed
175.Pp
176It cannot be shared between threads.
177.Sh RETURN VALUES
178.Fn BN_RECP_CTX_new
179returns the newly allocated
180.Vt BN_RECP_CTX
181or
182.Dv NULL
183on error.
184.Pp
185For the other functions, 1 is returned for success or 0 on error.
186The error codes can be obtained by
187.Xr ERR_get_error 3 .
188.Sh SEE ALSO
189.Xr BN_add 3 ,
190.Xr BN_CTX_new 3 ,
191.Xr BN_new 3
192.Sh HISTORY
193.Fn BN_mod_mul_reciprocal
194first appeared in SSLeay 0.5.1 and has been available since
195.Ox 2.4 .
196.Pp
197.Vt BN_RECP_CTX
198was added in SSLeay 0.9.0.
199Before that, a function
200.Fn BN_reciprocal
201was used instead, and the
202.Fn BN_mod_mul_reciprocal
203arguments were different.
204.Pp
205.Fn BN_RECP_CTX_new ,
206.Fn BN_RECP_CTX_init ,
207.Fn BN_RECP_CTX_free ,
208.Fn BN_RECP_CTX_set ,
209and
210.Fn BN_div_recp
211first appeared in SSLeay 0.9.1 and have been available since
212.Ox 2.6 .
213.Sh CAVEATS
214.Fn BN_RECP_CTX_init
215must not be called on a context that was used previously, or
216memory used by the embedded
217.Vt BIGNUM
218structures is leaked immediately.
219Besides, it must not be called on a context created with
220.Fn BN_RECP_CTX_new ,
221or the context itself will likely be leaked later.
222It can only be used on a static
223.Vt BN_RECP_CTX
224structure, on one located on the stack, or on one
225.Xr malloc 3 Ap ed
226manually, but all these options are discouraged because they
227will no longer work once
228.Vt BN_RECP_CTX
229is made opaque.
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