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1.\" $OpenBSD: BN_mod_mul_montgomery.3,v 1.16 2025/03/09 15:24:25 tb Exp $
2.\" full merge up to: OpenSSL 6859cf74 Sep 25 13:33:28 2002 +0000
3.\" selective merge up to: OpenSSL 24a535ea Sep 22 13:14:20 2020 +0100
4.\"
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8.\" Copyright (c) 2021 Ingo Schwarze <schwarze@openbsd.org>
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22.\" The original file was written by Ulf Moeller <ulf@openssl.org>.
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69.Dd $Mdocdate: March 9 2025 $
70.Dt BN_MOD_MUL_MONTGOMERY 3
71.Os
72.Sh NAME
73.Nm BN_MONT_CTX_new ,
74.Nm BN_MONT_CTX_free ,
75.Nm BN_MONT_CTX_set ,
76.Nm BN_MONT_CTX_set_locked ,
77.Nm BN_MONT_CTX_copy ,
78.Nm BN_mod_mul_montgomery ,
79.Nm BN_from_montgomery ,
80.Nm BN_to_montgomery
81.Nd Montgomery multiplication
82.Sh SYNOPSIS
83.In openssl/bn.h
84.Ft BN_MONT_CTX *
85.Fo BN_MONT_CTX_new
86.Fa void
87.Fc
88.Ft void
89.Fo BN_MONT_CTX_free
90.Fa "BN_MONT_CTX *mont"
91.Fc
92.Ft int
93.Fo BN_MONT_CTX_set
94.Fa "BN_MONT_CTX *mont"
95.Fa "const BIGNUM *m"
96.Fa "BN_CTX *ctx"
97.Fc
98.Ft BN_MONT_CTX *
99.Fo BN_MONT_CTX_set_locked
100.Fa "BN_MONT_CTX **pmont"
101.Fa "int lock"
102.Fa "const BIGNUM *m"
103.Fa "BN_CTX *ctx"
104.Fc
105.Ft BN_MONT_CTX *
106.Fo BN_MONT_CTX_copy
107.Fa "BN_MONT_CTX *to"
108.Fa "const BN_MONT_CTX *from"
109.Fc
110.Ft int
111.Fo BN_mod_mul_montgomery
112.Fa "BIGNUM *r"
113.Fa "const BIGNUM *a"
114.Fa "const BIGNUM *b"
115.Fa "BN_MONT_CTX *mont"
116.Fa "BN_CTX *ctx"
117.Fc
118.Ft int
119.Fo BN_from_montgomery
120.Fa "BIGNUM *r"
121.Fa "const BIGNUM *a"
122.Fa "BN_MONT_CTX *mont"
123.Fa "BN_CTX *ctx"
124.Fc
125.Ft int
126.Fo BN_to_montgomery
127.Fa "BIGNUM *r"
128.Fa "const BIGNUM *a"
129.Fa "BN_MONT_CTX *mont"
130.Fa "BN_CTX *ctx"
131.Fc
132.Sh DESCRIPTION
133These functions implement Montgomery multiplication.
134They are used automatically when
135.Xr BN_mod_exp 3
136is called with suitable input, but they may be useful when several
137operations are to be performed using the same modulus.
138.Pp
139.Fn BN_MONT_CTX_new
140allocates and initializes a
141.Vt BN_MONT_CTX
142structure.
143.Pp
144.Fn BN_MONT_CTX_set
145sets up the
146.Fa mont
147structure from the modulus
148.Fa m
149by precomputing its inverse and a value R.
150.Pp
151.Fn BN_MONT_CTX_set_locked
152is a wrapper around
153.Fn BN_MONT_CTX_new
154and
155.Fn BN_MONT_CTX_set
156that is useful if more than one thread intends to use the same
157.Vt BN_MONT_CTX
158and none of these threads is exclusively responsible for creating
159and initializing the context.
160.Fn BN_MONT_CTX_set_locked
161first acquires the specified
162.Fa lock
163using
164.Xr CRYPTO_lock 3 .
165If
166.Pf * Fa pmont
167already differs from
168.Dv NULL ,
169no action occurs.
170Otherwise, a new
171.Vt BN_MONT_CTX
172is allocated with
173.Fn BN_MONT_CTX_new ,
174set up with
175.Fn BN_MONT_CTX_set ,
176and a pointer to it is stored in
177.Pf * Fa pmont .
178Finally, the
179.Fa lock
180is released.
181.Pp
182.Fn BN_MONT_CTX_copy
183copies the
184.Vt BN_MONT_CTX
185.Fa from
186to
187.Fa to .
188.Pp
189.Fn BN_MONT_CTX_free
190frees the components of the
191.Vt BN_MONT_CTX ,
192and, if it was created by
193.Fn BN_MONT_CTX_new ,
194also the structure itself.
195If
196.Fa mont
197is a
198.Dv NULL
199pointer, no action occurs.
200.Pp
201.Fn BN_mod_mul_montgomery
202computes
203.Pp
204.D1 Mont Ns Po Fa a , Fa b Pc := Fa a No * Fa b No * R^-1
205.Pp
206and places the result in
207.Fa r .
208.Pp
209.Fn BN_from_montgomery
210performs the Montgomery reduction
211.Pp
212.D1 Fa r No = Fa a No * R^-1
213.Pp
214.Fn BN_to_montgomery
215computes
216.Pp
217.D1 Mont Ns Po Fa a , No R^2 Pc = Fa a No * R
218.Pp
219Note that
220.Fa a
221must be non-negative and smaller than the modulus.
222.Pp
223For all functions,
224.Fa ctx
225is a previously allocated
226.Vt BN_CTX
227used for temporary variables.
228.Pp
229.Sy Warning :
230The inputs must be reduced modulo
231.Fa m ,
232otherwise the result will be outside the expected range.
233.Sh RETURN VALUES
234.Fn BN_MONT_CTX_new
235returns the newly allocated
236.Vt BN_MONT_CTX
237or
238.Dv NULL
239on error.
240.Pp
241.Fn BN_MONT_CTX_set_locked
242returns a pointer to the existing or newly created context or
243.Dv NULL
244on error.
245.Pp
246For the other functions, 1 is returned for success or 0 on error.
247The error codes can be obtained by
248.Xr ERR_get_error 3 .
249.Sh SEE ALSO
250.Xr BN_add 3 ,
251.Xr BN_CTX_new 3 ,
252.Xr BN_new 3 ,
253.Xr CRYPTO_lock 3
254.Sh HISTORY
255.Fn BN_MONT_CTX_new ,
256.Fn BN_MONT_CTX_free ,
257.Fn BN_MONT_CTX_set ,
258.Fn BN_mod_mul_montgomery ,
259.Fn BN_from_montgomery ,
260and
261.Fn BN_to_montgomery
262first appeared in SSLeay 0.6.1 and have been available since
263.Ox 2.4 .
264.Pp
265.Fn BN_MONT_CTX_copy
266first appeared in SSLeay 0.9.1 and has been available since
267.Ox 2.6 .
268.Pp
269.Fn BN_MONT_CTX_set_locked
270first appeared in OpenSSL 0.9.8 and has been available since
271.Ox 4.0 .
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-05-06 17:53:26 +0000