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1.Dd $Mdocdate: February 23 2015 $
2.Dt BN_ADD 3
3.Os
4.Sh NAME
5.Nm BN_add ,
6.Nm BN_sub ,
7.Nm BN_mul ,
8.Nm BN_sqr ,
9.Nm BN_div ,
10.Nm BN_mod ,
11.Nm BN_nnmod ,
12.Nm BN_mod_add ,
13.Nm BN_mod_sub ,
14.Nm BN_mod_mul ,
15.Nm BN_mod_sqr ,
16.Nm BN_exp ,
17.Nm BN_mod_exp ,
18.Nm BN_gcd
19.Nd arithmetic operations on BIGNUMs
20.Sh SYNOPSIS
21.In openssl/bn.h
22.Ft int
23.Fo BN_add
24.Fa "BIGNUM *r"
25.Fa "const BIGNUM *a"
26.Fa "const BIGNUM *b"
27.Fc
28.Ft int
29.Fo BN_sub
30.Fa "BIGNUM *r"
31.Fa "const BIGNUM *a"
32.Fa "const BIGNUM *b"
33.Fc
34.Ft int
35.Fo BN_mul
36.Fa "BIGNUM *r"
37.Fa "BIGNUM *a"
38.Fa "BIGNUM *b"
39.Fa "BN_CTX *ctx"
40.Fc
41.Ft int
42.Fo BN_sqr
43.Fa "BIGNUM *r"
44.Fa "BIGNUM *a"
45.Fa "BN_CTX *ctx"
46.Fc
47.Ft int
48.Fo BN_div
49.Fa "BIGNUM *dv"
50.Fa "BIGNUM *rem"
51.Fa "const BIGNUM *a"
52.Fa "const BIGNUM *d"
53.Fa "BN_CTX *ctx"
54.Fc
55.Ft int
56.Fo BN_mod
57.Fa "BIGNUM *rem"
58.Fa "const BIGNUM *a"
59.Fa "const BIGNUM *m"
60.Fa "BN_CTX *ctx"
61.Fc
62.Ft int
63.Fo BN_nnmod
64.Fa "BIGNUM *r"
65.Fa "const BIGNUM *a"
66.Fa "const BIGNUM *m"
67.Fa "BN_CTX *ctx"
68.Fc
69.Ft int
70.Fo BN_mod_add
71.Fa "BIGNUM *r"
72.Fa "BIGNUM *a"
73.Fa "BIGNUM *b"
74.Fa "const BIGNUM *m"
75.Fa "BN_CTX *ctx"
76.Fc
77.Ft int
78.Fo BN_mod_sub
79.Fa "BIGNUM *r"
80.Fa "BIGNUM *a"
81.Fa "BIGNUM *b"
82.Fa "const BIGNUM *m"
83.Fa "BN_CTX *ctx"
84.Fc
85.Ft int
86.Fo BN_mod_mul
87.Fa "BIGNUM *r"
88.Fa "BIGNUM *a"
89.Fa "BIGNUM *b"
90.Fa "const BIGNUM *m"
91.Fa "BN_CTX *ctx"
92.Fc
93.Ft int
94.Fo BN_mod_sqr
95.Fa "BIGNUM *r"
96.Fa "BIGNUM *a"
97.Fa "const BIGNUM *m"
98.Fa "BN_CTX *ctx"
99.Fc
100.Ft int
101.Fo BN_exp
102.Fa "BIGNUM *r"
103.Fa "BIGNUM *a"
104.Fa "BIGNUM *p"
105.Fa "BN_CTX *ctx"
106.Fc
107.Ft int
108.Fo BN_mod_exp
109.Fa "BIGNUM *r"
110.Fa "BIGNUM *a"
111.Fa "const BIGNUM *p"
112.Fa "const BIGNUM *m"
113.Fa "BN_CTX *ctx"
114.Fc
115.Ft int
116.Fo BN_gcd
117.Fa "BIGNUM *r"
118.Fa "BIGNUM *a"
119.Fa "BIGNUM *b"
120.Fa "BN_CTX *ctx"
121.Fc
122.Sh DESCRIPTION
123.Fn BN_add
124adds
125.Fa a
126and
127.Fa b
128and places the result in
129.Fa r
130.Pq Li r=a+b .
131.Fa r
132may be the same
133.Vt BIGNUM
134as
135.Fa a
136or
137.Fa b .
138.Pp
139.Fn BN_sub
140subtracts
141.Fa b
142from
143.Fa a
144and places the result in
145.Fa r
146.Pq Li r=a-b .
147.Pp
148.Fn BN_mul
149multiplies
150.Fa a
151and
152.Fa b
153and places the result in
154.Fa r
155.Pq Li r=a*b .
156.Fa r
157may be the same
158.Vt BIGNUM
159as
160.Fa a
161or
162.Fa b .
163For multiplication by powers of 2, use
164.Xr BN_lshift 3 .
165.Pp
166.Fn BN_sqr
167takes the square of
168.Fa a
169and places the result in
170.Fa r
171.Pq Li r=a^2 .
172.Fa r
173and
174.Fa a
175may be the same
176.Vt BIGNUM .
177This function is faster than
178.Fn BN_mul r a a .
179.Pp
180.Fn BN_div
181divides
182.Fa a
183by
184.Fa d
185and places the result in
186.Fa dv
187and the remainder in
188.Fa rem
189.Pq Li dv=a/d , rem=a%d .
190Either of
191.Fa dv
192and
193.Fa rem
194may be
195.Dv NULL ,
196in which case the respective value is not returned.
197The result is rounded towards zero; thus if
198.Fa a
199is negative, the remainder will be zero or negative.
200For division by powers of 2, use
201.Fn BN_rshift 3 .
202.Pp
203.Fn BN_mod
204corresponds to
205.Fn BN_div
206with
207.Fa dv
208set to
209.Dv NULL .
210.Pp
211.Fn BN_nnmod
212reduces
213.Fa a
214modulo
215.Fa m
216and places the non-negative remainder in
217.Fa r .
218.Pp
219.Fn BN_mod_add
220adds
221.Fa a
222to
223.Fa b
224modulo
225.Fa m
226and places the non-negative result in
227.Fa r .
228.Pp
229.Fn BN_mod_sub
230subtracts
231.Fa b
232from
233.Fa a
234modulo
235.Fa m
236and places the non-negative result in
237.Fa r .
238.Pp
239.Fn BN_mod_mul
240multiplies
241.Fa a
242by
243.Fa b
244and finds the non-negative remainder respective to modulus
245.Fa m
246.Pq Li r=(a*b)%m .
247.Fa r
248may be the same
249.Vt BIGNUM
250as
251.Fa a
252or
253.Fa b .
254For more efficient algorithms for repeated computations using the same
255modulus, see
256.Xr BN_mod_mul_montgomery 3
257and
258.Xr BN_mod_mul_reciprocal 3 .
259.Pp
260.Fn BN_mod_sqr
261takes the square of
262.Fa a
263modulo
264.Fa m
265and places the result in
266.Fa r .
267.Pp
268.Fn BN_exp
269raises
270.Fa a
271to the
272.Fa p Ns -th
273power and places the result in
274.Fa r
275.Pq Li r=a^p .
276This function is faster than repeated applications of
277.Fn BN_mul .
278.Pp
279.Fn BN_mod_exp
280computes
281.Fa a
282to the
283.Fa p Ns -th
284power modulo
285.Fa m
286.Pq Li r=(a^p)%m .
287This function uses less time and space than
288.Fn BN_exp .
289.Pp
290.Fn BN_gcd
291computes the greatest common divisor of
292.Fa a
293and
294.Fa b
295and places the result in
296.Fa r .
297.Fa r
298may be the same
299.Vt BIGNUM
300as
301.Fa a
302or
303.Fa b .
304.Pp
305For all functions,
306.Fa ctx
307is a previously allocated
308.Vt BN_CTX
309used for temporary variables; see
310.Xr BN_CTX_new 3 .
311.Pp
312Unless noted otherwise, the result
313.Vt BIGNUM
314must be different from the arguments.
315.Sh RETURN VALUES
316For all functions, 1 is returned for success, 0 on error.
317The return value should always be checked, for example:
318.Pp
319.Dl if (!BN_add(r,a,b)) goto err;
320.Pp
321The error codes can be obtained by
322.Xr ERR_get_error 3 .
323.Sh SEE ALSO
324.Xr bn 3 ,
325.Xr BN_add_word 3 ,
326.Xr BN_CTX_new 3 ,
327.Xr BN_set_bit 3 ,
328.Xr ERR_get_error 3
329.Sh HISTORY
330.Fn BN_add ,
331.Fn BN_sub ,
332.Fn BN_sqr ,
333.Fn BN_div ,
334.Fn BN_mod ,
335.Fn BN_mod_mul ,
336.Fn BN_mod_exp ,
337and
338.Fn BN_gcd
339are available in all versions of SSLeay and OpenSSL.
340The
341.Fa ctx
342argument to
343.Fn BN_mul
344was added in SSLeay 0.9.1b.
345.Fn BN_exp
346appeared in SSLeay 0.9.0.
347.Fn BN_nnmod ,
348.Fn BN_mod_add ,
349.Fn BN_mod_sub ,
350and
351.Fn BN_mod_sqr
352were added in OpenSSL 0.9.7.
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-12-09 08:03:39 +0000