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1.\" $OpenBSD: BN_generate_prime.3,v 1.25 2023/12/29 19:12:46 tb Exp $
2.\" full merge up to: OpenSSL f987a4dd Jun 27 10:12:08 2019 +0200
3.\"
4.\" This file is a derived work.
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21.\" The original file was written by Ulf Moeller <ulf@openssl.org>
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70.Dd $Mdocdate: December 29 2023 $
71.Dt BN_GENERATE_PRIME 3
72.Os
73.Sh NAME
74.Nm BN_is_prime_ex ,
75.Nm BN_is_prime_fasttest_ex ,
76.Nm BN_generate_prime_ex ,
77.Nm BN_GENCB_call ,
78.Nm BN_GENCB_new ,
79.Nm BN_GENCB_free ,
80.Nm BN_GENCB_set ,
81.Nm BN_GENCB_get_arg ,
82.Nm BN_GENCB_set_old
83.\" Nm BN_prime_checks_for_size is intentionally undocumented
84.\" because it should not be used outside of libcrypto.
85.Nd generate primes and test for primality
86.Sh SYNOPSIS
87.In openssl/bn.h
88.Ft int
89.Fo BN_is_prime_ex
90.Fa "const BIGNUM *a"
91.Fa "int nchecks"
92.Fa "BN_CTX *ctx"
93.Fa "BN_GENCB *cb"
94.Fc
95.Ft int
96.Fo BN_is_prime_fasttest_ex
97.Fa "const BIGNUM *a"
98.Fa "int nchecks"
99.Fa "BN_CTX *ctx"
100.Fa "int do_trial_division"
101.Fa "BN_GENCB *cb"
102.Fc
103.Ft int
104.Fo BN_generate_prime_ex
105.Fa "BIGNUM *ret"
106.Fa "int bits"
107.Fa "int safe"
108.Fa "const BIGNUM *modulus"
109.Fa "const BIGNUM *remainder"
110.Fa "BN_GENCB *cb"
111.Fc
112.Ft int
113.Fo BN_GENCB_call
114.Fa "BN_GENCB *cb"
115.Fa "int state_code"
116.Fa "int serial_number"
117.Fc
118.Ft BN_GENCB *
119.Fn BN_GENCB_new void
120.Ft void
121.Fo BN_GENCB_free
122.Fa "BN_GENCB *cb"
123.Fc
124.Ft void
125.Fo BN_GENCB_set
126.Fa "BN_GENCB *cb"
127.Fa "int (*cb_fp)(int, int, BN_GENCB *)"
128.Fa "void *cb_arg"
129.Fc
130.Ft void *
131.Fo BN_GENCB_get_arg
132.Fa "BN_GENCB *cb"
133.Fc
134.Pp
135Deprecated:
136.Pp
137.Ft void
138.Fo BN_GENCB_set_old
139.Fa "BN_GENCB *cb"
140.Fa "void (*cb_fp)(int, int, void *)"
141.Fa "void *cb_arg"
142.Fc
143.Sh DESCRIPTION
144.Fn BN_is_prime_ex
145and
146.Fn BN_is_prime_fasttest_ex
147test whether the number
148.Fa a
149is prime.
150In LibreSSL, both functions behave identically
151and use the Baillie-Pomerance-Selfridge-Wagstaff algorithm
152combined with
153.Fa checks
154Miller-Rabin rounds.
155The
156.Fa do_trial_division
157argument is ignored.
158.Pp
159It is unknown whether any composite number exists that the
160Baillie-PSW algorithm misclassifies as a prime.
161Some suspect that there may be infinitely many such numbers,
162but not a single one is currently known.
163It is known that no such number exists below 2\(ha64.
164.Pp
165In order to reduce the likelihood of a composite number
166passing the primality tests
167.Fn BN_is_prime_fasttest_ex
168and
169.Fn BN_is_prime_ex ,
170a number of rounds of the probabilistic Miller-Rabin test is performed.
171If
172.Fa checks
173is positive, it is used as the number of rounds;
174if it is zero or the special value
175.Dv BN_prime_checks ,
176a suitable number of rounds is calculated from the bit length of
177.Fa a .
178.Pp
179If
180.Dv NULL
181is passed for the
182.Fa ctx
183argument, these function allocate a
184.Vt BN_CTX
185object internally when they need one and free it before returning.
186Alternatively, to save the overhead of allocating and freeing
187that object for each call, the caller can pre-allocate a
188.Vt BN_CTX
189object and pass it in the
190.Fa ctx
191argument.
192.Pp
193.Fn BN_generate_prime_ex
194generates a pseudo-random prime number of at least bit length
195.Fa bits
196and places it in
197.Fa ret .
198Primality of
199.Fa ret
200is tested internally using
201.Fn BN_is_prime_ex .
202Consequently, for
203.Fa bits
204larger than 64, it is theoretically possible
205that this function might place a composite number into
206.Fa ret ;
207the probability of such an event is unknown but very small.
208.Pp
209The prime may have to fulfill additional requirements for use in
210Diffie-Hellman key exchange:
211.Bl -bullet
212.It
213If
214.Fa modulus
215is not
216.Dv NULL ,
217a prime is generated that fulfills the condition
218.Fa ret No % Fa modulus No = Fa remainder .
219If the
220.Fa remainder
221argument is
222.Dv NULL ,
2231 is used as the desired remainder.
224.It
225If the
226.Fa safe
227argument is non-zero, a safe prime is generated, that is,
228.Po Fa ret No \- 1 Pc Ns /2
229is also prime.
230.El
231.Pp
232If
233.Fa cb
234is not
235.Dv NULL ,
236it is used as follows:
237.Bl -bullet
238.It
239.Fn BN_GENCB_call cb 0 serial_number
240is called after generating a potential prime number.
241.It
242The
243.Fa state_code
244of 1 is reserved for callbacks during primality testing,
245but LibreSSL performs no such callbacks.
246.It
247When
248.Fa safe
249is non-zero and a safe prime has been found,
250.Fn BN_GENCB_call cb 2 serial_number
251is called.
252.It
253The callers of
254.Fn BN_generate_prime_ex
255may call
256.Fn BN_GENCB_call
257with other values as described in their respective manual pages; see
258.Sx SEE ALSO .
259.El
260.Pp
261In all cases, the
262.Fa serial_number
263is the number of candidates that have already been discarded
264for not being prime; that is,
265.Fa serial_number
266is 0 for the first candidate
267and then incremented whenever a new candidate is generated.
268.Pp
269.Fn BN_GENCB_call
270calls the callback function held in
271.Fa cb
272and passes the
273.Fa state_code
274and the
275.Fa serial_number
276as arguments.
277If
278.Fa cb
279is
280.Dv NULL
281or does not contain a callback function, no action occurs.
282.Pp
283.Fn BN_GENCB_new
284allocates a new
285.Vt BN_GENCB
286object.
287.Pp
288.Fn BN_GENCB_free
289frees
290.Fa cb .
291If
292.Fa cb
293is
294.Dv NULL ,
295no action occurs.
296.Pp
297.Fn BN_GENCB_set
298initialises
299.Fa cb
300to use the callback function pointer
301.Fa cb_fp
302and the additional callback argument
303.Fa cb_arg .
304.Pp
305The deprecated function
306.Fn BN_GENCB_set_old
307initialises
308.Fa cb
309to use the old-style callback function pointer
310.Fa cb_fp
311and the additional callback argument
312.Fa cb_arg .
313.Sh RETURN VALUES
314.Fn BN_is_prime_ex
315and
316.Fn BN_is_prime_fasttest_ex
317return 0 if the number is composite, 1 if it is prime with a very small
318error probability, or \-1 on error.
319.Pp
320.Fn BN_generate_prime_ex
321returns 1 on success or 0 on error.
322.Pp
323.Fn BN_GENCB_call
324returns 1 on success, including when
325.Fa cb
326is
327.Dv NULL
328or does not contain a callback function,
329or 0 on error.
330.Pp
331.Fn BN_GENCB_new
332returns a pointer to the newly allocated
333.Vt BN_GENCB
334object or
335.Dv NULL
336if memory allocation fails.
337.Pp
338The callback functions pointed to by the
339.Fa cb_fp
340arguments are supposed to return 1 on success or 0 on error.
341.Pp
342.Fn BN_GENCB_get_arg
343returns the
344.Fa cb_arg
345pointer that was previously stored in
346.Fa cb
347using
348.Fn BN_GENCB_set
349or
350.Fn BN_GENCB_set_old .
351.Pp
352In some cases, error codes can be obtained by
353.Xr ERR_get_error 3 .
354.Sh SEE ALSO
355.Xr BN_new 3 ,
356.Xr DH_generate_parameters 3 ,
357.Xr DSA_generate_parameters_ex 3 ,
358.Xr RSA_generate_key 3
359.Sh HISTORY
360.Fn BN_generate_prime_ex ,
361.Fn BN_is_prime_ex ,
362.Fn BN_is_prime_fasttest_ex ,
363.Fn BN_GENCB_call ,
364.Fn BN_GENCB_set_old ,
365and
366.Fn BN_GENCB_set
367first appeared in OpenSSL 0.9.8 and have been available since
368.Ox 4.5 .
369.Pp
370.Fn BN_GENCB_new ,
371.Fn BN_GENCB_free ,
372and
373.Fn BN_GENCB_get_arg
374first appeared in OpenSSL 1.1.0 and have been available since
375.Ox 6.3 .
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-12-23 13:31:50 +0000