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| 1 | .\" $OpenBSD: BN_kronecker.3,v 1.2 2022/11/15 17:55:00 schwarze Exp $ | ||
| 2 | .\" | ||
| 3 | .\" Copyright (c) 2022 Ingo Schwarze <schwarze@openbsd.org> | ||
| 4 | .\" | ||
| 5 | .\" Permission to use, copy, modify, and distribute this software for any | ||
| 6 | .\" purpose with or without fee is hereby granted, provided that the above | ||
| 7 | .\" copyright notice and this permission notice appear in all copies. | ||
| 8 | .\" | ||
| 9 | .\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES | ||
| 10 | .\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF | ||
| 11 | .\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR | ||
| 12 | .\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES | ||
| 13 | .\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN | ||
| 14 | .\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF | ||
| 15 | .\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. | ||
| 16 | .\" | ||
| 17 | .Dd $Mdocdate: November 15 2022 $ | ||
| 18 | .Dt BN_KRONECKER 3 | ||
| 19 | .Os | ||
| 20 | .Sh NAME | ||
| 21 | .Nm BN_kronecker | ||
| 22 | .Nd Kronecker symbol | ||
| 23 | .Sh SYNOPSIS | ||
| 24 | .In openssl/bn.h | ||
| 25 | .Ft int | ||
| 26 | .Fo BN_kronecker | ||
| 27 | .Fa "const BIGNUM *a" | ||
| 28 | .Fa "const BIGNUM *b" | ||
| 29 | .Fa "BN_CTX *ctx" | ||
| 30 | .Fc | ||
| 31 | .Sh DESCRIPTION | ||
| 32 | .Fn BN_kronecker | ||
| 33 | computes the Kronecker symbol | ||
| 34 | .Pq a | b , | ||
| 35 | which generalizes the Legendre and Jacobi symbols | ||
| 36 | for arbitrary integer numbers | ||
| 37 | .Fa b . | ||
| 38 | .Sh RETURN VALUES | ||
| 39 | .Fn BN_kronecker | ||
| 40 | returns \-1, 0, or 1 in case of success or \-2 on error. | ||
| 41 | .Sh SEE ALSO | ||
| 42 | .Xr BN_CTX_new 3 , | ||
| 43 | .Xr BN_gcd 3 , | ||
| 44 | .Xr BN_mod_sqrt 3 , | ||
| 45 | .Xr BN_new 3 | ||
| 46 | .Rs | ||
| 47 | .%A Henri Cohen | ||
| 48 | .%B A Course in Computational Algebraic Number Theory | ||
| 49 | .%I Springer | ||
| 50 | .%C Berlin | ||
| 51 | .%D 1993 | ||
| 52 | .%O Algorithm 1.4.10 | ||
| 53 | .Re | ||
| 54 | .Sh HISTORY | ||
| 55 | .Fn BN_kronecker | ||
| 56 | first appeared in OpenSSL 0.9.7 and has been available since | ||
| 57 | .Ox 3.2 . | ||