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Math::Prime::Util::PriUsertContributed PMath::Prime::Util::PrimalityProving(3)

NAME
       Math::Prime::Util::PrimalityProving - Primality proofs and certificates

VERSION
       Version 0.73

SYNOPSIS
DESCRIPTION
       Routines	to support primality proofs and	certificate verification.

FUNCTIONS
   primality_proof_lucas
       Given a positive	number "n" as input, performs a	full factorization of
       "n-1", then attempts a Lucas test on the	result.	 A Pratt-style
       certificate is returned.	 Note that if the input	is composite, this
       will take a very	long time to return.

   primality_proof_bls75
       Given a positive	number "n" as input, performs a	partial	factorization
       of "n-1", then attempts a proof using theorem 5 of Brillhart, Lehmer,
       and Selfridge's 1975 paper.  This can take a long time to return	if
       given a composite, though it should not be anywhere near	as long	as the
       Lucas test.

   convert_array_cert_to_string
       Takes as	input a	Perl structure certificate, used by Math::Prime::Util
       from version 0.26 through 0.29, and converts it to a multi-line text
       certificate starting with "[MPU - Primality Certificate]".  This	is the
       new format produced and processed by Math::Prime::Util,
       Math::Prime::Util::GMP, and associated tools.

   verify_cert
       Takes a MPU primality certificate and verifies that it does prove the
       primality of the	number it represents (the N after the "Proof for:"
       line).  For backwards compatibility, if given an	old-style Perl
       structure, it will be converted then verified.

       The return value	will be	0 (failed to verify) or	1 (verified).  A
       result of 0 does	not indicate the number	is composite; it only
       indicates the proof given is not	sufficient.

       If the certificate is malformed,	the routine will carp a	warning	in
       addition	to returning 0.	 If the	"verbose" option is set	(see
       "prime_set_config") then	if the validation fails, the reason for	the
       failure is printed in addition to returning 0.  If the "verbose"	option
       is set to 2 or higher, then a message indicating	success	and the
       certificate type	is also	printed.

       A later release may add support for Primo
       <http://www.ellipsa.eu/public/primo/primo.html> certificates, as	all
       the method verifications	are coded.

SEE ALSO
       Math::Prime::Util

AUTHORS
       Dana Jacobsen <dana@acm.org>

COPYRIGHT
       Copyright 2012-2013 by Dana Jacobsen <dana@acm.org>

       This program is free software; you can redistribute it and/or modify it
       under the same terms as Perl itself.

perl v5.32.1			  2018-1Math::Prime::Util::PrimalityProving(3)

NAME | VERSION | SYNOPSIS | DESCRIPTION | FUNCTIONS | SEE ALSO | AUTHORS | COPYRIGHT

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