James Wanless on Wed, 14 Feb 2018 22:45:26 +0100


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Re: New ECPP interface


All coolness... slight request (if you deem it appropriate too)
Could we have some sort of option to retain a pure 100% ecpp certificate, even once P-1 capability is added? [which I recognise will in general speed up certification]
J
PS Loving the new pthread exe on my 4-thread iMac...

On 14 Feb 2018, at 21:36, Karim Belabas wrote:

* Bill Allombert [2018-02-14 22:04]:
[...]
primecert(N,1): return P-1 certificate (old isprime(N,1))

More precisely, old isprime(P,1) *without* allowing calls to APRCL,
which basically declared a "tough" integer to be prime without
providing a certificate. Now that we have ECPP and decent general purpose
primality certificates (which P-1 can't provide because it must
factor large integers), it no longer made sense.

As a result, both primecert(N,1) and new isprime(N,1) are likely to be
much slower than the old isprime(N,1) unless all primes p occurring in
the certificate are such that p-1 is easy to factor. On the other hand
it now always produces a full certificate (without declaring an integer
to be prime "because our APRCL implementation said so").

Cheers,

   K.B.

P.S. Of course, except for testing/pedagogical purposes, one should just
use the default primecert(N). Which is currently slow in the rare
cases where primecert(N,1) is fast because our ECPP doesn't support N-1
certificates yet, but this won't last.

--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation http://www.math.u-bordeaux.fr/ ~kbelabas/ F-33405 Talence (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]
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