Karim Belabas on Thu, 19 Oct 2023 23:52:46 +0200


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Re: ECPP cerificate validation problem 

* Paul Underwood [2023-10-19 23:10]:
> Please see: https://www.mersenneforum.org/showthread.php?t=28940 about a problem with validation of certificates in your softwares,

Hi,

  I just read that thread and I disagree with frmky's post (2023-10-19, 17:55)
The claim is that vert rejects the certificate because q >= N and so we
(= pari) should as well.

But this q >= N assumption is irrelevant since the given data and checks
prove the primality of N assuming the primality of q. Whether q >= N holds
or not.

Granted, the logic of the proof is to produce a chain of prime numbers of
decreasing size to make sure it terminates (and q < N obviously
accomplishes this). But the proof terminates since you have a
certificate, all of whose steps are valid. It constitutes a valid
primality certificate and vcert is wrong to reject it.

Cheers,

    K.B.
-- 
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/