Talk:Primality certificate
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Atkin–Goldwasser–Kilian–Morain certificates
[edit]The current version of this section states: "\mathbb{Z}_n is only a field if n is prime" which is false (see finite fields).
Hence I feel that the exposition of Atkin–Goldwasser–Kilian–Morain certificates needs to be improved.
The certificates in the original Goldwasser-Killian paper weren't always valid, hence the need for "Atkin–Goldwasser–Kilian–Morain" certificates.
However, it is possible to make a very minor change to Goldwasser-Killian which always produces a valid certificate, which would be nice to include in the article as well. "An Overview of Elliptic Curve Primality Proving" (2011) at http://www.stanford.edu/class/cs259c/finalpapers/primalityproving.pdf by Frank Li contains a good exposition of that, for example.
I'm not sure whether I'm going to undertake these improvements myself, so if anyone is so inclined, please do.