Elliptic periods and primality proving
Jean-Marc Couveignes, Tony Ezome, Reynald Lercier
TL;DR
This paper introduces a novel elliptic curve-based approach to primality testing, extending the AKS criterion to elliptic periods for potentially more efficient primality proofs.
Contribution
It develops the concept of elliptic periods modulo n and formulates an elliptic version of the AKS primality test, providing a new method for primality proving.
Findings
Defined the ring of elliptic periods modulo n
Formulated an elliptic AKS primality criterion
Potential for more efficient primality testing
Abstract
We define the ring of elliptic periods modulo an integer and give an elliptic version of the AKS primality criterion.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Coding theory and cryptography · Analytic Number Theory Research