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On Two Problems About Isogenies of Elliptic Curves Over Finite Fields

2020
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Communications in Mathematical Research
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Isogenies occur throughout the theory of elliptic curves. Recently, the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic protocols. Given two elliptic curves E 1 ,E 2 defined over a finite field k with the same trace, there is a nonconstant isogeny β from E 2 to E 1 defined over k. This study gives out the index of Hom k (E 1 ,E 2 )β as a nonzero left ideal in End k (E 2 ) and figures out the correspondence between isogenies and kernel

doi:10.4208/cmr.2020-0071
fatcat:qqurztll5zda5bhou4qldqyfty