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On Two Problems About Isogenies of Elliptic Curves Over Finite Fields
2020
Communications in Mathematical Research
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