Extension of elliptic curves on Krasner hyperfields
Vahid Vahedi, Morteza Jafarpour, Hossien Aghabozorgi, Irina Cristea · Communications in Algebra · 2019
The aim of the article is to initiate a new study in the framework of algebraic hyperfields, with an applicative impact in cryptography. First we define the notions of generalized Weierstrass equation and elliptic hypercurve on Krasner hyperfields, as a generalization of the notion of elliptic curve on fields. Then we investigate properties of the hypergroups derived from elliptic hypercurves and of the associated Hv-groups. Finally, we present a class of canonical hypergroups, which can be used as an alphabet in a special cryptographic system.