Extension of elliptic curves on Krasner hyperfields. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Vahedi, Vahid; Jafarpour, Morteza; Aghabozorgi, Hossien; Cristea, Irina
• Is Part Of: Communications in algebra. Volume 47:Issue 11(2019)
• Page Start: 4806
• Page End: 4823
• Publication Date: 2019-11-02
• Subjects: Hypergroup -- hyperring -- hyperfield -- elliptic (hyper)curve -- generalized Weierstrass equation -- cryptography; 20N20 -- 14H52; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2019.1596279
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: 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.