Derived Hyperstructures from Hyperconics

Vahid Vahedi, Morteza Jafarpour, Sarka Hoskova-Mayerova, Hossein Aghabozorgi, Violeta Leoreanu-Fotea and Svajone Bekesiene
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Vahid Vahedi: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Morteza Jafarpour: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Sarka Hoskova-Mayerova: Department of Mathematics and Physics, University of Defence in Brno, Kounicova 65, 662 10 Brno, Czech Republic
Hossein Aghabozorgi: Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan 7718897111, Iran
Violeta Leoreanu-Fotea: Department of Mathematics, Al. I. Cuza University, 6600 Iashi, Romania
Svajone Bekesiene: Departament of Defence Technologies, The General Jonas Žemaitis Military Academy of Lithuania, Silo g.5, 10322 Vilnius, Lithuania

Mathematics, 2020, vol. 8, issue 3, 1-15

Abstract: In this paper, we introduce generalized quadratic forms and hyperconics over quotient hyperfields as a generalization of the notion of conics on fields. Conic curves utilized in cryptosystems; in fact the public key cryptosystem is based on the digital signature schemes (DLP) in conic curve groups. We associate some hyperoperations to hyperconics and investigate their properties. At the end, a collection of canonical hypergroups connected to hyperconics is proposed.

Keywords: hypergroup; hyperring; hyperfield; (hyper)conics; quadratic forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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