Year: 2020
Author: Lixia Luo, Guanju Xiao, Yingpu Deng
Communications in Mathematical Research , Vol. 36 (2020), Iss. 4 : pp. 460–488
Abstract
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 ideals. In addition, some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0071
Communications in Mathematical Research , Vol. 36 (2020), Iss. 4 : pp. 460–488
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Elliptic curve isogeny kernel ideal minimal degree.