@Article{CMR-36-460,
author = {Luo , LixiaXiao , Guanju and Deng , Yingpu},
title = {On Two Problems About Isogenies of Elliptic Curves over Finite Fields},
journal = {Communications in Mathematical Research },
year = {2020},
volume = {36},
number = {4},
pages = {460--488},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2020-0071},
url = {http://global-sci.org/intro/article_detail/cmr/18362.html}
}