On Two Problems About Isogenies of Elliptic Curves Over Finite Fields

作     者：Lixia Luo Guanju Xiao Yingpu Deng Lixia Luo;Guanju Xiao;Yingpu Deng

作者机构：Key Laboratory of Mathematics MechanizationNCMISAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China. School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049P.R.China. 

出 版 物：《Communications in Mathematical Research》 (数学研究通讯（英文版）)

年 卷 期：2020年第36卷第4期

页      面：460-488页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Key Research and Development Project No.2018YFA0704705 

主　　题：Elliptic curve isogeny kernel ideal minimal degree 

摘      要：Isogenies occur throughout the theory of elliptic ***,the cryptographic protocols based on isogenies are considered as candidates of quantum-resistant cryptographic *** two elliptic curves E1,E2 defined over a finite field k with the same trace,there is a nonconstant isogeny b from E2 to E1 defined over *** study gives out the index of Homk(E1,E2)b as a nonzero left ideal in Endk(E2)and figures out the correspondence between isogenies and kernel *** addition,some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided.