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On Two Problems About Isogenies of Elliptic Curves Over Finite Fields
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作者 Lixia Luo Guanju Xiao Yingpu Deng 《Communications in Mathematical Research》 CSCD 2020年第4期460-488,共29页
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 E1,E... 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 E1,E2 defined over a finite field k with the same trace,there is a nonconstant isogeny b from E2 to E1 defined over k.This 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 ideals.In addition,some results about the non-trivial minimal degree of isogenies between two elliptic curves are also provided. 展开更多
关键词 Elliptic curve isogeny kernel ideal minimal degree
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On fixity of arc-transitive graphs
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作者 Florian Lehner Primoz Potocnik Pablo Spiga 《Science China Mathematics》 SCIE CSCD 2021年第12期2603-2610,共8页
The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a pe... The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a permutation group on the vertex-set of the graph.We prove in this paper that the relative xity of connected 2-arc-transitive graphs of a xed valence tends to 0 as the number of vertices grows to in nity.We prove the same result for the class of arc-transitive graphs of a xed prime valence,and more generally,for any class of arc-transitive locally-L graphs,where L is a xed quasiprimitive graph-restrictive permutation group. 展开更多
关键词 permutation group xity minimal degree GRAPH automorphism group VERTEX-TRANSITIVE arc-transitive xed points
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