The Isomorphism Of Twisted Jacobi Intersection Curves Over Prime Fields

Elliptic curve cryptosystem has a wide application in fields as e-commerce,e-government,computer network security and so on. Theoretical research of which isconcerned in long time.In this paper,we present the following results that based on Twisted Jacobi Inter-section (TJI for short) curves and Jacobi Intersection (JI for short) curves:(1)When p≡1(mod 4),there not exist supersingular elliptic curve over theprime fields Fp;when p≡3(mod 4),there exist supersingular elliptic curves over theprime fields Fp,and the relation of supersingular elliptic curve and its parameters isgiven.(2)The isomorphism transform between two arbitrary TJI curves over the fieldsFˉp.(3)The necessary and sufficient conditions of isomorphism of a TJI curve and aJI curve over the prime fields Fp.(4) The number of isomorphism classes of TJI curves and JI curves.when p≡3(mod 4),the number of isomorphism classes of JI curves is as same asTJI curves's; when p≡1(mod 4),the number of isomorphism classes of JI curvesis less than TJI curves's.Although it is difficult to obtain the number of isomorphismclasses of JI curves,it is solved in this paper.