Twisted jacobi intersections curves

Authors:
Rongquan Feng;Menglong Nie;Hongfeng Wu
Affiliations:
LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R China;LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R China;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P.R China
Venue:
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Year:
2010

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Abstract

In this paper, the twisted Jacobi intersections which contains Jacobi intersections as a special case is introduced We show that every elliptic curve over the prime field with three points of order 2 is isomorphic to a twisted Jacobi intersections curve Some fast explicit formulae for twisted Jacobi intersections curves in projective coordinates are presented These explicit formulae for addition and doubling are almost as fast as the Jacobi intersections In addition, the scalar multiplication can be more effective in twisted Jacobi intersections than in Jacobi intersections Moreover, we propose new addition formulae which are independent of parameters of curves and more effective in reality than the previous formulae in the literature.