Twisted Jacobi Intersections Curves

  • Rongquan Feng
  • Menglong Nie
  • Hongfeng Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6108)


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.


elliptic curves Jacobi intersections twisted Jacobi intersections scalar multiplication cryptography 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rongquan Feng
    • 1
  • Menglong Nie
    • 1
  • Hongfeng Wu
    • 2
  1. 1.LMAM, School of Mathematical SciencesPeking UniversityBeijingP.R. China
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingP.R. China

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