Advances in Applied Mathematics
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic Curves: Number Theory and Cryptography
Elliptic Curves: Number Theory and Cryptography
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Hi-index | 5.23 |
In this paper, the twisted Jacobi intersections curve which contains Jacobi intersections curve as a special case is introduced. We show that every elliptic curve over a field of odd characteristic with three points of order 2 is isomorphic to a twisted Jacobi intersections curve. The isomorphism classes of twisted Jacobi intersections curves over finite fields are enumerated. 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. Moreover, we propose new addition formulae which are independent of parameters of curves and are more effective in reality than the previous formulae in the literature. In addition, an example shows that the scalar multiplication can be more effective in twisted Jacobi intersections than in Jacobi intersections.