Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Twisted Edwards Curves Revisited
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
The Jacobi model of an elliptic curve and side-channel analysis
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
| Hi-index | 0.00 |
We provide several results on some families of twisted Jacobi quartics. We give new addition formulæ for two models of twisted Jacobi quartic elliptic curves, which represent respectively 1/6 and 2/3 of all elliptic curves, with respective costs 7M+3S+Da and 8M + 3 S+Da . These formulæ allow addition and doubling of points, except for points differing by a point of order two. Furthermore, we give an intrinsic characterization of elliptic curves represented by the classical Jacobi quartic, by the action of the Frobenius endomorphism on the 4-torsion subgroup. This allows us to compute the exact proportion of elliptic curves representable by various models (the three families of Jacobi quartics, plus Edwards and Huff curves) from statistics on this Frobenius action.