Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Journal of Cryptology
Speeding up the Arithmetic on Koblitz Curves of Genus Two
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
A Family of Jacobians Suitable for Discrete Log Cryptosystems
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Counting Points on Hyperelliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Genus Two Hyperelliptic Curve Coprocessor
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
Inversion-Free Arithmetic on Genus 3 Hyperelliptic Curves and Its Implementations
ITCC '05 Proceedings of the International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume I - Volume 01
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Hyperelliptic curve coprocessors on a FPGA
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Hi-index | 0.00 |
The most important and expensive operation in a hyperelliptic curve cryptosystem (HECC) is the scalar multiplication by an integer k, i.e., computing an integer k times a divisor D on the Jacobian. Using some recoding algorithms for the scalar, we can reduce the number of divisor class additions during the process of computing the scalar multiplication. On the other side, the divisor doublings will stay the same for all kinds of scalar multiplication algorithms. In this paper we accelerate the divisor doublings for genus 3 HECC over binary fields by using special types of curves. Depending on the degree of h, our explicit formulae only require 1I + 11M + 11S, 1I + 13M + 13S, 1I + 20M + 12S and 1I + 26M + 11S for divisor doublings in the best case, respectively. Especially, for the case of deg h = 1, our explicit formula improve the recent result in [GKP04] significantly by saving 31M at the cost of extra 7S. In addition, we discuss some cases which are not included in [GKP04]. By constructing birational transformation of variables, we derive explicit doubling formulae for special types of equations of the curve. For each type of curve, we analyze how many field operations are needed. So far no attack on any of the all curves suggested in this paper is known, even though some cases are very special. Our results allow to choose curves from a large variety which have extremely fast doubling needing only one third the time of an addition in the best case. Furthermore, an actual implementation of the new formulae on a Pentium-M processor shows their practical relevance.