Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Algebraic aspects of cryptography
Algebraic aspects of cryptography
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Theoretical Computer Science - Special issue: cryptography
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Designs, Codes and Cryptography
Speeding up the Arithmetic on Koblitz Curves of Genus Two
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
An algorithm for solving the discrete log problem on hyperelliptic curves
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Skew-Frobenius Maps on Hyperelliptic Curves
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Finite Fields and Their Applications
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In [8] Koblitz suggested to make use of a Frobenius expansion to speed up the scalar multiplications in the Jacobians of hyperelliptic curves over the characteristic 2 field. Recently, G眉nther et. al.[6] have modified Koblitz's Frobenius expansion method and applied it to the Koblitz curves of genus 2 over F2 to speed up the scalar multiplication. In this paper, we show that the method given in [6] can be extended to the case when the hyperelliptic curves are defined over the finite field of any characteristic. For cryptographic purposes, we restrict our interest only to those with genus 2, 3, 4. We give a theoretical efficiency of our method by comparing to the double-and-add method over the Jacobians. As a result, with some reference tables we can reduce the cost of double-and-add method to nearly 41%.