Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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
A survey of fast exponentiation methods
Journal of Algorithms
Computing discrete logarithms in real quadratic congruence function fields of large genus
Mathematics of Computation
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Genus Two Hyperelliptic Curve Coprocessor
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
On the distribution of the coefficients of normal forms for Frobenius expansions
Designs, Codes and Cryptography
Efficient doubling on genus two curves over binary fields
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Efficient doubling on genus 3 curves over binary fields
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
Sublinear scalar multiplication on hyperelliptic koblitz curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Finite Fields and Their Applications
| Hi-index | 0.00 |
Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations. In this paper, we generalize their ideas to hyperelliptic curves of genus 2. We consider the following two hyperelliptic curves Cα : v2 + uv = u5 + αu2 + 1 defined over F2 with α = 0, 1, and show how to speed up the arithmetic in the Jacobian JCα(F2n) by making use of the Frobenius automorphism. With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian. If we allow 6 precomputations, we are even able to speed up by a factor of 7.