A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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 Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Ate Pairing on Hyperelliptic Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
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
Pairing calculation on supersingular genus 2 curves
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Fast bilinear maps from the tate-lichtenbaum pairing on hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
IEEE Transactions on Information Theory
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Eta pairing computation on general divisors over hyperelliptic curves y2 = x7 - x ± 1
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Faster pairing computation on genus 2 hyperelliptic curves
Information Processing Letters
Hi-index | 0.00 |
Pairings on the Jacobians of (hyper-)elliptic curves have received considerable attention not only as a tool to attack curve based cryptosystems but also as a building block for constructing cryptographic schemes with new and novel properties. Motivated by the work of Scott, we investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of non-supersingular genus 2 hyperelliptic curves over prime fields. Our findings lead to new variants of Miller's algorithm in which the length of the main loop can be up to 4 times shorter than that of the original Miller's algorithm in the best case. We also implement the calculation of the Tate pairing on both a supersingular and a non-supersingular genus 2 curve with the same embedding degree of k= 4. Combining the new algorithm with known optimization techniques, we show that pairing computations on non-supersingular genus 2 curves over prime fields use up to 55.8% fewer field operations and run about 10% faster than supersingular genus 2 curves for the same security level.