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
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Overview of Elliptic Curve Cryptography
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
An Identity-Based Signature from Gap Diffie-Hellman Groups
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
On the performance of hyperelliptic cryptosystems
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient tate pairing computation for elliptic curves over binary fields
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
IEEE Transactions on Information Theory
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Hi-index | 0.00 |
Recent developments on the Tate or Eta pairing computation over hyperelliptic curves by Duursma-Lee and Barreto et al. have focused on degenerate divisors. We present two efficient methods that work for general divisors to compute the Eta paring over divisor class groups of the hyperelliptic curves H/F7n : y2 = x7 - x ± 1 of genus 3. The first method generalizes the method of Barreto et al. so that it holds for general divisors, and we call it the pointwise method. For the second method, we take a novel approach using resultant. We focus on the case that two divisors of the pairing have supporting points in H/F73n, not in H/F7n. Our analysis shows that the resultant method is faster than the pointwise method, and our implementation result supports the theoretical analysis. In addition to the fact that the two methods work for general divisors, they also provide very explicit algorithms.