Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Abelian varieties with prescribed embedding degree
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
Zeta function and cryptographic exponent of supersingular curves of genus 2
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Deterministic encoding and hashing to odd hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
A new method for constructing pairing-friendly abelian surfaces
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields
Designs, Codes and Cryptography
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An explicit construction of pairing-friendly hyperelliptic curves with ordinary Jacobians was firstly given by D. Freeman. In this paper, we give other explicit constructions of pairing-friendly hyperelliptic curves with ordinary Jacobians based on the closed formulae for the order of the Jacobian of a hyperelliptic curve of type y2= x5+ ax. We present two methods in this paper. One is an analogue of the Cocks-Pinch method and the other is a cyclotomic method. By using these methods, we construct a pairing-friendly hyperelliptic curve y2= x5+ axover a finite prime field ${\mathbb F}_p$ whose Jacobian is ordinary and simple over ${\mathbb F}_p$ with a prescribed embedding degree. Moreover, the analogue of the Cocks-Pinch produces curves with ρ≈ 4 and the cyclotomic method produces curves with 3 ≤ ρ≤ 4.