Journal of Cryptology
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
On the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Elliptic curves in cryptography
Elliptic curves in cryptography
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
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory 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
Two Topics in Hyperelliptic Cryptography
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields
Journal of Cryptology
Efficient computations of the Tate pairing for the large MOV degrees
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors
WISA'04 Proceedings of the 5th international conference on Information Security Applications
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
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
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing calculation on supersingular genus 2 curves
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
On the efficiency and security of pairing-based protocols in the type 1 and type 4 settings
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
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
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Pairings on elliptic curves recently obtained a lot of attention not only as a means to attack curve based cryptography but also as a building block for cryptosystems with special properties like short signatures or identity based encryption. In this paper we consider the Tate pairing on hyperelliptic curves of genus g. We give mathematically sound arguments why it is possible to use particular representatives of the involved residue classes in the second argument that allow to compute the pairing much faster, where the speed-up grows with the size of g. Since the curve arithmetic takes about the same time for small g and constant group size, this implies that g1 offers advantages for implementations. We give two examples of how to apply the modified setting in pairing based protocols such that all parties profit from the idea. We stress that our results apply also to non-supersingular curves, e. g. those constructed by complex multiplication, and do not need distortion maps. They are also applicable if the co-factor is nontrivial.