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
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
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
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
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Efficient Algorithms for Tate Pairing
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Introduction to Identity-Based Encryption (Information Security and Privacy Series)
Introduction to Identity-Based Encryption (Information Security and Privacy Series)
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
Refinements of Miller's algorithm for computing the Weil/Tate pairing
Journal of Algorithms
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
IEEE Transactions on Information Theory
A variant of Miller's formula and algorithm
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Information Theory
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The calculation of pairing plays a key role in pairing-based cryptography. Usually, the calculation is based on Miller's algorithm. However, most of the optimisations of Miller's algorithm are of serial structure. In this paper, we propose a method to parallel compute Tate pairing efficiently. We split the divisor in Miller's algorithm into three parts. Then we use efficiently computation endomorphism and precomputation method to reduce computational cost. Compared with general version of Miller's algorithm in serial structure, our method has a gain of around 50.0%.