A remark concerning m-divisibility and 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
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
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
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
Proceedings of the 14th ACM conference on Computer and communications security
Computing pairings using x-coordinates only
Designs, Codes and Cryptography
Another elliptic curve model for faster pairing computation
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Cryptographic pairings based on elliptic nets
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
The tate-lichtenbaum pairing on a hyperelliptic curve via hyperelliptic nets
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from Zn to a ring that satisfy a certain recurrence relation. We explain how an elliptic net is associated to an elliptic curve and reflects its group structure. Then we give a formula for the Tate pairing in terms of values of the net. Using the recurrence relation we can calculate these values in linear time. Computing the Tate pairing is the bottleneck to efficient pairing-based cryptography. The new algorithm has time complexity comparable to Miller's algorithm, and should yield to further optimisation.