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
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Short Signatures from the Weil Pairing
Journal of Cryptology
Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three
IEEE Transactions on Computers
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
A Reconfigurable Processor for the Cryptographic nT Pairing in Characteristic 3
ITNG '07 Proceedings of the International Conference on Information Technology
An Algorithm for the nt Pairing Calculation in Characteristic Three and its Hardware Implementation
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Some efficient algorithms for the final exponentiation of ηT pairing
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Efficient implementation of pairing on BREW mobile phones
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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The ηT pairing on supersingular is one of the most efficient algorithms for computing the bilinear pairing [3]. The ηT pairing defined over finite field F3n has embedding degree 6, so that it is particularly efficient for higher security with large extension degree n. Note that the explicit algorithm over F3n in [3] is designed just for n = 1 (mod 12), and it is relatively complicated to construct an explicit algorithm for n ≢ 1 (mod 12). It is better that we can select many n's to implement the ηT pairing, since n corresponds to security level of the ηT pairing. In this paper we construct an explicit algorithm for computing the ηT pairing with arbitrary extension degree n. However, the algorithm should contain many branch conditions depending on n and the curve parameters, that is undesirable for implementers of the ηT pairing. This paper then proposes the universal ηT pairing (ηT pairing), which satisfies the bilinearity of pairing (compatible with Tate pairing) without any branches in the program, and is as efficient as the original one. Therefore the proposed universal ηT pairing is suitable for the implementation of various extension degrees n with higher security.