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
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
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
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and ηT pairing. In this paper we discuss how to enhance the speed of the final exponentiation of the ηT pairing in the extension field F36n. Indeed, we propose some efficient algorithms using the torus T2(F33n that can efficiently compute an inversion and a powering by 3n + 1. Consequently, the total processing cost of computing the ηT pairing can be reduced by 16% for n = 97.