Abstract—Pairings on hyperelliptic curves have been applied to many cryptographic schemes, and it is important to exploit methods that increase the speed of various pairings and their curves. Additionally, multiple pairings should be performed efficiently in some cryptographic application such as attribute-based encryption or functional encryption. We propose an efficient extension field construction method that defines a curve and its ηT pairing. We also implemented the parallel arithmetic on extension fields and multiple ηT pairings in parallel and reported experimental timing results. We achieved timing of 12.7ms and 52.0ms per pairing when computed 1248 pairings by using GPU Tesla K20c. We took the extension degree of base field m = 487 which is greater than the parameter m = 367, 439 that was appropriate for the ηT pairing at the 128-bit security level. By normalization of experimental result, we achieved a certain level of speeding up of the ηT pairing compared to the state-of-the-art CPU implementation. In addition, we achieved scalability with the extension degree of base field in our parallel implementation by performing Karatsuba multiplications between multiple elements of extension field in parallel.

Index Terms—ƞT pairing, multiple pairings, GPU implementation, CUDA, karatsuba method, DLP in finite field of small characteristic, security level.

M. Ishii is with Nara Institute of Science and Technology, Nara, Japan (e-mail: masahiro-i@is.naist.jp).
A. Inomata is with Initiative Center, Nara Institute of Science and Technology, Nara, Japan (e-mail: atsuo@itc.naist.jp).
K. Fujikawa is with Information Initiative Center, Nara Institute of Science and Technology, Nara, Japan (e-mail: fujikawa@itc.naist.jp).

Cite:M. Ishii, A. Inomata, and K. Fujikawa, "Parallel GPU Implementation of ƞT Pairing over Fields of Characteristic Two," International Journal of Computer and Communication Engineering vol. 3, no. 3, pp. 193-198, 2014.