An efficient implementation of Tate and Ate pairings

초록

Most implementations of pairing-based cryptography are using pairing-friendly curves with an embedding degree k ≤ 12. They have security levels of up to 128 bits. In this paper, we consider a family of pairing-friendly curves with embedding degree k = 24, which have an enhanced security level of 192 bits. We also describe an efficient implementation of Tate and Ate pairings using field arithmetic in Fq24; this includes a careful selection of the parameters with small hamming weight and a novel approach to final exponentiation, which reduces the number of computations required. When comparing with the latest implementation available in the research community, ours is 15% faster due to both our selection of efficient elliptic curve parameters and faster multiplication on Fq24. Therefore, it can significantly contribute to most contemporary identity-based or attributed-based encryption or signature schemes whose basic and essential operations are based on paring, known as one of the most time-consuming operations.

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