Abstract
Eta pairing over supersingular elliptic curves is widely used in designing many cryptographic protocols. Because of efficiency considerations, curves over finite fields of small characteristics are preferred. In this paper, we report several of our implementations of eta pairing over finite fields of characteristics two and three. We exploit SIMD features available in Intel processors to speed up eta-pairing computations. We study two ways of vectorizing the computations: horizontal (intra-pairing) and vertical (inter-pairing). We report our experimental results using SSE2 and AVX2 features supported by the Haswell microarchitecture. Our implementations use two popular curves. Recently proposed discrete-logarithm algorithms make these curves less secure than previously thought. We discuss the implications of these developments in the context of our implementations.
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