Paper 2007/426 Original: eprint.iacr.org/2007/426 ↗

Implementing Cryptographic Pairings over Curves of Embedding Degrees 8 and 10

Abstract

In this paper, we will describe efficient implementations of the Tate and Ate pairings over ordinary elliptic curves of embedding degrees 8 and 10. We will discuss the possible curve-dependent optimizations that can be applied to evaluate the pairings. We pay particular attention to the use of elliptic curve twists and the denominator elimination method to make computations more efficient. Our main goal is to draw together the best possible optimizations that can be used to efficiently evaluate the Tate and the Ate pairings in both curves and to give timings and appropriate interpretation on the rate of change on the running time of our programs for both curves. To come up with an adequate conclusion, we will compare the performance of the curves we chose to an already experimented curve of embedding degree 12.