Implementation of Bilinear Pairings over Elliptic Curves with Embedding Degree 24

Abstract

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 F-q24 ; 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.