Constructing Elliptic Curve Including Subgroup with Low Hamming Order

Abstract

In practical applications of pairing-based cryptosystems, the efficiency of pairing computation is a crucial factor. Recently, there have been many improvements for the computation of Tate pairing, which focuses on the arithmetical operations under given elliptic curve. Based to the characteristics that Miller’s algorithm will be improved tremendous if there are subgroups with order of low hamming prime above the elliptic curve, an algorithm of generating primes of low hamming with weight 3 is given in this paper. Then, we present an effective generation method of elliptic curve, which enable it feasible that there is certain some subgroup of low hamming prime order. The improvement of paring computation is marked above the elliptic curve generating by our method.