For AES 128 security level there are several natural choices for pairing-friendly elliptic curves. In particular, as we will explain, one might choose curves with k = 9 or curves w...
In this paper we introduce the concept of an optimal pairing, which by definition can be computed using only log2 r/(k) basic Miller iterations, with r the order of the groups invo...
The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius t. However, not all pairing-friendl...
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with ...
Scott uses an efficiently computable isomorphism in order to optimize pairing computation on a particular class of curves with embedding degree 2. He points out that pairing implem...