Algorithms and arithmetic operators for computing the eta(T) pairing in characteristic three
Since their introduction in constructive cryptographic applications, pairings over (hyper) elliptic curves are at the heart of an ever increasing number of protocols. With software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the eta T pairing in characteristic three and suggest further improvements. These algorithms involve addition, multiplication, cubing, inversion, and sometimes cube root extraction over F(3m). We propose a hardware accelerator based on a unified arithmetic operator able to perform the operations required by a given algorithm. We describe the implementation of a compact coprocessor for the field F(397) given by F(3)[x]/(x(97) + x(12) + 2), which compares favorably with other solutions described in the open literature.
eta(t) pairing elliptic curve hardware accelerator finite field arithmetic fpga