Software Implementation of Finite Fields of Characteristic Three, for Use in Pairing-based Cryptosystems

Abstract

In this paper, the authors examine a number of ways of implementing characteristic three arithmetic for use in cryptosystems based on the Tate pairing. Three alternative representations of the field elements are examined, and the resulting algorithms for the field addition, multiplication and cubing are compared. Issues related to the arithmetic of supersingular elliptic curves over fields of characteristic three are also examined. Details of how to compute the Tate pairing itself are not covered, since these are well documented elsewhere.