Computing Tate Pairing on Smartcards

Abstract

In this paper, we present the results of computing the Tate pairing using a supersingular elliptic curve defined over a prime field. The aim of this work is to demonstrate the feasibility of the primitives of identity based cryptosystem for application in embedded processors such as a smartcard. The most computationally intensive operation in an Identity Based Protocol is the calculation of a pairing function. We report the timing of Tate pairing computation for a PC platform and for the 32-bit ST22 smartcard microprocessor. The use of supersingular elliptic curves permits the use of a field where the characteristic is a large prime p with low Hamming weight. This results in a faster modular reduction operation when compared to the use of Montgomery modular multiplication used in literature where MNT curves are adopted.