A pairing SW implementation for Smart-Cards

The aim of this work is to show the feasibility of the primitives of the identity based cryptosystems for applications in Smart-Cards. Several observations are applied to easily choose many supersingular elliptic curves over a prime field Fp,p>3,p≡3mod4, in such a way that the size of the torsion subgroup, the curve order and the finite field characteristic are of minimal Hamming weight. We modify the Chudnovsky elliptic curve point representation to settle a dedicated coordinate system for pairings and to minimize the number of operations in the finite field. The encouraging timing results obtained for ST22 Smart-Card architecture show the feasibility of pairing primitives for embedded devices.