Embedded implementation of Edwards curve- and extended Jacobi quartic curve-based cryptosystems

This research addresses the computationally-effective implementation of cryptographic protocols based on elliptic curves, and targets in particular cryptosystems that should be hosted on embedded programmable processors. In principle, the implementation of Elliptic Curve Cryptography (ECC) requires one to deal with different design options, which stem from the available degrees of freedom: elliptic curve family, coordinate system, and point multiplication procedure. On the other hand, theoretical studies already proved that exist only a few setups leading to computational efficient implementations. The goal of present paper is to analyze from an applicative point of view such setups, which mainly involve two specific families of elliptic curves: Edwards curves and extend Jacobi quartic curves. The presented experimental session shows a few interesting outcomes; first, ECC schemes implemented by using either Edwards curves or extended Jacobi quartic curves can obtain remarkable performances in terms of computational efficiency also on low-cost, low-resources processors. Second, the experiments showed that in some cases the number of Fp operations is not enough to accurately estimate the overall performance of an ECC-based cryptosystem.