Edwards Curves and Extended Jacobi Quartic-Curves for Efficient Support of Elliptic-Curve Cryptosystems in Embedded Systems

The efficient support of cryptographic protocols based on elliptic curves is crucial when embedded processors are adopted as the target hardware platforms. The implementation of Elliptic Curve Cryptography (ECC) offers a variety of design options, mostly covering the specific family of curves and the related coordinate system. At the same time, theory shows that a limited set of solutions can actually lead to efficient computational implementations. This paper analyzes these configurations from an applicative perspective, and mainly addresses two families of curves, namely, Edwards curves and extended Jacobi quartic curves, under a variety of coordinate systems. The experimental results prove that the ECC schemes based on either Edwards curves or extended Jacobi quartic curves can attain remarkable performances in terms of computational efficiency on low-cost, lowresources processors. Edwards curves, in particular, yield best performances when expressed in inverted coordinates.