Implementation of binary edwards curves for very-constrained devices

Abstract

Elliptic Curve Cryptography (ECC) is considered as the best candidate for Public-Key Cryptosystems (PKC) for ubiquitous security. Recently, Elliptic Curve Cryptography (ECC) based on Binary Edwards Curves (BEC) has been proposed and it shows several interesting properties, e.g., completeness and security against certain exceptional-points attacks. In this paper, we propose a hardware implementation of the BEC for extremely constrained devices. The w-coordinates and Montgomery powering ladder are used. Next, we also give techniques to reduce the register file size, which is the largest component of the embedded core. Thirdly, we apply gated clocking to reduce the overall power consumption. The implementation has a size of 13,427 Gate Equivalent (GE), and 149.5 ms are required for one point multiplication. To the best of our knowledge, this is the first hardware implementation of binary Edwards curves.