Efficient software implementation of laddering algorithms over binary elliptic curves

Abstract

Designing efficient and secure implementations of Elliptic Curve Cryptography (ECC) has attracted enormous interest from both theoreticians and practitioners. The main contenders in terms of performance are curves defined over binary extension fields or large prime characteristic fields. In addition to the efficiency requirements, security advantages such as implementation simplicity and resistance to side-channel attacks are receiving increasing attention in research and commercial applications. In this paper, we keep pushing in this direction and study efficient implementation of regular scalar multiplication algorithms for binary curves equipped with efficient endomorphisms. Our focus is on implementing the Galbraith-Lin-Scott (GLS) family of binary curves by exploring the space of different models and laddering algorithms, for their high performance, reasonable implementation simplicity, lower memory consumption and side-channel resistance. Our results demonstrate that laddering implementations can be competitive with window-based methods by obtaining a new speed record for laddering implementations of elliptic curves on high-end Intel processors.