Faster binary curve software: A case study

Abstract

For decades, elliptic curves over binary fields appear in numerous standards including those mandated by NIST, SECG, and ANSI X9.62. Many popular security protocols such as TLS explicitly support these named curves, along with implementations of those protocols such as OpenSSL and NSS. Over the past few years, research in improving the performance and/or security of these named curve implementations has pushed forward the state-of-the-art: e.g. projective lambda coordinates (Oliveira et al.) and commodity microprocessors featuring carryless multiplication instructions for native polynomial arithmetic (Intel, ARM, Qualcomm). This work aggregates some of these new techniques as well as classical ones to bring an existing library closer to the state-of-the art. Using OpenSSL as a case study to establish the practical impact of these techniques on real systems, results show significant performance improvements while at the same time adhering to the existing software architecture.