LUT-based high-speed point multiplier for Goldilocks-Curve448

Abstract

Recent studies have shown that existing elliptic curve-based cryptographic standards provide backdoors for manipulation and hence compromise the security. In this regard, two new elliptic curves known as Curve448 and Curve25519 are recently recommended by IETF for transport layer security future generations. Hence, cryptosystems built over these elliptic curves are expected to play a vital role in the near future for secure communications. A high-speed elliptic curve cryptographic processor (ECCP) for the Curve448 is proposed in this study. The area of the ECCP is optimised by performing different modular operations required for the elliptic curve Diffie–Hellman protocol through a unified architecture. The critical path delay of the proposed ECCP is optimised by adopting the redundant-signed-digit technique for arithmetic operations. The segmentation approach is introduced to reduce the required number of clock cycles for the ECCP. The proposed ECCP is developed using look-up-tables (LUTs) only, and hence it can be ported to any field-programmable gate array family or standard ASIC libraries. The authors' ECCP design offers higher speed without any significant area overhead to recent designs reported in the literature.