Lightweight Elliptic Curve Cryptography Accelerator over 25519 Curves

Abstract

This study introduces a lightweight accelerator architecture optimized for elliptic curve cryptography across three 255-bit curves: Weierstrass, Montgomery, and Twisted Edwards. Regarding Montgomery curves, a combination of projective coordinates and Montgomery ladder (ML) point multiplication (PntMlt) method is widely recognized for its efficiency and effectiveness. However, this study uses affine coordinates for lightweight design. In this study, we applied some lightweight techniques used in curve P-256 to 255-bit curves. Although adapting these techniques to the modified finite field posed certain challenges, we effectively redefined the essential equations to minimize speed and area overhead. In addition, the proposed accelerator supports the three curves interchangeably through curve mapping, thereby enabling versatile cryptographic applications. At a maximum clock frequency of 200 MHz, PntMlt on all three curves could be computed within 1 ms, and only 60 k gate equivalents of resources were required in the application-specific integrated circuit (ASIC) implementation.