Lightweight Elliptic Curve Cryptography Accelerator Over 25519 Curves

This paper presents a lightweight hardware accelerator optimized for elliptic curve cryptography (ECC), supporting three standardized curves over the prime field GF( $2^{255}-19$ ): Weierstrass, Montgomery, and Twisted Edwards. In implementations of these 25519 curves, the Montgomery ladder method with projective coordinates is widely adopted for efficient point multiplication (PntMlt); however, this work deliberately employs affine coordinates to reduce hardware complexity and area. Although several affine-coordinate optimization techniques were originally proposed for the NIST Curve P-256, they could not be directly applied to the targeted curves due to fundamental differences in the underlying finite field structure. To address this incompatibility, we reformulated the core mathematical expressions, enabling effective adaptation of the P-256-based methods to our context in a lightweight and efficient manner. The proposed architecture supports all three curves interchangeably through lightweight curve mapping, allowing integration into a wide range of ECC-based systems. Synthesized under a 180 nm application specific integrated circuit (ASIC) process technology, the design achieves full PntMlt computation within 1 ms at 200 MHz, consuming only 60 k gate equivalents.