Elliptic-Curve Digital-Signature System Based on Radix-2w Arithmetic

Abstract

The Elliptic Curve Digital Signature Algorithm (ECDSA) is a widely recognized cryptographic tool that plays a crucial role in verifying the authenticity and preserving the integrity of digital messages. What distinguishes ECDSA from its peers is its exceptional ability to provide robust security with smaller key sizes, making it highly efficient, particularly in resource-constrained applications. Based on the flexibility of the Radix-2w arithmetic, we propose new simple methods to ECDSA implementation handling efficiently the intricacies of elliptic curve point multiplication (PM) and double point multiplication (DPM) operations. The implementation incorporates a Radix-2w method for PM and a simultaneous Radix-22 method for DPM. Both methods are streamlined one-pass recode/evaluation processes. These methods reduce the number of point additions (ADDs) to a near-optimal limit in a sublinear computational time without increasing the number of point doublings (DBLs). They also have the advantage to require a minimal number of point-precomputations. In addition, they show high resilience against side-channel attacks. In comparison to the standard binary method used in PM and DPM, the new Radix-2w methods shows substantial savings in computational time.