Algorithm-level error detection for Montgomery ladder-based ECSM

Abstract

For security reasons, especially to provide resistance against fault-based attacks, it is very important to verify the correctness of computations in elliptic curve cryptographic applications. In this article, we deal with protections to fault attacks against elliptic curve scalar multiplication (ECSM) at algorithm level. To this end, we use the concepts of point verification (PV) and coherency check (CC). We investigate the error detection coverage of PV and CC for the Montgomery ladder ECSM algorithm. Additionally, we consider the case where an attacker can mount a double-fault attack. We show that even with this stronger fault model, it is possible to avoid such attacks utilizing the concept of point blinding.