Abstract:

Verification of the correctness of computations is very important to provide resistance against fault-based attacks. In elliptic curve cryptography (ECC), point validation (PV) alone is not sufficient against all fault analysis attacks. In this talk, error-detecting and fault-tolerant schemes for elliptic curve scalar multiplication (ECSM) are considered. For the purpose of detecting errors, we present structures based on re-computation and parallel computation along with PV. These structures use encoding techniques that rely on proprieties of elliptic curves and provide a high probability of detection of errors caused by faults occurred naturally or injected by an attacker. Additionally, we show that using parallel computation along with either PV or re-computation, it is possible to have fault-tolerant structures for the ECSM. Prototypes of the proposed structures for error detection and fault-tolerance have been implemented and experimental results have been presented.