Locality Does Matter: An Assessment Metric Adapted for Cluster-Based Side-Channel Analysis on Public Key Cryptosystems

Cluster-based side-channel analysis (SCA) is a commonly used side-channel analysis method for public key cryptography systems. This paper focuses on assessment metrics to improve the efficiency and accuracy of key recovery in cluster-based SCA processes. We introduce a novel metric called adjacent distance coefficient (AD coefficient). Different from traditional metrics like silhouette coefficient, membership degree, and information entropy, the AD coefficient, by considering local density and avoiding the computation of cluster centers, is less influenced by the shape and size of data, thereby overcoming limitations of traditional metrics. Experiments on RSA, SM2, and ECC demonstrate that the AD coefficient exhibits higher accuracy compared to traditional metrics, especially under conditions with noise and random delays, where it shows significant robustness. Incorporating the AD coefficient, we propose an assessment method to detect whether cryptographic devices are resistant to cluster-based SCA attacks, offering a convenient quantitative measure for the security evaluation of cryptographic devices.