Bridging Side-channel Evaluation Gap: From Interpretable Leakage Models to Concrete Evidence-based Attacks

Side-channel evaluations of cryptographic implementations have been mandated at high security levels. Leakage assessments and attack evaluations are two fundamental aspects. However, there exists a mismatch between leakage assessment outcomes and attack evaluation results. Specifically, popular leakage assessment methods employ well-known statistical tools such as Mutual Information (MI) to quantify the amount of information leaked. Yet, no evidence is provided to further address the more critical problem of whether the theoretically assessed leakages are exploitable in a concrete attack. As is now widely recognized, statistical guidelines offer limited interpretability for resistance against specific attacks. This work bridges this long-standing gap through three major contributions. First, we leverage a family of globally convex/concave and coercive functions to profile a novel noisy leakage model that is grounded in geometric theory. This model enables leakage assessments within an interpretable geometric paradigm. Second, we derive multi-order leakage evidence from the model and demonstrate its exploitability in developing attacks. This is also an evaluation of leakage exploitability. We propose three novel evidence-based distinguishers to validate our claimed exploitability. Third, we formulate worst-case leakage assessments as constrained problems and develop a convergent algorithm to approximate the first-order worst-case leakage bound as an example. The improved distinguisher is derived based on the worst-case evidence. Theoretical analysis has demonstrated that the multi-order leakage evidence is consistently achievable and uniquely characterizable. Furthermore, the convergence rate toward approximating the first-order worst-case bound is ensured to be at least sublinear. Experimental analyses validate the theory, confirming its effectiveness in practical applicability.