Paper 2026/1990

Bounded Information: PAC Certification of Multivariate Side-Channel Traces

Abstract

Side-channel leakage certification aims to quantify what an attacker can learn about a secret variable from observed leakage. Existing information-theoretic estimators, such as perceived information (PI), hypothetical information (HI), and nonparametric mutual information (MI), aim to quantify distributional leakage, but they become unstable in high-dimensional traces and do not provide a finite-sample certificate of the best attacker. We introduce \emph{Bounded Information} (BI), a probably approximately correct (PAC)-style finite-sample certification method that upper-bounds the exact-recovery success of a fixed attacker scope on unseen traces. The attacker suite certificate, $\mathrm{BI}^{\mathrm{suite}}$, applies a KL-binomial confidence interval with a union bound over a fixed suite that contains every trained attacker, preprocessing choice, and hyperparameter. BI therefore turns standard profiled-attack evaluation into an auditable certificate with an explicit attacker scope and confidence level. We further define $\mathrm{BI}^{\mathrm{loc}}(\varepsilon)$ to bound the recovery success of attackers whose normalized scores differ by at most $\varepsilon$ from those of a model in the suite. Across eight side-channel benchmarks with trace dimensions up to $7{,}000$, BI provides stable certificates without density estimation, and its tightness diagnostics tell an evaluator whether a certified value is a genuine measurement of leakage or a conservative bound that more attack traces would tighten.