Physical and side-channel attacks often expose noisy or partial information about cryptographic secrets rather than exact key values. As the deployment of post-quantum cryptography (PQC) progresses, this risk is amplified by the widespread use of compact secret seeds that are deterministically expanded into large key material. Even probabilistic, bitwise leakage about such seeds may therefore reduce the effective security of deployed PQC implementations. This work adopts the bitwise Bayesian leakage model (BBLM) as a practical abstraction for leakage scenarios in which adversaries obtain per-bit posterior information about a secret, as commonly occurs in cold-boot attacks, partial key exposure, and classifier-based side-channel analysis. Within this model, we study a posterior-guided seed-recovery framework that ranks candidates using likelihood-based scores and validates them through a deterministic public-key oracle under explicit time and memory constraints. We instantiate the framework in the context of cold-boot leakage and evaluate its behavior for abstract seed lengths up to 256 bits. The results indicate that posterior-guided enumeration combined with oracle-based validation can substantially improve recovery efficiency compared to uninformed search, even for algebraically structureless seeds. To illustrate practical applicability, we describe how deterministic validation oracles arise naturally in representative post-quantum schemes, including RYDE, UOV, and FAEST. While the experimental evaluation focuses on cold-boot attacks, the framework applies more broadly to other probabilistic leakage sources, providing a resource-aware methodology for assessing key-recovery risks in deployed and emerging PQC systems.
Ochoa et al. (Thu,) studied this question.