Security proofs for RLWE-based homomorphic encryption require fresh, independent, and uniform evaluation-key masks, but this assumption is rarely tested against real library outputs. We present GaloisProbe, a reproducible key-only audit framework that formalizes this check as a statistical distinguishing problem on the mask component ksk1 and instantiates five calibrated distinguishers for collisions, linear dependence, covariance structure, regression dependence, and coefficient bias. To our knowledge, this is the first end-to-end framework that maps these proof-level assumptions to a unified, reproducible distinguisher suite for deployed HE libraries. We evaluate Microsoft SEAL 4.1.2, OpenFHE 1.4.2, and HElib 2.3.0 across four parameter settings, with three independent key generations per library and SEAL-based control injections to validate detector behavior. Within these tested settings, we observe no detectable deviation from the ideal RLWE-style randomness model: collisions and rank deficits are absent, and covariance, regression, and bias statistics stay near null expectations. The main contribution is a reusable cryptographic-auditing methodology and empirical baseline for evaluation-key randomness in deployed HE libraries.
AYUSH MESHRAM (Sat,) studied this question.