A five-line mathematical proof just replaced a brute-force verification task that usually takes 33 million evaluations.
April 24, 2026
Original Paper
From Finite Enumeration to Universal Proof: Ring-Theoretic Foundations for PQC Hardware Masking Verification
arXiv · 2604.18717
The Takeaway
Verification for post-quantum cryptographic hardware typically requires checking every possible value of a variable. This computational burden creates a massive bottleneck for engineers trying to ensure security. The new formal proof works for all possible values of q simultaneously. It turns a slow and expensive checking process into a trivial logic exercise in Lean 4. Engineers can now verify hardware designs instantly instead of waiting for days of compute.
From the abstract
Formal verification of masking in post-quantum cryptographic (PQC) hardware relies on SMT solvers over finite domains. Our prior work established structural dependency analysis at scale [1] and quantified the security margin of partial NTT masking [2]. QANARY, our structural dependency analysis framework, verified 1.17 million cells across 30 modules of the Adams Bridge ML-DSA/ML-KEM accelerator [3, 4], but its core soundness result (Theorem 3.9.1) was machine-checked only at $q = 5$ via $2^{25}