A Lean 4 formalization proves that value-independence implies identical marginal distributions for masking verification across all positive integers q.
We have 𝑤(0 − 0,0) = [0 = 0] = true but 𝑤(1 − 0,0) = [1 = 0], which is false because 1 ≠ 0 in ℤ𝑞 when 𝑞 ≥ 2
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From Finite Enumeration to Universal Proof: Ring-Theoretic Foundations for PQC Hardware Masking Verification
A Lean 4 formalization proves that value-independence implies identical marginal distributions for masking verification across all positive integers q.