Machine-Checked Cardinality Bounds for Masked Barrett Reduction: A 1-Bit Side-Channel Leakage Barrier in Post-Quantum Cryptographic Hardware

Barrett reduction is the nonlinear core of every practical NTT-based post-quantum cryptography implementation. Existing composition frameworks ISW, t-SNI, PINI, DOM address Boolean masking over GF2; none provides a machine-checked characterization of Barrett's leakage under first-order arithmetic...