Barrett reduction's masked internal map has preimage sizes in {0,1,2}, establishing a universal 1-bit leakage barrier, with the trichotomy and PF-PINI properties machine-checked in Lean 4.
The NTT butterfly is affine in the mask. Composition for nonlinear gadgets such as Barrett reduction remains future work
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Machine-Checked Cardinality Bounds for Masked Barrett Reduction: A 1-Bit Side-Channel Leakage Barrier in Post-Quantum Cryptographic Hardware
Barrett reduction's masked internal map has preimage sizes in {0,1,2}, establishing a universal 1-bit leakage barrier, with the trichotomy and PF-PINI properties machine-checked in Lean 4.