Replication Package: Benchmarking Cryptographic Linear Layers as Reversible CNOT Circuits: Exact Interfaces, Structural Lower Bounds, and Topology-Native Synthesis

This repository contains the official replication package, exact deterministic verification tools, and empirical circuit traces for the paper "Benchmarking Cryptographic Linear Layers as Reversible CNOT Circuits: Exact Interfaces, Structural Lower Bounds, and Topology-Native Synthesis". To ensure strict reproducibility and mathematical exactness, this archive provides the standalone Python verification script (which avoids all external numerical libraries and floating-point arithmetic), the execution logs, and representative circuit traces evaluated in the paper. Repository Contents: checker.py: The complete deterministic Python program. It exactly reconstructs finite-field multiplication in $\mathbb{F}_2[X]/(X^8+X^4+X^3+X+1)$, builds the $32\times32$ binary expansions for AES MixColumns and InvMixColumns, and computes every directed off-diagonal cut-rank to deterministically certify the 512-CNOT path lower bound. output_log.txt: The terminal execution log of checker.py. It confirms the SHA-256 packed-matrix digests, exact matrix weights, maximum bipartite degrees, and exact path demands reported in the structural lower bounds section of the manuscript. Circuit_Traces/: A directory containing CNOT circuit traces evaluated in the empirical benchmarks (Section 11). xiang_forward_92_cnot.txt: The 92-gate sequential-XOR realization of AES MixColumns (Xiang et al., 2020). debrugiere_forward_138_cnot.txt: The 138-gate sparse-LU heuristic trace for AES MixColumns (de Brugière et al., 2021). README.txt & SHA256SUMS.txt: Documentation and cryptographic checksums for data integrity verification. Usage Instructions: To rigorously verify the structural lower bounds, finite-field expansion identities, and the SHA-256 matrix fingerprints, run the checker script using Python 3: python3 checker.py