Structured Variational Key Concentration for a Reduced AES Cipher

Abstract

Grover search provides the generic quantum baseline for symmetric-key recovery by amplifying a reversible public-verification oracle. We investigate whether public round structure can instead shape a variational key register before exact verification. For simplified AES (S-AES), we construct phase separators from S-box differential-distribution constraints, candidate-key-dependent inverse diagnostics, and a global residual Hamming-shell term. Each component has a reversible compute-phase-uncompute realization. We prove a one-sided completeness statement for these diagnostics and derive a conditional lower-tail bound for false keys under a weakly correlated diagnostic model. On ten random three-pair 16-bit S-AES instances, an 18-layer schedule optimized with Adam achieves a mean public-consistent-key probability of 46.78 percent, ranks the correct key first in every run, and limits the largest observed false-key probability to 1.11 percent. The 16-bit study evaluates the induced key-register dynamics without shot sampling, while a separate gate-level S-DES experiment validates the reversible oracle pattern without a key-space phase table. The results establish a controlled reduced-cipher benchmark; they do not claim an attack on full AES or an asymptotic advantage over Grover. Within these limits, the construction provides a useful framework for analyzing how AES structure can be incorporated into quantum algorithms.