Capability-Adaptive Cryptanalysis with Reduced-Space Quantum Verification

2026-08-12

AI Summary

This work addresses the fundamental challenge of efficiently integrating classical cryptanalytic evidence with quantum verification in hybrid cryptanalysis. We propose a capability-adaptive unified framework that synergistically combines linear, differential, and side-channel analyses. By constructing a mathematical model for candidate space reduction, the framework establishes a theoretical linkage between spatial compression and the complexity of quantum verification, while incorporating a Hamiltonian formulation to ensure physical realizability. Experimental results demonstrate that the initial key hypothesis space of 4,096 candidates is reduced to just 13 (a compression rate of 99.683%), and the number of Grover iterations required for verification drops from 50 to 2—yielding an approximate 25-fold efficiency gain—with a target state success probability of 94.53%.

Abstract

Efficient integration of cryptanalytic evidence with quantum verification remains a fundamental challenge in hybrid classical-quantum cryptanalysis. This work presents a capability-adaptive cryptanalytic framework that unifies linear cryptanalysis, differential cryptanalysis, and side-channel leakage analysis within a common candidate-space reduction architecture, followed by reduced-space quantum verification through amplitude amplification. A formal mathematical model is developed for candidate-space construction, adaptive filtering, verification-space reduction, and complexity characterization, supported by the oretical results establishing the relationship between candidate-space contraction and quantum verification effort. A Hamiltonian formulation is further introduced to provide a physically realizable interpretation of the reduced-space verification process. Evaluation using statistically generated cryptanalytic observations demonstrates that the proposed framework reduces an initial candidate-key hypothesis space of 4096 candidates to an effective candidate space of 13 hypotheses, corresponding to an overall reduction of approximately 99.683%. Consequently, the Grover verification requirement decreases from 50 iterations to only 2 iterations, yielding an approximately 25-fold reduction in verification effort, while reduced-space amplitude amplification achieves a target-state success probability of approximately 94.53%. These results demonstrate that adaptive cryptanalytic filtering can substantially reduce quantum verification complexity while preserving cryptanalytic admissibility, providing a practical foundation for capability-aware hybrid cryptanalysis and reduced-space quantum search.

Problem

• hybrid classical-quantum cryptanalysis
• quantum verification
• candidate-space reduction
• cryptanalytic evidence integration
• verification complexity

Innovation

• capability-adaptive cryptanalysis
• reduced-space quantum verification
• amplitude amplification
• candidate-space reduction
• hybrid classical-quantum cryptanalysis