结构化变分密钥集中用于简化AES密码

中文摘要 AI 辅助

Grover搜索通过放大可逆的公开验证预言机，为对称密钥恢复提供了通用的量子基线。我们研究公开的轮结构是否可以在精确验证之前塑造变分密钥寄存器。对于简化AES（S-AES），我们根据S盒差分分布约束、候选密钥相关的逆诊断以及全局残差汉明壳项构建相位分离器。每个组件都有可逆的计算-相位-反计算实现。我们证明了这些诊断的单侧完备性陈述，并在弱相关诊断模型下推导了错误密钥的条件下尾界。在十个随机的三对16位S-AES实例上，使用Adam优化的18层调度实现了46.78%的平均公开一致密钥概率，在每次运行中都将正确密钥排在首位，并将观察到的最大错误密钥概率限制在1.11%。16位研究在不进行射击采样的情况下评估了诱导的密钥寄存器动力学，而独立的门级S-DES实验验证了可逆预言机模式，无需密钥空间相位表。结果建立了受控的简化密码基准；它们并不声称对完整AES的攻击或对Grover的渐近优势。在这些限制内，该构造为分析AES结构如何纳入量子算法提供了有用的框架。

英文摘要

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.

发表机构

• Henan University（河南大学）

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