一种紧凑的QUBO编码用于计算逻辑公式的演示：在密码学构造中
A compact QUBO encoding of computational logic formulae demonstrated on cryptography constructions
AI总结：
本文提出一种紧凑QUBO编码方法，用于密码学算法，通过减少逻辑变量数量提升效率，展示在AES、MD5等算法中的应用效果。
摘要：
我们旨在推进二次无约束二元优化（QUBO）公式的最新进展，聚焦于密码算法。由于优化问题线性约束的最小QUBO编码是整数线性规划（ILP）问题的解，通过求解特殊布尔逻辑公式（如ANF和DNF）的整数系数，可以方便地处理任何范式或多输入AND、OR或XOR操作的QUBO形式。为了展示所提出方法的效率，我们考虑了最广泛使用的密码算法，包括AES-128/192/256、MD5、SHA1和SHA256。对于这些算法，我们实现了比之前发表的结果减少数千个逻辑变量的QUBO实例，同时保持QUBO矩阵稀疏且系数幅度低。在AES-256密码函数的特定情况下，我们实现了比以前结果多8倍的变量减少。所展示的QUBO尺寸减少显著增加了密码算法对未来能够嵌入约30000个逻辑变量的量子退火机的脆弱性。
英文摘要：
We aim to advance the state-of-the-art in Quadratic Unconstrained Binary Optimization formulation with a focus on cryptography algorithms. As the minimal QUBO encoding of the linear constraints of optimization problems emerges as the solution of integer linear programming (ILP) problems, by solving special boolean logic formulas (like ANF and DNF) for their integer coefficients it is straightforward to handle any normal form, or any substitution for multi-input AND, OR or XOR operations in a QUBO form. To showcase the efficiency of the proposed approach we considered the most widespread cryptography algorithms including AES-128/192/256, MD5, SHA1 and SHA256. For each of these, we achieved QUBO instances reduced by thousands of logical variables compared to previously published results, while keeping the QUBO matrix sparse and the magnitude of the coefficients low. In the particular case of AES-256 cryptography function we obtained more than 8x reduction in variable count compared to previous results. The demonstrated reduction in QUBO sizes notably increases the vulnerability of cryptography algorithms against future quantum annealers, capable of embedding around $30$ thousands of logical variables.
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