As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of $n$-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small $n$ cases in a D-Wave machine, showing its capacity of devising bent functions, the most relevant set of cryptographic Boolean functions. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.

中文翻译：

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量子计算密码学：使用 2000 量子比特 D 波量子计算机通过量子退火寻找密码布尔函数

作为对称密码学的构建块，设计满足多种性质的布尔函数是序列密码、分组密码和散列函数中的一个重要问题。然而，由于空间的超指数大小 $\mathcal{O}(2^{2^n})$，搜索满足全局密码约束的 $n$ 变量布尔函数在计算上是困难的。在这里，我们介绍了伊辛哈密顿量基态中与密码相关的约束的编码，允许我们在量子退火器中自然地对其进行编码，这似乎提供了量子加速。此外，我们在 D-Wave 机器中对 $n$ 小案例进行了基准测试，展示了它设计弯曲函数的能力，这是最相关的一组加密布尔函数。我们通过局部搜索和链修复对其进行了补充，以提高与低连接性相关的 D-Wave 量子退火器性能。这项工作展示了如何将超指数密码问题编码到量子退火器中，并为通过设计合理的芯片实现量子霸权铺平了道路。