Several cryptographic systems depend upon the computational difficulty of reversing cryptographic hash functions. Robust hash functions transform inputs to outputs in such a way that the inputs cannot be later retrieved in a reasonable amount of time even if the outputs and the function that created them are known. Consequently, hash functions can be cryptographically secure, and they are employed in encryption, authentication, and other security methods. It has been suggested that such cryptographically-secure hash functions will play a critical role in the era of post-quantum cryptography (PQC), as they do in conventional systems. In this work, we introduce a procedure that leverages the principle of reversibility to generate circuits that invert hash functions. We provide a proof-of-concept implementation and describe methods that allow for scaling the hash function inversion approach. Specifically, we implement one manifestation of the algorithm as part of a more general automated quantum circuit synthesis, compilation, and optimization toolkit. We illustrate production of reversible circuits for crypto-hash functions that inherently provide the inverse of the function, and we describe data structures that increase the scalability of the hash function inversion approach.

翻译：多种密码系统依赖于对加密哈希函数进行逆向求解的计算难度。鲁棒哈希函数将输入转换为输出，其设计使得即使已知输出和生成该输出的函数，也无法在合理时间内重构原始输入。因此，哈希函数具有密码学安全性，并被广泛应用于加密、认证及其他安全机制。有研究表明，这类密码学安全的哈希函数将在后量子密码时代（PQC）发挥关键作用——正如其在传统系统中的地位。本文提出了一种利用可逆性原理生成逆向哈希函数电路的方法。我们提供了概念验证实现，并阐述了可扩展哈希函数逆向方法的途径。具体而言，我们将该算法的一种表现形式集成至更通用的自动量子电路综合、编译与优化工具包中。通过为加密哈希函数生成具备固有逆向功能的可逆电路，我们展示了其实现过程，并描述了可提升哈希函数逆向方法可扩展性的数据结构。