Automated Quantum Circuit Generation for Computing Inverse Hash Functions

Abstract: 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.