Automated Quantum Circuit Generation for Computing Inverse Hash Functions

• Main Authors: Henderson, Elena R, Henderson, Jessie M, Oxford, William V, Thornton, Mitchell A
• Format: Journal Article
• Language: English
• Published: 25-04-2024
• Subjects: Computer Science - Cryptography and Security; Physics - Quantum Physics
• DOI: 10.48550/arxiv.2404.17142

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.