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This paper reviews quantum one-way functions and related quantum-state primitives, highlighting their potential as analogues to classical one-way functions in cryptography. The authors analyze various constructions, including one-way state generators and pseudorandom quantum states, while discussing their computational and information-theoretic security under different adversarial models. Key findings emphasize the importance of physical realizability and robustness to noise, paving the way for future advancements in practical quantum cryptographic systems beyond key distribution.
Quantum one-way functions could redefine the landscape of cryptographic security, offering new primitives that withstand adversarial attacks better than their classical counterparts.
Quantum cryptographic primitives beyond key distribution remain a less well understood area of research. In classical cryptography, one-way functions underpin nearly all standard cryptographic protocols, motivating the search for meaningful quantum analogues and for a clear understanding of the physical and computational mechanisms that could enforce one-wayness. In this article, we review quantum one-way functions and a range of closely related quantum-state primitives, including one-way state generators, pseudorandom quantum states, and efficiently indistinguishable pairs of states. We discuss both computational and information-theoretic notions of quantum one-wayness, emphasizing the different adversarial models and security assumptions that underlie these constructions. We compare and contrast the various proposed primitives, and clarify their conceptual relationships. Particular emphasis is placed on questions of physical realizability, experimental feasibility, and robustness to noise. Finally, we outline open problems and future directions toward the development of practical quantum cryptographic primitives beyond key distribution, and the emergence of a broader quantum-cryptographic ecosystem.
