Quantum one-way function (QOWF) was proposed for quantum cryptography, which was computable but almost irreversible in quantum polynomial time. Full quantum one-way function (F-QOWF) is one of the most important models of QOWF, which deals with quantum states. Although the universal construction of full quantum one-way function has been proposed, there is still little further discussion on the entangled input, specific function instantiation and application scenarios of F-QOWF. In this paper, we introduce quantum hypergraph states into the universal construction of F-QOWF. Quantum hypergraph states are highly entangled multi-party states constructed from the hypergraph. By applying quantum hypergraph states to the new F-QOWF, we generalize the universal construction of F-QOWF to entangled states. The application to quantum aggregate signature shows that quantum hypergraph states help the new F-QOWF be well applied to quantum multi-party cryptographic protocols.
Quantum one-way function (QOWF) was proposed for quantum cryptography, which was computable but almost irreversible in quantum polynomial time. Full quantum one-way function (F-QOWF) is one of the most important models of QOWF, which deals with quantum states. Although the universal construction of full quantum one-way function has been proposed, there is still little further discussion on the entangled input, specific function instantiation and application scenarios of F-QOWF. In this paper, we introduce quantum hypergraph states into the universal construction of F-QOWF. Quantum hypergraph states are highly entangled multi-party states constructed from the hypergraph. By applying quantum hypergraph states to the new F-QOWF, we generalize the universal construction of F-QOWF to entangled states. The application to quantum aggregate signature shows that quantum hypergraph states help the new F-QOWF be well applied to quantum multi-party cryptographic protocols.
One-way functions are fundamental tools for cryptography. Until now, quantum one-way functions have several input-output categories such as “classical-to-classical,” “classical-to-quantum,” and “quantum-to-classical,” which are used for postquantum cryptography or quantum cryptography. However, there are still no intrinsic “quantum-to-quantum” quantum one-way functions. In this article, we propose the full quantum one-way function to design full quantum cryptographic schemes. By concatenating the “quantum-classical” one-way function and the rotation operation of single qubit, the full quantum one-way function has the input and output of quantum states. We prove its one-way property from “easy computation” and “computationally difficult to invert.” Then we apply the full quantum one-way function to quantum identity authentication. Security analysis shows that the proposed quantum identity authentication scheme based on the full quantum one-way function is secure even under active attacks.
Hypergraph states, a generalization of graph states, constitute a large class of quantum states with intriguing nonlocal properties, and they have promising applications in quantum information science and technology. In this paper, we study some features of an independently proposed generalization of hypergraph states to qudit hypergraph states, i.e., each vertex in the generalized hypergraph (multi-hypergraph) represents a d-level system instead of a two-level one. It is shown that multi-hypergraphs and d-level hypergraph states have a one-to-one correspondence, and the structure of a multi-hypergraph exhibits the entanglement property of the corresponding quantum state. We discuss their relationship with some well-known state classes, e.g., real equally weighted states and stabilizer states. The Bell nonlocality, an important resource in fulfilling many quantum information tasks, is also investigated.
In classical cryptography, one-way functions are necessary for most of cryptography. In the quantum world, however, Kretschmer at {TQC'21} and subsequent works have demonstrated that quantum versions of various primitives in minicrypt, such as signatures and private-key encryption, do not require quantum-computable one-way functions (\textsf{qOWF}s). However, the question of the necessity of \textsf{qOWF}s for primitives in Cryptomania like public-key encryption with classical public keys and ciphertexts (\textsf{qPKE}) has remained open.
We provide a comprehensive picture of the relationship between \textsf{qPKE} and \textsf{qOWF}. First, our main result is a black-box separation between \textsf{qOWF}s and \textsf{qPKE}. In particular, we show that relative to a unitary, real, and self-inverse oracle, there exists a \textsf{qPKE} scheme (with classical keys and ciphertexts), but \textsf{qOWF}s do not exist. Further, our oracles admit a point-function obfuscation construction, thus ruling out black-box construction of \textsf{qOWF} from point function obfuscations.
On the positive side, we construct \textsf{qPKE} from quantum indistinguishability obfuscation for quantum circuits with classical obfuscated descriptions and efficiently verifiable one-way puzzles, which is known to be a potentially weaker assumption than \textsf{qOWF}s, due to an existing black-box separation. Our construction is the quantum analog of the classical construction of \textsf{PKE} from one-way functions and indistinguishability obfuscation in the quantum computation with classical communication (QCCC) setting.
In the rapidly developing field of quantum cryptography, graph theory provides a useful mathematical foundation for complex relationships and structures.Applications for it are becoming more and more common.Vertices, edges, connectivity, and graph states, all components of graph theory help illustrate multi-party entanglement, network connection, and protocol designs in quantum cryptography systems.The connection between graph theory and quantum cryptography is examined in this article.It shows that, graph theory and quantum cryptography design can be used to create scalable, reliable quantum secure networks.The basics of graph theory, including network modeling and graph-state entanglement, are covered.It then gives a summary of modern graph-based quantum cryptography methods, including those used for secure computing, secret sharing, and key distribution.The study highlights current issues while contrasting their approaches and resource requirements.Graph states are used in current methods for secret sharing and multi-party key agreement.Additionally, they use graph structures for protocol creation and graph networks for routing in quantum key distribution (QKD).However, significant obstacles remain, such as the experimental construction of large graph-state networks, securing against different types of assaults, and using sophisticated graphtheoretic methods.Novel graph structures such as hypergraphs and quotient graphs should be the focus of future research.It should also develop graph-based solutions for post-quantum and multi-party cryptographic primitives and include classical-quantum network analysis.
It is an important question to find constructions of quantum cryptographic protocols which rely on weaker computational assumptions than classical protocols. Recently, it has been shown that oblivious transfer and multi-party computation can be constructed from one-way functions, whereas this is impossible in the classical setting in a black-box way. In this work, we study the question of building quantum public-key encryption schemes from one-way functions and even weaker assumptions. Firstly, we revisit the definition of IND-CPA security to this setting. Then, we propose three schemes for quantum public-key encryption from one-way functions, pseudorandom function-like states with proof of deletion and pseudorandom function-like states, respectively.