In this research article, we worked on construction of quantum hash function utilizing quantum walks over Petersen graph. We chose the Petersen graph, known for its highly symmetric structure and robust connectivity, as the underlying graph for the quantum walk dynamics. Quantum walks show excellent probabilistic behavior and strong mixing properties, providing a powerful mathematical framework for designing cryptographic primitives. The proposed quantum hash function demonstrates high sensitivity and essential diffusion-confusion metrics. Our results highlight the application of quantum walks to quantum cryptography, offering a scalable and stable quantum hash function.
In this research article, we worked on construction of quantum hash function utilizing quantum walks over Petersen graph. We chose the Petersen graph, known for its highly symmetric structure and robust connectivity, as the underlying graph for the quantum walk dynamics. Quantum walks show excellent probabilistic behavior and strong mixing properties, providing a powerful mathematical framework for designing cryptographic primitives. The proposed quantum hash function demonstrates high sensitivity and essential diffusion-confusion metrics. Our results highlight the application of quantum walks to quantum cryptography, offering a scalable and stable quantum hash function.
In this research article, we design a quantum hash function model from hybrid quantum walks on finite path graph. The hybrid evolution operator consisting of integrated framework of continuous time quantum walks and lackadaisical quantum walks as per choice of bits in binary input message, acts on initial quantum state and generate quantum hash values from probability distribution of final quantum state. The quantum hash values generated through the proposed method is showing strong cryptographic properties in sensitivity analysis, collision analysis, statistical features analysis, birthday attack and uniform analysis. Our proposed framework is showing successful results utilizing mathematically well defined structure of hybrid quantum walks based on quantum mechanics phenomena.
Quantum hash function is an important area of interest in the field of quantum cryptography. Quantum hash function based on controlled alternate quantum walk is a mainstream branch of quantum hash functions by virtue of high efficiency and flexibility. In recent development of this kind of schemes, evolution operators determined by an input message depend on not only coin operators, but also direction-determine transforms, which usually are hard to extend. Moreover, the existing works ignore the fact that improper choice of initial parameters may cause some periodic quantum walks, and further collisions. In this paper, we propose a new quantum hash function scheme based on controlled alternate lively quantum walks with variable hash size and provide the selection criteria for coin operators. Specifically, each bit of an input message determines the magnitude of an additional long-range hop for the lively quantum walks. Statistical analysis results show excellent performance in the aspect of collision resistance, message sensitivity, diffusion and confusion property, and uniform distribution property. Our study demonstrates that a fixed coin operator, along with different shift operators, can effectively work on the design of a quantum hash function based on controlled alternate quantum walks, and shed new light on this field of quantum cryptography.
Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.
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.
We introduce a novel, \textit{fully} quantum hash (FQH) function within the quantum walk on a cycle framework. We incorporate deterministic quantum computation with a single qubit to replace classical post-processing, thus increasing the inherent security. Further, our proposed hash function exhibits zero collision rate and high reliability. We further show that it provides $ > 50\%$ avalanche on average, and is highly sensitive to the initial conditions. We show comparisons of several performance metrics for the proposed FQH with different settings as well as with existing protocols to prove its efficacy. FQH requires minimal quantum resources to produce a large hash value, providing security against the birthday attack. This innovative approach thus serves as an efficient hash function and lays the foundation for potential advancements in quantum cryptography by integrating the fully quantum hash generation protocol.
We investigate quantum walk-based hash functions, which are generated from the count distribution generated by a quantum walker on graphs. The method is expected to be one of the promising approaches for generating robust hash functions; however, the quantum computation in small systems is susceptible to spoofing via classical imitation. To address this issue, it is necessary to perform calculations in a quantum space size that classical algorithms are difficult to simulate. In such cases, simply increasing the quantum space size leads to an increase in the number of quantum circuit measurements, thereby increasing the time required to generate the ideal measurement distribution. Based on these facts, we propose a quantum hybrid algorithm combining a quantum walk with a shot-based random projection architecture. This method compresses the output into a fixed-length 256-bit hash by weighting and binarizing the measurement counts of each node. We investigate the proposed method through the numerical simulations of quantum walks on the Hanoi Network (HN4) withN=4096. The results demonstrate no hash collisions and an avalanche effect of approximately 49%, which is close to the ideal value of 50%. Additionally, we achieved the consensus robustness of up to 94%, compared to the ideal value of 100%. These results suggest the feasibility of a scalable quantum hash function for Proof of Quantum Work (PoQ) on quantum devices.