Modern quantum technologies are NISQ (Noisy Intermediate-Scale Quantum) devices, which are used to create insufficiently accurate quantum computers with low computing power. However, quantum technologies have advanced considerably during the past years. Thus, the issue of demonstrating “quantum supremacy” in the era of NISQ technologies is on the agenda. This study demonstrates that “quantum supremacy” is forthcoming. We propose procedures for constructing a universal family of hash functions based on a quantum hashing process that maps the original sequence w to a quantum hash state and then by random transformation to the state |ψ) and generating the sequence u, which is an approximate description of the state |ψ). We proved that the proposed procedure generates a family of nondeterministic hash functions F, which allow us to reliably distinguish between different arguments. The F family can be considered an E-universal family of nondeterministic hash functions. We assume that the development of this research area will cast light on the effect of “quantum supremacy” and will also have a certain impact on the advance of post-quantum cryptography.
Modern quantum technologies are NISQ (Noisy Intermediate-Scale Quantum) devices, which are used to create insufficiently accurate quantum computers with low computing power. However, quantum technologies have advanced considerably during the past years. Thus, the issue of demonstrating “quantum supremacy” in the era of NISQ technologies is on the agenda. This study demonstrates that “quantum supremacy” is forthcoming. We propose procedures for constructing a universal family of hash functions based on a quantum hashing process that maps the original sequence w to a quantum hash state and then by random transformation to the state |ψ) and generating the sequence u, which is an approximate description of the state |ψ). We proved that the proposed procedure generates a family of nondeterministic hash functions F, which allow us to reliably distinguish between different arguments. The F family can be considered an E-universal family of nondeterministic hash functions. We assume that the development of this research area will cast light on the effect of “quantum supremacy” and will also have a certain impact on the advance of post-quantum cryptography.
In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical ∈ -universal hash family and a given family of functions-quantum hash generator. In particular, using the relationship between ∈ -universal hash families and Freivalds fingerprinting schemas we present explicit quantum hash function and prove that this construction is optimal in the sense of number of qubits needed for construction.
The scientific article reviews and analyzes the current stage of cryptography development in the context of the inevitable post-quantum era. It is emphasized that post-quantum cryptography (PQC) is gaining the status of a key priority in the national security strategies of the world's leading developed countries, which are actively preparing for a fundamental transition to quantum-safe cryptographic practices. The consequence of the above is the urgent need for intensive development of the latest cryptographic algorithms, which by their nature will be resistant to attacks from powerful quantum computers. Today, several promising approaches to the creation of such quantum-safe algorithms based on various mathematical concepts and cryptographic primitives are already being actively studied. The article pays special attention to cryptography based on hash functions, which is considered one of the most promising areas in the context of developing reliable quantum-safe cryptographic tools. The potential for cracking cryptographic hash functions using quantum algorithms is analyzed. The article considers an original approach to assessing the quantum stability of hash functions, which consists in encoding the hash function itself in a quantum oracle, rather than its separate solution. A simplified (toy) hash function is used to clearly demonstrate the proposed idea. Based on the results of the experimental study, important conclusions are formulated, which indicate that quantum computers are indeed capable of significantly accelerating the process of inversion of cryptographic hash functions. This, in turn, provides strong grounds for serious concern about the cryptographic stability of various cryptographic primitives based on combinatorial problems. It is worth emphasizing that this problem is not limited to hash functions. This critically important observation means that to maintain a similar level of cryptographic security in the coming quantum era, the size of the input value of hash functions will likely need to be increased by at least half to compensate for the speedup provided by quantum algorithms.
In the paper we propose a method of quantum hashing which mostly combines the existing constructions of universal hash families with quantum one-way functions. Next, we define the concept of a quantum hash generator and present an approach for building a large number of various quantum hash functions. The construction is based on the integration of a classical e-universal hash family and a given family of functions quantum hash generator. The proposed construction combines the properties of robust representation of information by classical error-correcting codes together with the possibility of highly reliable representation of information by quantum systems. In particular, we present a quantum hash function based on the Reed-Solomon code and prove that this construction is optimal in the sense of the number of qubits needed.
In the paper, we define the concept of the quantum hash generator and offer design, which allows to build a large amount of different quantum hash functions. The construction is based on composition of classical ε-universal hash family and a given family of functions -- quantum hash generator. The proposed construction combines the properties of robust presentation of information by classical error-correcting codes together with the possibility of highly compressed presentation of information by quantum systems. In particularly, we present quantum hash function based on Reed-Solomon code, and we proved, that this construction is optimal in the sense of number of qubits needed.
The quest for quantum advantage, wherein quantum computers surpass the computational capabilities of classical computers executing state-of-the-art algorithms on well-defined tasks, represents a pivotal race in the domain of quantum computing. NISQ (Noisy Intermediate-Scale Quantum) computing has witnessed remarkable advancements, culminating in significant milestones on the journey towards the realization of universal fault-tolerant quantum computers. This transformative turning point, known as quantum supremacy, has been achieved amid a series of breakthroughs, signifying the dawn of the quantum era. Quantum hardware has undergone substantial integration and architectural evolution, contrasting with its nascent stages. In this review, we critically examine the quantum supremacy experiments conducted thus far, shedding light on their implications and contributions to the evolving landscape of quantum computing. Additionally, we endeavor to illuminate a range of cutting-edge proof-of-principle investigations in the realm of applied quantum computing, providing an insightful overview of the current state of applied quantum research and its prospective influence across diverse scientific, industrial, and technological frontiers.
The rapid advancement of quantum computing presents a fundamental challenge to modern cryptographic security, particularly in the domain of hash functions that ensure data integrity, authentication, and blockchain security. Traditional crypto graphic hash functions such as SHA-256, SHA-3, and BLAKE2 rely on computational hardness assumptions that become obsolete in the presence of large-scale quantum computers. Shor’s algorithm can efficiently break RSA and ECC-based cryptosys tems, while Grover’s algorithm reduces the security of traditional hash functions by square root complexity, significantly weakening their preimage and collision resistance. This quantum threat necessitates the development of post-quantum secure hashing techniques that remain resilient against both classical and quantum adversaries. This paper proposes Quantum Hashing, a novel cryptographic framework that integrates quantum entanglement, lattice-based cryptography, and hybrid quantum classical hashing to construct post-quantum secure hash functions. We introduce a formal model for Quantum Collision Resistance (QCR) and provide entropy-based ran domness enhancement to ensure unpredictable hash outputs. Unlike classical hashing approaches, our framework leverages the hardness of lattice problems (e.g., Shortest Vector Problem, Learning with Errors) to withstand quantum attacks while incorpo rating Quantum Key Distribution (QKD) mechanisms to enhance entropy and key management. Furthermore, we evaluate the security of Quantum Hashing under various attack models, comparing its resistance against Grover’s search and collision attacks. We benchmark its performance against NIST Post-Quantum Cryptography (PQC) final ists, including CRYSTALS-DILITHIUM, SPHINCS+, and Falcon, demonstrating that our approach offers superior resilience while maintaining computational feasibility. Additionally, we present an implementation of Quantum Hashing using Qiskit, show casing its practical applicability in quantum circuits and quantum-secure blockchain architectures. Our findings highlight that Quantum Hashing provides a scalable, entropy-efficient, and post-quantum resilient cryptographic primitive suitable for next-generation cryptographic applications. This work paves the way for secure post-quantum digital signatures, blockchain consensus mechanisms, and zero-knowledge proof systems that require tamper-resistant hashing in a quantum computing era.