In the paper we define a notion of quantum resistant ((δ, є)-resistant) hash function which combine together a notion of pre-image (one-way) resistance (δ-resistance) property and the notion of collision resistance (є-resistance) properties. We present a discussion that supports the idea of quantum hashing oriented for cryptographical purposes. We propose a quantum setting of a classical digital signature scheme do demonstrate a theoretical possibilities and restrictions of (δ, є)-hashing. The assumption we use is that a set of qubits (quantum hash) we generate, send, and receive during the execution of a protocol can be stored for a certain (a large enough) amount of time; next, the scheme requires the high degree of entanglement between the qubits which makes such a quantum hash. These properties make quantum hash cryptographically efficient.
In the paper we define a notion of quantum resistant ((δ, є)-resistant) hash function which combine together a notion of pre-image (one-way) resistance (δ-resistance) property and the notion of collision resistance (є-resistance) properties. We present a discussion that supports the idea of quantum hashing oriented for cryptographical purposes. We propose a quantum setting of a classical digital signature scheme do demonstrate a theoretical possibilities and restrictions of (δ, є)-hashing. The assumption we use is that a set of qubits (quantum hash) we generate, send, and receive during the execution of a protocol can be stored for a certain (a large enough) amount of time; next, the scheme requires the high degree of entanglement between the qubits which makes such a quantum hash. These properties make quantum hash cryptographically efficient.
In the letter we define the notion of a quantum resistant ( -resistant) hash function which consists of a combination of pre-image (one-way) resistance ( ε -resistance) and collision resistance ( δ -resistance) properties. We present examples and discussion that supports the idea of quantum hashing. We present an explicit quantum hash function which is ‘balanced’, one-way resistant and collision resistant and demonstrate how to build a large family of quantum hash functions. Balanced quantum hash functions need a high degree of entanglement between the qubits. We use a phase transformation technique to express quantum hashing constructions, which is an effective way of mapping hash states to coherent states in a superposition of time-bin modes. The phase transformation technique is ready to be implemented with current optical technology.
In the paper we define a notion of a resistant quantum hash function which combines a notion of pre-image (one-way) resistance and the notion of collision resistance. In the quantum setting one-way resistance property and collision resistance property are correlated: the "more" a quantum function is one-way resistant the "less" it is collision resistant and vice versa. We present an explicit quantum hash function which is "balanced" one-way resistant and collision resistant and demonstrate how to build a large family of balanced quantum hash functions.
We present a version of quantum hash functions based on non-binary discrete functions. The proposed quantum procedure is 'classical-quantum', that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance); in addition it has properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. We also show that the proposed function can be naturally used in a quantum digital signature protocol.
We present a version of quantum hash function based on non-binary discrete functions. The proposed quantum procedure is "classical-quantum", that is, it takes a classical bit string as an input and produces a quantum state. The resulting function has the property of a one-way function (pre-image resistance), in addition it has the properties analogous to classical cryptographic hash second pre-image resistance and collision resistance. This function can be naturally used in a quantum digital signature protocol.
The rapid advancement of quantum computing technology presents a significant challenge to the field of cryptography, particularly affecting the security of hash functions that form the foundation of many cryptographic protocols. Hash functions are widely used to ensure data integrity, generate digital signatures, and securely store passwords. However, the emergence of quantum algorithms—such as Grover’s algorithm—threatens to undermine the security assumptions on which these hash functions are based by significantly reducing their effective security levels. This paper aims to provide a comprehensive analysis of the vulnerabilities introduced by quantum computing to traditional hash functions, detailing how these weaknesses can be exploited by quantum adversaries. We explore the fundamental properties of hash functions, including pre-image resistance, second pre-image resistance, and collision resistance, and assess how these properties are affected in a quantum context. Furthermore, we examine the implications of these vulnerabilities for existing cryptographic systems and emphasize the urgent need for the development of post-quantum cryptographic standards. In response to these challenges, we review ongoing research efforts focused on designing hash functions that are resilient to quantum attacks. We evaluate several promising candidates for post-quantum hash functions, considering their security properties, performance metrics, and practical applicability. The findings of this paper highlight the necessity of transitioning to post-quantum cryptographic solutions to safeguard sensitive information in an increasingly quantum-capable world. Ultimately, we advocate for proactive measures within the cryptographic community to adopt and implement these new standards, thereby ensuring robust data security in the age of quantum computing.
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.