Quantum computers have the potential to solve a number of hard problems that are believed to be almost impossible to solve by classical computers. This observation has sparked a surge of research to apply quantum algorithms against the cryptographic systems to evaluate its quantum resistance. In assessing the security strength of the cryptographic algorithms against the upcoming quantum threats, it is crucial to precisely estimate the quantum resource requirement (generally in terms of circuit depth and quantum bit count). The National Institute of Standards and Technology by the US government specified five quantum security levels so that the relative quantum strength of a given cipher can be compared to the standard ones. There have been some progress in the NIST-specified quantum security levels for the odd levels (i.e., 1, 3 and 5), following the work of Jaques et al. (Eurocrypt’20). However, levels 2 and 4, which correspond to the quantum collision finding attacks for the SHA-2 and SHA-3 hash functions, quantum attack complexities are arguably not well-studied. This is where our article fits in. In this article, we present novel techniques for optimizing the quantum circuit implementations for SHA-2 and SHA-3 algorithms in all the categories specified by NIST. After that, we evaluate the quantum circuits of target cryptographic hash functions for quantum collision search. Finally, we define the quantum attack complexity for levels 2 and 4, and comment on the security strength of the extended level. We present new concepts to optimize the quantum circuits at the component level and the architecture level.
Quantum computers have the potential to solve a number of hard problems that are believed to be almost impossible to solve by classical computers. This observation has sparked a surge of research to apply quantum algorithms against the cryptographic systems to evaluate its quantum resistance. In assessing the security strength of the cryptographic algorithms against the upcoming quantum threats, it is crucial to precisely estimate the quantum resource requirement (generally in terms of circuit depth and quantum bit count). The National Institute of Standards and Technology by the US government specified five quantum security levels so that the relative quantum strength of a given cipher can be compared to the standard ones. There have been some progress in the NIST-specified quantum security levels for the odd levels (i.e., 1, 3 and 5), following the work of Jaques et al. (Eurocrypt’20). However, levels 2 and 4, which correspond to the quantum collision finding attacks for the SHA-2 and SHA-3 hash functions, quantum attack complexities are arguably not well-studied. This is where our article fits in. In this article, we present novel techniques for optimizing the quantum circuit implementations for SHA-2 and SHA-3 algorithms in all the categories specified by NIST. After that, we evaluate the quantum circuits of target cryptographic hash functions for quantum collision search. Finally, we define the quantum attack complexity for levels 2 and 4, and comment on the security strength of the extended level. We present new concepts to optimize the quantum circuits at the component level and the architecture level.
The rapid advancements in quantum technologies have introduced significant threats to the security of conventional cryptographic systems. In particular, the evaluation of quantum resource requirements—measured in terms of circuit depth and qubit count—has become essential for analyzing the resilience of widely used schemes such as AES and RSA, as well as cryptographic hash functions like SHA-2. At the same time, the widespread adoption of Internet of Things (IoT) applications has increased the exposure to cybersecurity risks, which are further exacerbated by the emerging capabilities of quantum adversaries. To address these challenges, the U.S. National Institute of Standards and Technology (NIST) launched a competition to standardize lightweight hash functions and defined five quantum security levels to assess their robustness. In this work, we conduct a resource analysis of the NIST Lightweight Hash Function finalists against the Grover search algorithm, providing detailed insights into their quantum resistance. The findings contribute to a more comprehensive understanding of the security strength of lightweight hash functions in the post-quantum era.
Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ASCON, including both symmetric-key encryption and hashing algorithms, as a part of the lightweight cryptography standardization by NIST (National Institute of Standards and Technology). As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme, which is a symmetric-key algorithm. Also, our quantum circuit implementation of the ASCON-HASH achieves a reduction of more than 88.9% in the Toffoli depth and more than 80.5% in the full depth compared to the previous work. As per our understanding, the most effective strategy against Grover’s search involves minimizing the depth of the quantum circuit for the target cipher. We showcase the optimal Grover’s search cost for ASCON and introduce a proposed quantum circuit optimized for depth. Furthermore, we utilize the estimated cost to evaluate post-quantum security strength of ASCON, employing the relevant evaluation criteria and the latest advancements in research.
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.
MD5 and SHA-1 are widely studied hash functions in cryptanalysis, owing to their well-structured round functions and historical significance in cryptography. This paper presents improved quantum circuit implementations of MD5 and SHA-1 specifically optimized for quantum cryptanalysis. We reduce the quantum implementation cost of auxiliary functions and eliminate the use of ancilla qubits, while reducing circuit depth (the number of sequential gate layers) by parallelizing multiple additions in the round operations of MD5 and SHA-1. Additionally, the quantum implementations of MD5 and SHA-1 are optimized by considering a fixed input size under the attack scenario. The proposed implementations achieve a 63% improvement in the depth - qubit count metric for MD5 and a 27% improvement for SHA-1 compared to previous works. By providing reduced quantum resources, this work establishes an improved baseline for the quantum cryptanalysis of MD5 and SHA-1. We analyze quantum attacks on MD5 and SHA-1, showing that the preimage attacks require a full depth of 279 and 296 for MD5 and SHA-1, respectively, while the collision attacks require a full depth of 254 and 264. For a realistic evaluation, we also estimate the quantum resources for fault-tolerant quantum computation, including the number of physical qubits and the runtime, to break MD5 and SHA-1.
A quantum computer capable of running the Grover search algorithm, which reduces the complexity of brute-force attacks by a square root, has the potential to undermine the security strength of symmetric-key cryptography and hash functions. Recently, studies on quantum approaches have proposed analyzing potential quantum attacks using the Grover search algorithm in conjunction with optimized quantum circuit implementations for symmetric-key cryptography and hash functions. Analyzing quantum attacks on a cipher (i.e., quantum cryptanalysis) and estimating the necessary quantum resources are related to evaluating post-quantum security for the target cryptography algorithms. In this paper, we revisit quantum implementations of CHAM block cipher, an ultra lightweight cipher, with a focus on optimizing the linear operations in its key schedule. We optimized the linear equations of CHAM as matrices by applying novel optimized decomposition techniques. Using the improved CHAM quantum circuits, we estimate the cost of Grover’s key search and evaluate the post-quantum security strength with further reduced costs.
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.