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Quantum Engineering

Quantum algorithms for hash preimage attacks

Ping Wang, Shengping Tian, Zhiwei Sun, Ning Xie

Published Apr 7, 2020• 15 citations
Publisher

Abstract

Cryptographic hash functions are important building blocks of many security systems. A preimage attack on hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage. The current paper presents a new quantum algorithm for hash preimage attacks, which can break the preimage resistance with circuit complexity O(2n/3) using O(2n/3) running times, where n is the input bit length of the hash function. The quantum circuit complexity is apparently reduced from O(2n/2) to O(2n/3) at the cost of O(2n/3) running times requirements compared with the existing algorithms.

DOI
10.1002/que2.36

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Cryptographic hash functions are important building blocks of many security systems. A preimage attack on hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage. The current paper presents a new quantum algorithm for hash preimage attacks, which can break the preimage resistance with circuit complexity O(2n/3) using O(2n/3) running times, where n is the input bit length of the hash function. The quantum circuit complexity is apparently reduced from O(2n/2) to O(2n/3) at the cost of O(2n/3) running times requirements compared with the existing algorithms.
We propose a preimage attack against cryptographic hash functions based on the speedup enabled by quantum computing. Preimage resistance is a fundamental property cryptographic hash functions must possess. The motivation behind this work relies in the lack of conventional attacks against newly introduced hash schemes such as the recently elected SHA-3 standard. The proposed algorithm consists of two parts: a classical one running in O(log |S|), where S represents the searched space, and a quantum part that contains the bulk of the Deutsch-Jozsa circuit. The mixed approach we follow makes use of the quantum parallelism concept to check the existence of an argument (preimage) for a given hash value (image) in the preestablished search space. For this purpose, we explain how a non-unitary measurement gate can be used to determine if S contains the target value. Our method is entirely theoretical and is based on the assumptions that a hash function can be implemented by a quantum computer and the key measurement gate we describe is physically realizable. Finally, we present how the algorithm finds a solution on S.
Hash functions are a basic cryptographic primitive. Certain hash functions try to prove security against collision and preimage attacks by reductions to known hard problems. These hash functions usually have some additional properties that allow for that reduction. Hash functions which are additive or multiplicative are vulnerable to a quantum attack using the hidden subgroup problem algorithm for quantum computers. Using a quantum oracle to the hash, we can reconstruct the kernel of the hash function, which is enough to find collisions and second preimages. When the hash functions are additive with respect to the group operation in an Abelian group, there is always an efficient implementation of this attack. We present concrete attack examples to provable hash functions, including a preimage attack to ⊕\oplus⊕-linear hash functions and for certain multiplicative homomorphic hash schemes.
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.
We propose a quantum hash function based on Gaussian boson sampling on a photonic quantum computer, aiming to provide quantum-resistant security. Extensive simulations demonstrate that this hash function exhibits strong properties of preimage, second preimage, and collision resistance, which are essential for cryptographic applications. Notably, the estimated number of attempts required for a successful collision attack increases exponentially with the mode counts of the photonic quantum computer, suggesting robust resistance against birthday attacks. We also analyze the sampling cost for physical implementation and discuss potential applications to blockchain technologies, where the inherent quantum nature of the hash computation could provide quantum-resistant security. The high dimensionality of the quantum state space involved in the hashing process poses significant challenges for quantum attacks, indicating a path towards quantum security. Our work lays the foundation for a new paradigm of quantum-resistant hashing with applications in emerging quantum-era information systems.
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.