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arXiv:1902.08709 · Lecture notes in computer science

Quantum Security of Hash Functions and Property-Preservation of Iterated Hashing

Ben Hamlin, Fang Song

Published Jan 1, 2019• 14 citations
arXivHTMLPDF
DOI
10.1007/978-3-030-25510-7_18

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Hash functions play a fundamental role in cryptography, offering one-way and collision-resistant properties essential for digital security. Chameleon hashing, an extension of traditional hash functions, allows controlled collision generation using a private trapdoor, enabling various cryptographic applications such as online/offline digital signatures and commitment schemes. However, existing identity-based chameleon hash (IBCH) functions largely rely on number-theoretic assumptions, which are vulnerable to quantum attacks. To address this issue, we propose a novel IBCH function built upon post-quantum lattice-based cryptography. Specifically, our construction leverages the Short Integer Solution (SIS) problem to achieve quantum-resistant security guarantees. The proposed scheme enables identitybased key management, allowing users to generate hash values using public identity information while preserving the trapdoorcontrolled collision property. We rigorously analyze the security of our scheme, demonstrating its resistance against quantum adversaries under standard lattice assumptions. Furthermore, we compare our construction with existing functions in terms of computational efficiency and security, showing that our approach provides a feasible and secure alternative for post-quantum applications.
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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.