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International Conference on Network and System Security

NSS 2022: Network and System Security pp 687–711Cite as

Evaluating the Security of Merkle-Damgård Hash Functions and Combiners in Quantum Settings

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13787))

Abstract

In this work, we evaluate the security of Merkle-Damgård (MD) hash functions and their combiners (XOR and concatenation combiners) in quantum settings. Two main quantum scenarios are considered, including the scenario where a substantial amount of cheap quantum random access memory (qRAM) is available and where qRAM is limited and expensive to access. We first convert a rich set of known tools invented for generic attacks in the classical setting to quantum versions. That includes Joux’s multi-collision, expandable message, diamond structure, and interchange structure. With these basic tools in hand, we then present generic quantum attacks on the MD hash functions and hash combiners, and carefully analyze the complexities under both quantum scenarios. The considered securities are fundamental requirements for hash functions, including the resistance against collision, (second-)preimage, and herding attacks. The results are consistent with the conclusions in the classical setting, that is, the considered resistances of the MD hash functions and their combiners are far less than ideal, despite the significant differences in the expected security bounds between the classical and quantum settings. Particularly, the generic attacks can be improved significantly using quantum computers under both scenarios. These results serve as an indication that classical hash constructions require careful security re-evaluation before being deployed to the post-quantum cryptography schemes.

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Notes

  1. 1.

    In graph \( \mathcal {G} \), if there exists a set of edges, no two of which share a vertex, then the set of edges is called a matching. M is a maximum matching in \( \mathcal {G} \) if no matching in \( \mathcal {G} \) contains more edges than M does. If matching M in \( \mathcal {G} \) contains every vertex, then M is called a perfect matching. Our goal here, is to find a perfect matching in \( \mathcal {G} = (\mathcal {V}, \mathcal {E}) \), of which the vertex set is \( \mathcal {V} = \{x_1, \ldots , x_{2^t} \} \) and \( (x_i, x_j) \in \mathcal {E} \) if \( x_i \) and \( x_j \) generate an obtained collision.

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Authors and Affiliations

  1. School Of Physical And Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Zhenzhen Bao, Jian Guo, Shun Li & Phuong Pham

  2. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Shun Li

  3. Institute for Network Sciences and Cyberspace, Tsinghua University, Beijing, China

    Zhenzhen Bao

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  1. Zhenzhen Bao
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  2. Jian Guo
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  3. Shun Li
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  4. Phuong Pham
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Corresponding authors

Correspondence to Zhenzhen Bao , Jian Guo , Shun Li or Phuong Pham .

Editor information

Editors and Affiliations

  1. Monash University, Clayton, VIC, Australia

    Xingliang Yuan

  2. The University of Queensland, Queensland, QLD, Australia

    Guangdong Bai

  3. University of Malaga, Málaga, Spain

    Cristina Alcaraz

  4. Concordia University, Montreal, QC, Canada

    Suryadipta Majumdar

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Bao, Z., Guo, J., Li, S., Pham, P. (2022). Evaluating the Security of Merkle-Damgård Hash Functions and Combiners in Quantum Settings. In: Yuan, X., Bai, G., Alcaraz, C., Majumdar, S. (eds) Network and System Security. NSS 2022. Lecture Notes in Computer Science, vol 13787. Springer, Cham. https://doi.org/10.1007/978-3-031-23020-2_39

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  • DOI: https://doi.org/10.1007/978-3-031-23020-2_39

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