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Quantum security analysis of Rocca

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Abstract

The recent developments in the creation of large-scale, commercially feasible quantum computers puts both symmetric and asymmetric encryption at risk. As they assess the security of 5G and beyond, the telecommunication standards groups are now inviting recommendations that take the threat posed by quantum adversaries into account. Rocca is the first cipher designed that complies with 6G specifications. In this paper we analyze the security of Rocca against quantum adversaries. We first construct the quantum circuit of Rocca and estimate the cost of implementing Grover’s algorithm for key recovery. We also compute the cost under the NISTs MAXDEPTH restriction. We then find a differential distinguisher for 5 and 6 rounds in secret key settings and related key settings respectively. In the nonce-respecting settings, we discover that Rocca is susceptible to a quantum forging attack with a complexity of \({\mathcal {O}}(2^{75})\) in the Q2 settings, i.e., if the adversary is given access to quantum superposition queries to the cryptographic oracle. This complexity is considerably less than the complexity of \({\mathcal {O}}(2^{128})\) claimed by the authors. Thus we propose that the number of initialization rounds in Rocca can be reduced without compromising its security and the tag length should be increased to 256-bits.

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Notes

  1. As described in Remark 2, it is enough to obtain two 256 bit plaintext-ciphertext pairs to obtain the unique key using Grover’s search algorithm. Thus in the estimation of Grover’s search algorithm for the secret key we fix \( |m| =1\).

  2. In differential cryptanalysis, the attacker first chooses a pair of an input difference and an output difference that will be propagated with a high probability. Th propagation of the difference in the attack between the chosen differences is called differential cryptanalysis.

  3. A byte with non-zero difference through the AES SubBytes operation is called an active byte with respect to the difference, or simply an active byte.

  4. The differences in the input values to the cipher E.

  5. The differences in the output values from the cipher E.

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Acknowledgements

We would like to thank the authors of [5] for sharing their ideas on how to construct quantum circuits and especially the computation of resource estimation of the circuits which we have used in Sect. 2.3.

Funding

This research was conducted under a contract of “Research and development on new generation cryptography for secure wireless communication services” among “Research and Development for Expansion of Radio Wave Resources (JPJ000254)”, which was supported by the Ministry of Internal Affairs and Communications, Japan.

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Authors and Affiliations

  1. Graduate School of Information Sciences, University of Hyogo, Kobe, Japan

    Ravi Anand & Takanori Isobe

  2. National Institute of Information and Communication Technology, Organization, Koganei, Japan

    Takanori Isobe

  3. PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan

    Takanori Isobe

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  1. Ravi Anand
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Anand, R., Isobe, T. Quantum security analysis of Rocca. Quantum Inf Process 22, 164 (2023). https://doi.org/10.1007/s11128-023-03908-3

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