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Lecture notes in computer science

Misuse Attacks on Post-quantum Cryptosystems

Ciprian Băetu, F. Betül Durak, Loïs Huguenin-Dumittan, Abdullah Talayhan, Serge Vaudenay B

Published Jan 1, 2019• 47 citations
Publisher
DOI
10.1007/978-3-030-17656-3_26

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Research on the security of lattice-based public-key encryption schemes against misuse attacks is an important part of the cryptographic assessment of the National Institute of Standards and Technology (NIST) post-quantum cryptography (PQC) standardization process. In particular, many NIST-PQC cryptosystems follow the same meta-cryptosystem. At EUROCRYPT 2019, Ba˘etu et al. mounted a classical key recovery under plaintext checking attacks (KR-PCA) and a quantum key recovery under chosen ciphertext attacks (KR-CCA). They analyzed the security of the weak version of nine submissions to NIST. In this paper, we focus on learning with error (LWE)-based FrodoPKE, whose IND-CPA security is tightly related to the hardness of plain LWE problems. We first review the meta-cryptosystem and quantum algorithm for solving quantum LWE problems. Then, we consider the case where the noise follows a discrete Gaussian distribution and recompute the success probability for quantum LWE by using Hoeffding bound. Finally, we give a quantum key recovery algorithm based on LWE under CCA attack and analyze the security of Frodo. Compared with the existing work of Ba˘etu et al., our method reduces the number of queries from 22 to 1 with the same success probability.
Abstract Due to the development of quantum computing, there is a need for the development and analysis of cryptosystems resistant to attacks using a quantum computer (post-quantum cryptography algorithms). The security of many well-known post-quantum cryptosystems based on lattice theory depends on the complexity of solving the shortest vector problem (SVP). In this paper, a model of quantum oracle developed from Grover’s algorithm is described to implement a hybrid quantum–classical algorithm based on GaussSieve. This algorithm can be used for attacks on cryptosystems whose security depends on solving the SVP. Upper bounds for the number of qubits and the depth of the circuit were obtained for two implementations of the proposed quantum oracle model: minimizing the number of qubits and minimizing the circuit depth. The complexity of implementing the proposed quantum oracle model to attack post-quantum lattice-based cryptosystems that are finalists of the NIST post-quantum cryptography competition is analyzed.