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Quantum key-recovery attack on Feistel constructions: Bernstein–Vazirani meet Grover algorithm

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Abstract

The development of quantum computers has urged the cryptographic community to prepare cryptographic primitives for the eventual arrival of the post-quantum world. At Asiacrypt 2017, Leander and May combined Grover’s and Simon’s quantum algorithms to break the FX-based block ciphers. Technically this result is based on the combination of the quantum algorithms of Grover’s and Simon’s for the first time in the cryptographic setting. In this study, we using Bernstein–Vazirani’s and Grover’s algorithms to generate a new quantum key-recovery attacks on different rounds of Feistel constructions. An advantage of our attack is the keys can be divided into multiple blocks to enter the S-box and realize the process of recovery; this method greatly reduces the complexity of key recovery. Hence, it has strong practicability for key recovery (e.g., DES, Camellia, etc.). In order to show that, a detailed process has been provided in this paper.

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Acknowledgements

This work is supported by the 13th Five-Year National Cryptographic Fund, No. MMJJ20180217.

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Authors and Affiliations

  1. College of Cybersecurity, University of Science and Technology of China, Hefei, 230026, China

    Bao-Min Zhou & Zheng Yuan

  2. Beijing Electronic Science Technology Institute, Beijing, 100070, China

    Bao-Min Zhou & Zheng Yuan

  3. College of Cybersecurity, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Zheng Yuan

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  1. Bao-Min Zhou
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  2. Zheng Yuan
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Correspondence to Zheng Yuan.

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Zhou, BM., Yuan, Z. Quantum key-recovery attack on Feistel constructions: Bernstein–Vazirani meet Grover algorithm. Quantum Inf Process 20, 330 (2021). https://doi.org/10.1007/s11128-021-03256-0

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