4.4 Article

Using Bernstein-Vazirani algorithm to attack block ciphers

Journal

DESIGNS CODES AND CRYPTOGRAPHY
Volume 87, Issue 5, Pages 1161-1182

Publisher

SPRINGER
DOI: 10.1007/s10623-018-0510-5

Keywords

Post-quantum cryptography; Quantum cryptanalysis; Differential cryptanalysis; Block cipher

Funding

  1. National Natural Science Foundation of China [61672517]
  2. National Cryptography Development Fund [MMJJ201 70108]
  3. Fundamental theory and cutting edge technology Research Program of Institute of Information Engineering, CAS [Y7Z0301103]

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In this paper, we study applications of Bernstein-Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it, we propose new quantum distinguishers for the 3-round Feistel scheme and a new quantum algorithm to recover partial key of the Even-Mansour construction. Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential cryptanalysis respectively. We also propose a new kind of differential cryptanalysis, called quantum small probability differential cryptanalysis, based on the fact that the linear structures found by our algorithm are also the linear structure of each component function. To our knowledge, no similar method was proposed before. The efficiency and success probability of all attacks are analyzed rigorously. Since our algorithm treats the encryption function as a whole, it avoid the disadvantage of traditional differential cryptanalysis that it is difficult to extending the differential path.

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