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Linear hulls with correlation zero and linear cryptanalysis of block ciphers

Abstract

Linear cryptanalysis, along with differential cryptanalysis, is an important tool to evaluate the security of block ciphers. This work introduces a novel extension of linear cryptanalysis: zero-correlation linear cryptanalysis, a technique applicable to many block cipher constructions. It is based on linear approximations with a correlation value of exactly zero. For a permutation on n bits, an algorithm of complexity 2n-1 is proposed for the exact evaluation of correlation. Non-trivial zero-correlation linear approximations are demonstrated for various block cipher structures including AES, balanced Feistel networks, Skipjack, CLEFIA, and CAST256. As an example, using the zero-correlation linear cryptanalysis, a key-recovery attack is shown on 6 rounds of AES-192 and AES-256 as well as 13 rounds of CLEFIA-256.

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Correspondence to Andrey Bogdanov.

Additional information

Communicated by L. R. Knudsen.

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Bogdanov, A., Rijmen, V. Linear hulls with correlation zero and linear cryptanalysis of block ciphers. Des. Codes Cryptogr. 70, 369–383 (2014). https://doi.org/10.1007/s10623-012-9697-z

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Keywords

  • Block ciphers
  • Correlation
  • Linear cryptanalysis

Mathematical Subject Classification

  • 94A60