Nonlinear Approximations in Cryptanalysis Revisited


  • Christof Beierle Interdisciplinary Centre for Security, Reliability and Trust (SnT) , University of Luxembourg, Luxembourg, Luxembourg
  • Anne Canteaut Inria, Paris, France
  • Gregor Leander Horst Görtz Institute for IT Security, Ruhr-Universität Bochum, Bochum, Germany



Block cipher, Nonlinear invariant, Invariant subspace attack, Nonlinear approximations, Linear cryptanalysis, Midori


This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts.



How to Cite

Beierle, C., Canteaut, A., & Leander, G. (2018). Nonlinear Approximations in Cryptanalysis Revisited. IACR Transactions on Symmetric Cryptology, 2018(4), 80–101.