Column Parity Mixers


  • Ko Stoffelen Digital Security Group, Radboud University, Nijmegen, The Netherlands
  • Joan Daemen Digital Security Group, Radboud University, Nijmegen, The Netherlands; STMicroelectronics, Diegem, Belgium



mixing layers, iterative permutations, iterative block ciphers


We present column parity mixers (CPM), a generalization of the Θ mixing layer that is used in Keccak. Thanks to our description using matrix arithmetic, we can easily derive algebraic, diffusion, and mask propagation properties, leading to a surprising distinction between two types of CPMs. We compare CPMs to other popular types of mixing layers and argue that CPMs can be more efficient. While Keccak has a bit-oriented structure, we make the case that CPMs are also suitable for nibble- or byte-oriented designs. We outline a general substitution-permutation-network-based design strategy using a CPM, for which we show how one can attain strong bounds for differential and linear trails. We apply this strategy concretely to design a 256-bit permutation with an efficient inverse and strong trail bounds. Our permutation design uses a number of ideas that are of independent interest and allows a fast bitsliced implementation that compares quite well with other established ciphers and permutations.



How to Cite

Stoffelen, K., & Daemen, J. (2018). Column Parity Mixers. IACR Transactions on Symmetric Cryptology, 2018(1), 126–159.