International Association for Cryptologic Research

International Association
for Cryptologic Research


Column Parity Mixers

Ko Stoffelen , Digital Security Group, Radboud University, Nijmegen
Joan Daemen , Digital Security Group, Radboud University, Nijmegen, The Netherlands; STMicroelectronics
DOI: 10.13154/tosc.v2018.i1.126-159
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Abstract: We present column parity mixers (CPM), a generalization of the ╬ś 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.
  title={Column Parity Mixers},
  journal={IACR Trans. Symmetric Cryptol.},
  publisher={Ruhr-Universit├Ąt Bochum},
  volume={2018, Issue 1},
  author={Ko Stoffelen and Joan Daemen},