Column Parity Mixers

Authors

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

DOI:

https://doi.org/10.13154/tosc.v2018.i1.126-159

Keywords:

mixing layers, iterative permutations, iterative block ciphers

Abstract

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.

Published

2018-03-01

Issue

Section

Articles

How to Cite

Column Parity Mixers. (2018). IACR Transactions on Symmetric Cryptology, 2018(1), 126-159. https://doi.org/10.13154/tosc.v2018.i1.126-159