Paper 2017/990

Bounds on Differential and Linear Branch Number of Permutations

Sumanta Sarkar and Habeeb Syed

Abstract

Nonlinear permutations (S-boxes) are key components in block ciphers. The differential branch number measures the diffusion power of a permutation, whereas the linear branch number measures resistance against linear cryptanalysis. There has not been much analysis done on the differential branch number of nonlinear permutations of $\mathbb{F}_2^n$, although it has been well studied in case of linear permutations. Similarly upper bounds for the linear branch number have also not been studied in general. In this paper we obtain bounds for both the differential and the linear branch number of permutations (both linear and nonlinear) of $\mathbb{F}_2^n$. We also prove that in the case of $\mathbb{F}_2^4$, the maximum differential branch number can be achieved only by affine permutations.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. ACISP 2018
Keywords
PermutationS-boxdifferential branch numberlinear branch numberblock cipherGriesmer bound.
Contact author(s)
sumanta sarkar @ gmail com
History
2018-05-11: revised
2017-10-11: received
See all versions
Short URL
https://ia.cr/2017/990
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/990,
      author = {Sumanta Sarkar and Habeeb Syed},
      title = {Bounds on  Differential and  Linear Branch Number of Permutations},
      howpublished = {Cryptology ePrint Archive, Paper 2017/990},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/990}},
      url = {https://eprint.iacr.org/2017/990}
}
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