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Paper 2017/990

Bounds on the Differential Branch Number of Permutations

Sumanta Sarkar and Habeeb Syed

Abstract

Nonlinear permutations (S-boxes) are key components in block ciphers. Differential branch number measures the diffusion power of a permutation. Differential branch number of nonlinear permutations of $\mathbb{F}_2^n$ has not been analyzed, although it is well studied for linear permutations. In this paper we obtain a bound on differential branch number of permutations (both linear and nonlinear) of $\mathbb{F}_2^n$. We also show that in case of $\mathbb{F}_2^4$, the maximum differential branch number can be achieved only by affine permutations.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
PermutationS-boxdifferential branch numberblock cipherGriesmer bound
Contact author(s)
sumanta sarkar1 @ tcs com
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
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