Robustness of Affine and Extended Affine Equivalent Surjective S-Box(es) against Differential Cryptanalysis

Abstract

A Feistel Network (FN) based block cipher relies on a Substitution Box (S-Box) for achieving the non-linearity. S-Box is carefully designed to achieve optimal cryptographic security bounds. The research of the last three decades shows that considerable efforts are being made on the mathematical design of an S-Box. To import the exact cryptographic profile of an S-Box, the designer focuses on the Affine Equivalent (AE) or Extended Affine (EA) equivalent S-Box. In this research, we argue that the Robustness of surjective mappings is invariant under AE and not invariant under EA transformation. It is proved that the EA equivalent of a surjective mapping does not necessarily contribute to the Robustness against the Differential Cryptanalysis (DC) in the light of Seberry's criteria. The generated EA equivalent S-Box(es) of DES and other $6 \times 4$ mappings do not show a good robustness profile compared to the original mappings. This article concludes that a careful selection of affine permutation parameters is significant during the design phase to achieve high Robustness against DC and Differential Power Analysis (DPA) attacks.

Available format(s)
Category
Foundations
Publication info
Preprint.
Keywords
S-Box Block Ciphers Differential Cryptanalysis Robustness Differential Uniformity Affine Equivalence
Contact author(s)
sfahd phdismcs @ student nust edu pk
mehreenafzal @ mcs edu pk
dawoodshah254 @ gmail com
waseem iqbal @ mcs edu pk
atiyahai @ yahoo com
History
2022-11-29: last of 2 revisions
See all versions
Short URL
https://ia.cr/2022/1649

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BibTeX

@misc{cryptoeprint:2022/1649,
author = {Shah Fahd and Mehreen Afzal and Dawood Shah and Waseem Iqbal and Atiya Hai},
title = {Robustness of Affine and Extended Affine Equivalent Surjective S-Box(es) against Differential Cryptanalysis},
howpublished = {Cryptology ePrint Archive, Paper 2022/1649},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1649}},
url = {https://eprint.iacr.org/2022/1649}
}

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