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Paper: On the Feistel Counterpart of the Boomerang Connectivity Table: Introduction and Analysis of the FBCT

Authors:
Hamid Boukerrou , Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Paul Huynh , Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Virginie Lallemand , Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Bimal Mandal , Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Marine Minier , Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
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DOI: 10.13154/tosc.v2020.i1.331-362
URL: https://tosc.iacr.org/index.php/ToSC/article/view/8568
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Abstract: At Eurocrypt 2018, Cid et al. introduced the Boomerang Connectivity Table (BCT), a tool to compute the probability of the middle round of a boomerang distinguisher from the description of the cipher’s Sbox(es). Their new table and the following works led to a refined understanding of boomerangs, and resulted in a series of improved attacks. Still, these works only addressed the case of Substitution Permutation Networks, and completely left out the case of ciphers following a Feistel construction. In this article, we address this lack by introducing the FBCT, the Feistel counterpart of the BCT. We show that the coefficient at row Δi, ∇o corresponds to the number of times the second order derivative at points Δi, ∇o) cancels out. We explore the properties of the FBCT and compare it to what is known on the BCT. Taking matters further, we show how to compute the probability of a boomerang switch over multiple rounds with a generic formula.
BibTeX
@article{tosc-2020-30277,
  title={On the Feistel Counterpart of the Boomerang Connectivity Table: Introduction and Analysis of the FBCT},
  journal={IACR Transactions on Symmetric Cryptology},
  publisher={Ruhr-Universität Bochum},
  volume={2020, Issue 1},
  pages={331-362},
  url={https://tosc.iacr.org/index.php/ToSC/article/view/8568},
  doi={10.13154/tosc.v2020.i1.331-362},
  author={Hamid Boukerrou and Paul Huynh and Virginie Lallemand and Bimal Mandal and Marine Minier},
  year=2020
}