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

Hamid Boukerrou 1 Paul Huynh 1 Virginie Lallemand 1 Bimal Mandal 1 Marine Minier 1
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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.
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Submitted on : Monday, October 26, 2020 - 3:06:32 PM
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Hamid Boukerrou, Paul Huynh, Virginie Lallemand, Bimal Mandal, Marine Minier. On the Feistel Counterpart of the Boomerang Connectivity Table: Introduction and Analysis of the FBCT. IACR Transactions on Symmetric Cryptology, Ruhr Universität Bochum, 2020, 2020 (1), pp.331-362. ⟨10.13154/tosc.v2020.i1.331-362⟩. ⟨hal-02945065⟩

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