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.
The work is concerned with dead-beat stability of autonomous discrete-time switched linear systems, having in mind a potential application to cryptography. As far as control theory is concerned, we propose an algorithm to construct a switched system whose shorter dead-beat stabilizing sequence has a prescribed length. We discuss the pecularities when the dynamical systems under consideration are defined over finite fields. Then, it is shown how the algorithm can be used to addressed the design of self-synchronizing stream ciphers involving switched automata.
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