Discrete Lyapunov Exponent and Differential Cryptanalysis

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Partly motivated by the developments in chaos-based block cipher design, a definition of the discrete Lyapunov exponent for an arbitrary permutation of a finite lattice was recently proposed. The authors explore the relation between the discrete Lyapunov exponent and the maximum differential probability of a bijective mapping (i.e., an S-box or the mapping defined by a block cipher). Their analysis shows that "Good" encryption transformations have discrete Lyapunov exponents close to the discrete Lyapunov exponent of a mapping that has a perfect non-linearity. The converse does not hold.