Control-theoretical Concepts in the Design of Symmetric Cryptosystems

Abstract

In this chapter, it is shown how control-theoretical concepts can be useful in the design of symmetric cryptosystems. The authors first provide some background on cryptography with special emphasis on symmetric ciphering and, more specifically, on stream ciphers. It is explained how some permutation or substitution primitives can be derived from chaotic dynamical systems for cryptographic purposes. After a review of the most popular synchronization-based cryptosystems, a comparative study between these chaotic cryptosystems and the conventional symmetric ciphers, specifically stream ciphers, is carried out. In particular, it is shown that message-embedded chaotic ciphers and conventional self-synchronizing stream ciphers are structurally equivalent under the so-called flatness condition, a condition borrowed from control theory.