Secure chaotic system with application to chaotic ciphers

Chaotic cryptography has been widely investigated in the past few years. However, the undesirable dynamical properties of the underlying chaotic systems degrade the security of chaotic ciphers and thereby discourage their applications. To address this issue, this paper first presents discrimination criteria for secure chaotic systems (SCSs) whose dynamical properties make them useful for the construction of secure ciphers and then discusses a class of chaotic systems, digital dynamical filters (DDFs), that meet the SCS criteria. Then, a DDF-based pseudorandom bit generator (DDF-PRBG) for constructing stream ciphers is proposed. Theoretical analysis and simulation results demonstrate that both the DDF and the DDF-PRBG, which satisfy the SCS criteria, have desirable cryptographic properties. Consequently, the SCS criteria and the DDF reference model can be used to overcome the problems caused by the dynamical properties of the underlying chaotic systems and increase the security of chaotic ciphers.