Cryptanalysis of some self-synchronous chaotic stream ciphers and their improved schemes

In this paper, a cryptanalysis method that combines a chosen-ciphertext attack with a divide-and-conquer attack by traversing multiple non-zero component initial conditions (DCA- TMNCIC) is proposed. The method is used for security analysis of n-D (n=3,4,5,6,7,8) self- synchronous chaotic stream ciphers that employ a product of two chaotic variables and three chaotic variables (n-D SCSC-2 and n-D SCSC-3), taking 3-D SCSC-2 as a typical example for cryptanalysis. For resisting the combinational effect of the chosen-ciphertext attack and DCA- TMNCIC, several improved chaotic cipher schemes are designed, including 3-D SCSC based on a nonlinear nominal system (3-D SCSC-NNS) and n-D SCSC based on sinusoidal modulation (n-D SCSC-SM (n=3,4,5,6,7,8)). Theoretical security analysis validates the improved schemes.