Cryptanalysis of a Chaotic Stream Cipher and Its Improved Scheme

In this paper, the security performance for an 8D self-synchronous and feedback-based chaotic stream cipher with the low 8 bits of state variables for encryption is analyzed. According to known-plaintext attack and divide-and-conquer attack, only the second plain-pixel and its corresponding cipher-pixel are required to decipher the secret keys â_1i,â_2i,â_3i (i = 1, 2,⋯, 8) by properly setting 64 different kinds of initial conditions. Then, according to chosen-ciphertext attack and divide-and-conquer attack, it is found that under the condition of selecting the ciphertext as zero, the original chaotic equation is degenerated as a linear one. So, by setting appropriate initial conditions, the secret keys â_4i,â_5i,â_6i,â_7i,â_8i (i = 4, 5, 6, 7, 8) can be deciphered with only four iterative operations. As for the secret keys a_4i,a_5i,a_6i,a_7i,a_8i (i = 1, 2, 3) multiplied by ciphertext and the secret keys σ_i,∈_i (i = 1, 2, 3) related to nonlinear functions, maybe a more powerful attack method is required for these secret keys to be deciphered. Finally, an improved chaotic stream cipher scheme equipped with the low 8 bits derived from nonlinear operation of multiple state variables for encryption is proposed for improving the ability to resist divide-and-conquer attack and chosen-ciphertext attack.