Cryptanalysis of a Chaos-based Stream Cipher

In 2007, Fu Chong et al. proposed an improved chaos-based stream cipher. The secret key of Fu's cipher with 2¹⁵⁸ key space size composes of 3 independent chaos initial states. In this paper, the security of Fu's chaotic cipher is investigated and the information leak of chaos map that we call preimage compressibility is discovered. We guess one chaos initial state and obtain two sampling quantified sequences which are generated by other two chaos initial states. Then based on the preimage compressibility of chaos map, an inversion and compression attack is proposed to recover the chaos initial state from sampling quantified sequence. The success probability of the whole attack is 1 and the computational complexity is just about 2^60.7. The memory complexity and data complexity can be negligible.