Divide-and-conquer attack on XW chaotic cipher

For a block cryptosystem based on iterating chaotic map proposed by Xu Shu-jiang et al.,this paper found that the first several bits in quantified sequence generated by chaotic sequence were not sensitive to the least significant bits of chaos initial state.Under the chosen plaintexts attack,based on this information leakage,this paper proposed a divide-and-conquer attack to recover the chaos initial state from the consecutive segment of quantified sequence via attacking the higher significant bits first and the lower significant bits second.When the parameter r= 4 and the length of key is of 64-bit length,the success probability of the divide-and-conquer attack is 0.930 5 and the computational complexity is about 219.7,the memory complexity is about 211.6 and the data complexity is 1 chosen plaintext-ciphertext pair.