Analysis On Three Chaotic Ciphers

We analyze the security of three chaotic ciphers,and the results could be summarized as follows:For an improved block cryptosystem based on iterating chaotic map proposed by Xu Shu-jiang et al.,we find that the first several bits in quantified sequence generated by chaotic sequence are still not sensitive to the least significant bits of chaos initial state.Under the choosen plaintexts attack,we could obtain a consecutive segment of the quantified sequence through a choosen plaintext-ciphertext pair.Based on the above information leakage,we propose a divide-and-conquer attack to recover the chaos initial state from the consecutive segment of quantified sequence.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 0.9305 and the computational complexity is about 2^19.7,the memory complexity is about 2^11.6 and the data complexity is about 2^11.6.For a chao-based stream cipher proposed by Luo Qi-bin et al.,we find that the first several key stream bits of this chaotic cipher are not sensitive to the least significant bits of key.Based on this information leaking,a divide-and-conquer attack is presented to decrease the entropy of key.When the parameterα₁=1.8,α₂=2,b=0.85,j=1,N₁=1 and the length of key is 64-bit,the success probability of the divide-and-conquer attack is 0.9050 and the average computational complexity is abou 2^17.86.For a chaos-based video encryption algorithm proposed by Ding Wen-xia et al.,we find that this encryption algorithm is a shifted cipher.Then we give an attack on this shifted cipher and recover the quantified sequence generated by chaotic sequence.Furthermore,we find that the first several bits in quantified sequence are not sensitive to the least significant bits of chaos initial state.Based on this property,we propose a divide-and-conquer attack to recover the chaos initial state from quantified sequence.When the parameter k=4,r=4 and the length of key is 56-bit,the success probability of the divide-and-conquer attack is 0.9171 and the computational complexity is about 2²⁸ and the memory complexity is about 2²⁰.