It is pointed out that the two stream ciphers proposed respectively in "Generating nonlinear feedback stream ciphers via chaotic systems" and in "The theoretical design for a class of new chaotic feedback stream ciphers" have the property that the frontal values of the output sequences of the two stream ciphers are not sensitive to the least significant bits of the key.So they can be attacked effectively by the divide-and-conquer attack

which attacks the most significant bits of key at first and the least significant bits of key secondly

with the known chaotic transformations and known plaintexts.An optimal exhaustive attack with the minimum computing complexity is proposed under the condition that the distribution of the key is known.Furthermore

an improved divide-and-conquer attack is proposed and its computing complexity and success probability is analyzed.