We have proposed a chaotic cryptographic scheme based on iterating the logistic
map and updating the look-up table dynamically. However, it has been broken recently. In
this paper, the weaknesses of the original dynamic look-up table scheme are analyzed and
a more secure chaotic encryption scheme based on this dynamic look-up table concept is
proposed. Theoretical analysis indicates that the modified scheme can resist the reported
attacks. Moreover, simulation results show that this encryption scheme leads to a flat
ciphertext distribution.