Security of chaotic cryptosystems

In this thesis, we tried to show the weaknesses of chaotic cryptosystems. We break four chaos-based cryptosystems and proved our attacks.In our ? rst cryptanalysis, we broke a cryptosystem based on two dimensional chaotic maps. We ? rst reveal a portion of the secret key using a chosen-ciphertext attack. After revealing this porion, we used it to reveal the other portions of the secret key. We developed three types of attack using algebraic properties of the permutations in revealing the rest. We ? nally published two papers for this break.In our second cryptanalysis, we broke a cryptosystem that encrypts and decrypts images with chaotic map lattices. Here we ? rst show that the encryption algorithm is not invertible for some cases. We showed why these cases not work, and gave some suggestions to improve the algorithm. However, we showed that the algorithm still is not invertible due to ? nite precision arithmetic. Furthermore, we gave some suggestions to develop the algorithm. At the end of our work, we gave a break for the modi ? ed algorithm. Finally, we published a comment for the wrong cases.In our third cryptanalysis, we broke a chaos-based image encryption algorithm, which uses a two-dimensional chaotic map to shu ? e the image pixels and a three-dimensional chaotic map to change the gray levels of the pixels. We used a chosen-plaintext attack and a known-plaintext attack to break the algorithm. Applying either our chosen-plaintext attack or our known-plaintext attack the cryptosystem yields the secret parameters successfully. We published a paper for this break.Our ? nal cryptanalysis was on an image encryption algorithm based on two-dimensional chaotic maps. We showed that the chaotic map can be revealed using a chosen-ciphertext attack. The attack does not depend on which type of map isused. The attack uses some algebraic properties of permutations and graphs.