In recent years, a considerable number of chaotic cryptosystems have been proposed. The properties of chaotic systems, such as ergodicity, random-like behavior, and sensitivity to initial conditions, are useful in cryptography. The crucial points in chaotic cryptography are continuous-value information and the usage of continuous-value systems which may operate in continuous or discrete time. When speaking about conventional cryptography, it means cryptosystems which work on discrete values and in discrete time. In this thesis, we have divided the algorithms into block cipher, stream cipher, and single-character categories. At first, several stream and single-character algorithms have been investigated, but because of importance of block ciphers, these algorithms were studied further. In block ciphers, the substitution boxes (S-boxes) are their core component and have been widely used in almost all block ciphers. The discussion of block ciphers based on chaotic maps were studied into aspects, designing S-boxes and designing of block cipher , that these two issues are investigated separately. Accordingly, the first few S-boxes based on chaotic map were introduced and investigated their design criteria. As a result, by comparing criteria of S-boxes based on chaotic maps and AES S-box, which considered ideal, it was found that the statistical criteria of S-boxes based on chaotic maps are much weaker than AES S-box. In addition, we introduced several block cipher algorithms based on chaotic maps which have been proposed in recent years and one of them were analyzed and based on its flaws we introduced a novel attack on it. Keywords: Chaotic maps, Cryptography, Block cipher, S-box
