In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of chaotic systems. Chaos could be helpful in the three functional components of compression, encryption, and modulation in a digital communication system. To successfully use chaos theory in cryptography, chaotic maps must be built in such a way that the entropy they produce can provide the necessary confusion and diffusion. A chaotic map is used in the first layer of such cryptosystems to create confusion, and a second chaotic map is used in the second layer to create diffusion and create a ciphertext from a plaintext. A secret key generation mechanism and a key exchange method are frequently left out, and many researchers just assume that these essential components of any effective cryptosystem are always accessible. We review such cryptosystems by using a cryptosystem of our design, in which confusion in plaintext is created using Arnold's Cat Map, and logistic mapping is employed to create sufficient dispersion and ultimately get a matching ciphertext. We also address the development of key exchange protocols and secret key schemes for these cryptosystems, as well as the possible outcomes of using cryptanalysis techniques on such a system.