A pseudo-random numbers generator based on a novel 3D chaotic map with an application to color image encryption

In this work, we propose a novel 3D chaotic map obtained by coupling the piecewise and logistic maps. Showing excellent properties, like a high randomness, a high complexity and a very long period, this map has enabled us to implement and investigate a new chaotic pseudo-random number generator (CPRNG). The produced pseudo-random numbers exhibit a uniform distribution and successfully pass the NIST SP 800-22 randomness tests suite. In addition, an application in the field of color image encryption is proposed where the encryption key is strongly correlated with the plain image and is then used to perform the confusion and diffusion stages. Furthermore, the ability to expand the size of our map has an impact on the complexity of the system and increases the size of the key space, making our cryptosystems more efficient and safer. We also give some statistical tests and computer simulations which confirm that the proposed algorithm has a high level of security.