There have been strong links between chaotic theory and cryptographic theory for the last three decades. The characterization of behaviors of the Chaotic system, such as: highly responsive to initial states, mixing attributes, deterministic existence, and often unable to predict long-term returns, allows researchers improve the security of cryptography systems. As a result, there are growing numbers of experiments that have been proposed using chaotic-based random number generators. Furthermore, These proposed generators suffer from minimal key space and those centered on a 1D chaotic map have limited capacity to produce entropy due to their limited number of exponents of Lyapunov (s). Random binary sequence generator producing sequence of bits has been proposed in this paper. The proposed system model consists of two parts that use mouse device data constructively as the basis for the theory of non-determinism and chaos. The chaos theory includes three forms with the mouse cursor coordinates while moving as the initial seeds in this proposed system (1D logistic chaotic system, 2D Hénon system and 3D chaotic system) and combines the values produced in the algorithm. With 1D, 2D Hénon, 3D chaotic maps, the mouse cursor coordinates are treated as an initial random number with post processing to increase the randomness and security of the keys. In the suggested research, there is high key space and a very long time. It is also evident that the developed keys have successful statistical features that require purely random binary sequences that are optimal for use in essential cryptography systems provided by evaluating the results of 16 NIST hardness tests (National Institute of Standards and Technology).