This study presents a novel approach to generating high-quality random numbers using a two-dimensional logistic map with a unit transfer function (2DLMUTF). The method is built upon the chaotic dynamics of the logistic map, where the parameter \(\:r\) governs the system’s behavior, exhibiting chaotic nature in the range of 3.57 to 4. By applying a unit transfer function and modulus operation, the system’s output is constrained within the [0, 1] range, altering the phase space dynamics compared to traditional 2D logistic maps. Numerical simulations in MATLAB, with parameters \(\:{r}_{1}\) =4, \(\:{r}_{2}\) =3.8, and initial seed values \(\:{x}_{0}\) =0.2350 and \(\:{y}_{0}\) =0.3500, were run for \(\:{10}^{6}\) iterations. Statistical testing using the NIST SP 800 − 22 test suite showed superior randomness, with the method passing all 15 tests. Additionally, uniformity, autocorrelation, cross-correlation, and entropy analyses confirmed the method’s suitability for cryptographic applications. The generated random numbers were used to create substitution boxes (S-boxes) for image encryption, demonstrating strong encryption performance. Overall, 2DLMUTF offers a computationally efficient and secure solution for random number generation which is suitable for cryptographic and image encryption applications.
