Image encryption schemes based on chaos usually involve real number arithmetic operations to generate the chaotic orbits from the chaotic system. These operations are time-consuming and are normally performed with high-end processors. To overcome this drawback, this paper proposes a one round encryption scheme for the fast generation of large permutation and diffusion keys based on the sorting of the solutions of the Linear Diophantine Equation (LDE) whose coefficients are integers and dynamically generated from any type of chaotic systems. The high security and low computational complexity are achieved not only by using large permutation based on the sorting of the solutions of LDE but also by generating only one permutation from the sorting of the solutions of the LDE, then by dynamically updating d number of integers (d>2) in the permutation. The performance of the proposed scheme is evaluated using various types of analysis such as entropy analysis, difference analysis, statistical analysis, key sensitivity analysis, key space analysis and speed analysis. The experimental results indicate that the proposed algorithm is secure and fast as compared to the two round encryption scheme.