The real-time constraint for the codec execution and high security level protection are the two most important multimedia encryption requirements. In this paper, a method is presented for the fast generation of large permutation and diffusion keys, which are based on the sorting of the solutions of the linear Diophantine equation (LDE). The coefficients of the LDE are integers which can be dynamically generated from any type of dynamical chaotic systems, as the maximum precision of the computer can be used for the conversion of floating-point chaotic values into integers. This technique yields a fast image block encryption algorithm in which the security level is considerably strengthened. Although the architecture used in this cipher is the one for which the permutation and diffusion are considered as two separate stages, the generation speed of permutation and diffusion keys allows reducing the computational time required by the duplication of the image-scanning stage during the permutation and diffusion operations.