A complex encryption algorithm has been developed based on traditional RSA (public key encryption algorithm), SHA-3 (hashing algorithm), and a discrete quantum map. The features of the proposed algorithm and the developed computer program in C++ are described. To evaluate the performance of the algorithm, testing was carried out on three encrypted images that differed in the volume of transmitted information. A comparative analysis of the obtained images with the original ones showed the efficiency of the information encryption algorithm using a discrete quantum map. This algorithm can also be used to perform additional operations related to including information inside the encrypted image, which will provide an additional level of protection when transmitting information.