Summary This article puts forward a fast chaos‐RSA‐based hybrid cryptosystem to secure and authenticate secret images. The SHA‐512 is used to generate a 512‐bit initial key. The RSA system is used to encrypt the initial secret key and signature generation for both the sender and image authentication. In fact, a powerful block‐cipher algorithm is developed to encrypt and decrypt images with a high level of security. At this stage, a strong PRNG based on four chaotic systems is propounded to generate high‐quality keys. Therefore, an improved architecture is suggested. It performs confusion and diffusion of images with low computational complexity. In the final step, the encrypted secret key, signature, and encrypted image are combined together in order to obtain an encrypted signed image. The block‐cipher algorithm is evaluated in‐depth for several ordinary and medical images with different types, content, and size. The obtained simulation results demonstrate that the system enables high‐level security. The entropy has achieved a value of 7.9998 which is the most important feature of randomness. A comparative study against numerous recent encryption algorithms demonstrates that the proposed algorithm provides good results.