This paper proposes a new symmetric encryption system based on an elliptical curve and chaos, where the encryption is done in a single block and runs for 14 rounds. Here, the 15 encryption keys have the same size as the image and are generated using a solution point of a strong elliptic curve. Using a string of random numbers obtained with a logistic map, a permutation and its inverse are generated, which improve the encryption level and add diffusion to the cryptosystem. Another important contribution to this research is the generation of a substitution box with a non-linearity of 100, which strengthens the cryptosystem against differential and linear attacks that add confusion to the scheme. Moreover, the cryptographic properties of the proposed S-Box are compared with those of the S-Box of the Advanced Encryption Standard (AES) to ascertain that it is a suitable alternative that it is resistant to differential power analysis (DPA) attacks. To verify the robustness of proposed cryptosystem against cryptanalysis and the quality of the cipher text obtained, this system is subjected to different tests, such as entropy, correlation coefficient, ${\chi }^2$, Changing Pixel Rate (NPCR), and Unified Averaged Changing Intensity (UACI). The results are shown and compared with recently proposed systems.

A new symmetric cryptosystem is proposed in this paper which will be used to carry out image encryption without compression. The proposed system has been developed to encrypt images in BMP format. A significant contribution of this investigation is the use of one solution point of a zero valued constant elliptic curve in order to generate a set of 15 encryption keys. On the other hand, using a differential equation that produce chaotic numbers a permutation and its inverse permutation are generated. Every encryption key and both permutations are the same size as the image. The proposed cryptosystem is tested for the purpose of verifying its resistance against several cryptographic attacks as well as the randomness and quality of its ciphering. Results are showed and compared with some recent scientific articles published between 2017 and 2019.