## 1 Introduction  
Images are a representative source of information [1] in different fields. Some of them require privacy and security because of their sensitive content, such as medical registers and personal identification. In this sense, Cryptography provides symmetric and asymmetric schemes for protecting data before storing and transmitting it. For this reason, many robust cryptosystems have emerged to cipher images [2; 3; 4; 5; 6]. Furthermore, the study of hybrid algorithms has increased since the benefits of including the strengths of symmetric and asymmetric cryptosystems simultaneously. In this way, symmetric cryptosystems will have a less drastic security impact in the age of quantum computers [7], while an asymmetric scheme permits key distribution and digital signatures. For these reasons, this research proposes a hybrid cryptosystem, which generates a seed with the Diffie-Hellman protocol based on ElGammal. This seed is sent to the receiver according to the Block-Chain technique as a string of SHA-512 strings. Subsequently, a fourteen-round symmetric cryptosystem is built using the seed over the Lorenz equations solution and a bijective function. The substitution boxes, permutations, and round keys are dynamic. This means that they are all different in each encryption process and round. The authors call this cryptosystem an Algorithm of Image Cipher using Lorenz equations and the Diffie-Hellman protocol (AICLDH). It is compatible with 256 grayscale levels and color images and the schedule keys bytes size is equal to the image pixel size. On the other hand, related works with hybrid algorithms, which include symmetric and asymmetric algorithms have been proposed. For instance, Elliptic Curve Cryptography(ECC) with Hill Cipher (HC), ECC with Advanced Encryption Standard (AES), and ElGamal with Double Playfair Cipher [8]. [PERSON] et al. propose a hybrid cryptosystem applying the RSA cryptosystem for the generation of a pair of public and private keys [9] that precede the diffusion and confusion process. Its security depends on the RSA algorithm. Moreover, the Diffie-Hellman protocol and SHA-256 function were used to cipher images. The first 128 bits verify confidentiality and the remaining 128 bits for authentication [10]. Some image encryption algorithms compute their security results based on similar evaluations and parameters to this proposal, and part of the numerical results achieved in this proposal is superior to them. For instance, [PERSON] et al. reported a maximum entropy of 7.99930 [11], which indicates high-quality encryption, and this work achieved a superior one equal to 7.99938. A comparative table is included in the discussion section. The number of elements in the key space, and the cipher image resistance to noise attacks, are other differences with other developments [12; 13; 14; 15]. In this order of ideas, these proposals have a number of elements in the key set less than ours because it is smaller than the \(2^{1024}\) elements reached by AICLDH. In addition, they do not analyze the noise attack on encrypted images, and the developments that include it do not quantify the loss of sharpness [11; 16] with any instrument. In contrast, this work proposes the SP parameter to measure it. All cipher quality evaluations examine at least two parameters: entropy and correlation. Although compressed images with loss of information, such as JPEG, do not include them. Just the correlation parameter is considered [17], and the entropy achieves a value near 7.8 [18]. In contrast, the entropy of cipher images with the proposal is close to 7.999. Due to the absence of encryption measures, the present work does not consider lossy compressed images. Another argument is that the normativity of some countries does not allow lossy compression for images. One example is Mexico [19]. In this case, the proposal suggests and works over the possibility of storing images using BMP files or others without loss of information.