Images with sensitive content require encryption for storage and transmission. Symmetric schemes can cipher them, while an asymmetric cryptosystem can distribute the secret key safely. For this reason, we propose a dynamic hybrid cryptosystem, which ciphers images and transfers its private keys. It has a symmetric algorithm that applies the Lorenz equations for generating different boxes and permutations in every encryption process and round. Since the secret key concatenates two private numbers, an asymmetric algorithm is included for its key distribution. The proposal uses the Diffie–Hellman protocol with ElGamal for obtaining a seed and building 128 strings. Then, the SHA-512 is applied in each of them a number of times associated with the secret key value in its blockchain representation. The resultant strings are concatenated to conform to the public key. Finally, the tests indicate that the cryptosystem resists differential, linear, algebraic, and brute-force attacks. Its cipher quality is high according to the entropy, correlation, DFT, NPCR, UACI, AC, texture analysis, and goodness of fit test. Additionally, occlusion, additive, multiplicative, and the proposed ${\chi }^2$ noise attacks are simulated on encrypted images. Finally, the sharpness loss is measured with the Similarity Parameter and improved with a filter 5 × 5.

Today, safeguarding sensitive content through encryption is crucial. This work presents a hybrid cryptosystem for images that employs both asymmetric and symmetric encryption. The asymmetric component involves applying the Diffie–Hellman protocol and the ElGamal cryptosystem to securely transmit two constants. These constants are necessary for the symmetrical aspect to generate dynamic permutations, substitution boxes, and round keys. Following an encryption process with fourteen rounds, the encrypted images are processed by an algorithm proposed to enhance entropy, a critical metric for assessing encryption quality. It increases the frequencies of the basic colors to achieve a histogram closely resembling a uniform distribution, but it increases the image size by approximately 8%. This improves the entropy values achieved by the hybrid cryptosystem, bringing them remarkably close to the ideal value of 8.0. In specific instances, the entropy values were elevated from 7.99926 to 8.0. The proposed method exhibits resilience against various attacks, including differential, linear, brute force, and algebraic attacks, as evaluated through the entropy, correlation, goodness of fit, Discrete Fourier Transform (DFT), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Avalanche Criteria (AC), contrast, energy, and homogeneity. Further, encrypted images are subjected to noise attacks ranging from 20% to 50% noise, including additive, multiplicative, occlusion noise, as well as the newly introduced ${\chi }^2$ noise. The noise damage is quantified using the proposed Similarity Parameter (SP), and a 3 × 3 median filter is employed to enhance the visual quality.

The negative–positive transformation (NPT) is a widely employed technique for encrypting images on pixel blocks, commonly integrated into cryptosystems compatible with compression algorithms. The existing literature on NPT analysis can be categorized into two types: theoretical analyses with results that apply to any image, primarily focused on compression compatibility, and numerical analyses that report empirical results from specific images, some without explaining the causes of the security results, while others are only related to the compression performance. Consequently, there is a significant gap in understanding the implications of applying the NPT for data protection. For that reason, this paper conducts a theoretical statistical analysis, presenting, demonstrating, and verifying six theorems to understand the security contributions of NPT. Two theorems examine the shape of the image histogram and the scatter plot of adjacent pixels after the NPT application. The subsequent four theorems explore the influence of NPT on the mean, variance, covariance, and correlation within each pixel block. The findings indicate that the NPT generates images with symmetrical histograms, the correlation of pixel blocks remains invariant, and distinct vertical and horizontal reflections manifest on the scatter plot. These theorems are verified by encrypting the Lena image with four pixel-block sizes. The histogram symmetry passed the goodness-of-fit test at a significance level of 5%, revealing consistent results. The correlation of pixel blocks remained unchanged, and the scatter plot exhibited an x-shaped pattern. Therefore, as the NPT alone does not achieve desirable encryption results, such as uniform histograms, scatter plots, and decreasing correlation, cryptosystems should complement it with additional techniques.

Some images that contain sensitive information and travel through the network require security. Therefore, a symmetric cryptosystem that encrypts images and resists known attacks is developed. Subsequently, in this work, an encryption algorithm known as Image Cipher utilizing Lorenz equation and a Bijective Function—ICLEBF are proposed. In the proposal, the Lorenz equations and the Bijective function are used to generate boxes, the permutation, and schedule keys, considering that all these elements are different in each encryption process. The encryption procedure consists of 14 rounds, where a different box is applied in each round. In this type of algorithm, the impact of quantum computers will be less forceful and can be useful for that epoch. On the other hand, the quality of the encrypted images and the loss of sharpness in decoded images with damage are measured. In addition, an attack from five types of noise (one of which is a developed proposal) is carried out by applying it to encrypted images. Finally, the results of the proposed ICLEBF are compared with other recent image encryption algorithms, including the Advanced Encryption Standard. As a result, this proposal resists known attacks and others that the current standard does not support.

Given the large volumes of sensitive information transmitted over the Internet, digital signatures are essential for verifying message authenticity and integrity. A key challenge is minimizing computationally intensive operations, such as modular inverses, without compromising security. In this research, we propose the DSADH $$\pi$$ algorithm, which introduces a confusion step directly into the signature itself, rather than only applying it to the message, using a dynamic substitution box. It is generated with the number pi and changes with each signing. In addition, to enhance security, this work uses a 2048-bit prime, double the length frequently used. This proposal induces chaotic behavior in the signature, making it highly sensitive to any changes in the signer’s private key or message content, thereby enhancing authentication and integrity verification. Moreover, the proposed algorithm computes a single multiplicative modular inverse during verification and none during signing, unlike other approaches that require inverse computation in both stages. Since the required inverse is for the Diffie-Hellman session key, it always exists and can be precomputed per communication rather than per message. Consequently, DSADH $$\pi$$ is on average 45 times faster than DSA. Additionally, we introduce a method to assess signature security by constructing images from signature bytes generated by slight changes to the signer’s private key and message. Then, their chaotic behavior is evaluated with cryptographic metrics.

In this work, a proposal to quantify the security gap between Encryption-then-Compression (EtC) systems and the Substitution-Permutation Network (SPN) is presented. A new image transmission system for JPEG files, EtC with Quantization before Transformation (EtCQT) was developed to test the proposed comparison. SPN is a well-known model used for security comparisons but is incompatible with the lossy compression required for saving storage while transmitting images. EtC systems have been designed considering compression performance rather than security, and in most developments in this field, only compression parameters are evaluated. The proposed evaluation was carried out with the metrics used for SPN, and the results showed the weaknesses of the EtC systems by quantifying them. This could help to improve security while keeping compatibility in future designs. EtCQT is based on the EtC scheme combined with block scrambling, with a quantization step instead of a permutation in the color transformation stage. The impact of this modification is an important reduction of the original pixel values in the color distribution that increases the information security, preserving only 16.6% of the initial values compared to 50% in other EtC systems.