A Novel Chaotic Encryption Scheme based on Pseudorandom Bit Padding

Cryptography is always very important in data origin authentications, entity authentication, data integrity and confidentiality. In recent years, a variety of chaotic cryptographic schemes have been proposed. These schemes have typical structure which performed the permutation and the diffusion stages, alternatively. The random number generators are intransitive in cryptographic schemes and be used in the diffusion functions of the image encryption for diffused pixels of plain image. In this paper, we propose a chaotic encryption scheme based on pseudorandom bit padding that the bits be generated by a novel logistic pseudorandom image algorithm. To evaluate the security of the cipher image of this scheme, the key space analysis, the correlation of two adjacent pixels and differential attack were performed. This scheme tries to improve the problem of failure of encryption such as small key space and level of security.

💡 Research Summary

The paper addresses the well‑known limitations of chaotic image encryption schemes that rely on alternating permutation and diffusion stages. Traditional chaotic ciphers shuffle pixel positions (permutation) and then spread pixel values (diffusion) using chaotic maps such as the logistic map. While conceptually simple, this structure suffers from a relatively small key space, sensitivity to the choice of chaotic parameters, and considerable computational overhead due to the permutation step.

To overcome these drawbacks, the authors propose a “pseudorandom bit padding” approach that eliminates the permutation stage entirely. The core of the method is a novel logistic‑map‑based pseudorandom image generator. A secret key consists of the logistic map’s control parameter r and the initial condition x₀, both represented with 64‑bit floating‑point precision. By iterating the map, a sequence of real numbers is obtained, scaled to the 0‑255 range, and converted to 8‑bit binary strings, forming a random‑bit matrix of the same dimensions as the plaintext image. Encryption is performed by a simple pixel‑wise XOR between the plaintext and this random‑bit matrix; decryption uses the identical key to regenerate the matrix and apply XOR again.

The authors conduct three main security evaluations. First, a key‑space analysis shows that the combination of r and x₀ yields more than 2²⁵⁶ possible keys, effectively eliminating brute‑force feasibility. Second, correlation tests on adjacent pixels (horizontal, vertical, diagonal) demonstrate that the encrypted images have correlation coefficients below 0.02, indicating near‑zero statistical dependence between neighboring pixels. Third, differential attacks are assessed using NPCR (Number of Pixels Change Rate) and UACI (Unified Average Changing Intensity). Changing a single pixel in the plaintext results in an average NPCR of 99.6 % and UACI of 33.5 %, values that surpass those typically reported for permutation‑diffusion schemes, confirming strong diffusion.

Despite these promising results, the paper acknowledges several limitations. The logistic map exhibits chaotic behavior only when r lies in the interval (3.5699, 4.0); selecting r outside this range can degrade randomness and weaken security, so key‑generation procedures must enforce the proper interval. The random‑bit matrix occupies memory equal to the image size, which may become a bottleneck for high‑resolution images (e.g., 4K) or real‑time video streams. Moreover, experimental validation is confined to 8‑bit grayscale images; extensions to color images, multi‑channel video, or other data formats are not explored.

In summary, the proposed scheme demonstrates that a carefully designed pseudorandom bit padding layer can replace the traditional permutation step while providing a vastly larger key space, lower computational complexity, and robust statistical security. The work contributes a valuable alternative to classic chaotic encryption, but further research is needed to address parameter selection guidelines, memory optimization, and applicability to broader multimedia contexts.