Cryptanalyzing an Image Encryption Algorithm Underpinned by 2D Lag-Complex Logistic Map

TL;DR

This paper demonstrates a chosen-plaintext attack on an image encryption algorithm based on 2D lag-complex Logistic map, revealing vulnerabilities and reducing the number of required plaintexts for successful cryptanalysis.

Contribution

It introduces a divide-and-conquer attack strategy that exploits weaknesses in the 2D-LCLM-based encryption, significantly lowering the number of plaintexts needed for cryptanalysis.

Findings

The attack successfully compromises the encryption with fewer plaintexts.

The 2D-LCLM-based scheme has inherent vulnerabilities due to its pseudo-random sequence generation.

The required number of plaintexts scales with the image size, enabling practical cryptanalysis.

Abstract

This paper analyzes security performance of an image encryption algorithm using 2D lag-complex Logistic map (LCLM), which adopts it as a pseudo-random number generator, and uses the sum of all pixel values of the plain-image as its initial value to control the random combination of the basic encryption operations. However, multiple factors make the final pseudo-random sequences controlling the encryption process may be the same for different plain-images. Based on this point, we proposed a chosen-plaintext attack by attacking the six encryption steps with a strategy of divide and conquer. Using the pitfalls of 2D-LCLM, the number of required chosen plain-images is further reduced to $5\cdot\log_2(MN)+95$, where $\mathit{MN}$ is the number of pixels of the plain-image.