[Paper Review] Differential cryptanalysis of image cipher using block-based scrambling and image filtering

Feng Yu, Xinhui Gong+2 more|arXiv (Cornell University)|Dec 31, 2018

Chaos-based Image/Signal Encryption26 references4 citations

TL;DR

This paper presents a differential cryptanalysis attack on the IC-BSIF image encryption scheme, demonstrating that a linear relation between plain-images and cipher-images can be constructed using differential analysis. By building a codebook of $M imes N + 1$ plain-image and cipher-image pairs, the scheme is shown to be vulnerable to a codebook attack, leading to the proposal of an improved algorithm that resists this attack through randomized image rotation and enhanced diffusion, validated via NIST statistical tests.

ABSTRACT

Recently, an image encryption algorithm using block-based scrambling and image filtering has been proposed by Hua et al. In this paper, we analyze the security problems of the encryption algorithm in detail and break the encryption by a codebook attack. We construct an linear relation between plain-images and cipher-images by differential cryptanalysis. With this linear relation, we build a codebook containing $(M imes N + 1)$ pairs of plain-images and cipher-images, where $M imes N$ is the size of images. The proposed codebook attack indicates that the encryption scheme is insecure. To resist the codebook attack, an improved algorithm is proposed. Experimental results show that the improved algorithm not only inherits the merits of the original scheme, but also has stronger security against the differential cryptanalysis.

Motivation & Objective

• To analyze the security vulnerabilities of the IC-BSIF image encryption algorithm using block-based scrambling and image filtering.
• To demonstrate that the scheme is insecure by constructing a linear relation between plain-images and cipher-images via differential cryptanalysis.
• To develop a codebook attack requiring only $M imes N + 1$ known plain-image and cipher-image pairs to fully break the scheme.
• To propose a secure improved version of IC-BSIF that resists differential cryptanalysis and codebook attacks.
• To validate the improved algorithm’s security using NIST SP800-22 statistical randomness tests.

Proposed method

• Constructing a differential relation between plain-images and cipher-images by analyzing the output differences under small input changes.
• Using the differential relation to build a codebook containing $M imes N + 1$ pairs of plain-images and cipher-images for cryptanalysis.
• Introducing a random index-controlled image rotation step after block-based scrambling to disrupt the linear relation and prevent codebook attacks.
• Generating the random index from the chaotic logistic map using the sum of pixel values from previous cipher-images and subkeys.
• Employing a 3×3 filtering matrix and permutation via Latin square scrambling in each round to increase complexity.
• Validating security through NIST SP800-22 statistical tests on both cipher-images and differential cipher-images.

Experimental results

Research questions

• RQ1 Can a linear relation be established between plain-images and cipher-images in the IC-BSIF scheme despite its nonlinear structure?
• RQ2 To what extent can a codebook attack break IC-BSIF using only $M imes N + 1$ known plain-image and cipher-image pairs?
• RQ3 How does the introduction of random index-controlled image rotation affect the security of the IC-BSIF scheme against differential cryptanalysis?
• RQ4 Can the improved algorithm maintain strong randomness and resist statistical analysis, as verified by NIST SP800-22 tests?
• RQ5 Does the improved scheme preserve the original algorithm’s efficiency while enhancing resistance to differential and codebook attacks?

Key findings

• The IC-BSIF scheme is insecure due to a linear differential relation between plain-images and cipher-images, enabling a codebook attack with $M imes N + 1$ known pairs.
• The codebook attack fully breaks the original IC-BSIF scheme, demonstrating its vulnerability to known-plaintext attacks.
• The improved algorithm introduces random index-controlled image rotation, disrupting the linear relation and preventing the codebook attack.
• The improved scheme passes all 15 sub-tests of the NIST SP800-22 statistical test suite for both cipher-images and differential cipher-images.
• The differential image $ abla C'$ in the improved scheme shows strong randomness, unlike in the original IC-BSIF where $ abla C' = abla C$.
• For four-round encryption, the improved algorithm incurs about a 20% performance decrease, while for three rounds, it sees about a 20% performance increase.