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Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits
Chengqing Li, Dongdong Lin, Jinhu Lü
TL;DR
The paper asks whether a typical image-scrambling encryption algorithm, ISEA, provides adequate security against ciphertext-only and plaintext attacks. It re-evaluates ISEA using residual image correlations and its actual scrambling-domain structure. The analysis finds recoverable visual information from ciphertext and efficient known- and chosen-plaintext attacks, while focusing on the simpler ISEA version.
Problem
The security of a typical binary image-scrambling encryption algorithm against ciphertext-only, known-plaintext, and chosen-plaintext attacks requires comprehensive evaluation.
Method
The paper analyzes residual row and column correlations in cipher images and reinterprets ISEA as two cascaded permutations with domains of sizes M and 8N.
Results
The analysis observes important plain-image visual information from a single cipher image and develops efficient known- and chosen-plaintext attacks against ISEA.
Takeaways & Limitations
The study indicates that scrambling-domain size and internal correlation must be considered when assessing multimedia encryption security.
Takeaways & Limitations
The paper studies only the simpler ISEA version; the full version had already been comprehensively cryptanalyzed.
Abstract
from arXiv · showhide
Position scrambling (permutation) is widely used in multimedia encryption schemes and some international encryption standards, such as the Data Encryption Standard and the Advanced Encryption Standard. In this article, the authors re-evaluate the security of a typical image-scrambling encryption algorithm (ISEA). Using the internal correlation remaining in the cipher image, they disclose important visual information of the corresponding plain image in a ciphertext-only attack scenario. Furthermore, they found that the real scrambling domain--the position-scrambling scope of ISEA's scrambled elements--can be used to support an efficient known or chosen-plaintext attack on it. Detailed experimental results have verified these points and demonstrate that some advanced multimedia processing techniques can facilitate the cryptanalysis of multimedia encryption algorithms.
1. Introduction
The paper re-evaluates a typical image-scrambling encryption algorithm against ciphertext-only and plaintext attacks, focusing on its scrambling domains and attackability. It argues that the simpler ISEA version has exploitable structure despite the large theoretical number of scrambling relations.
- Motivation: Position scrambling protects multimedia data by permuting bits, pixels, blocks, coefficients, or other selected elements.The number of possible scrambling relations grows factorially with the number of scrambled elements.
- Prior cryptanalysis: Prior work established attack models and complexity bounds for multimedia scrambling encryption algorithms.One general result gives O(⌈log_L(MN)⌉) plaintexts and O(⌈log_L(MN)⌉·MN^2) computation, with later work reducing computation to O(⌈log_L(MN)⌉·MN).
- ISEA background: ISEA scrambles the binary representation of a grayscale image using a pseudo-random sequence generated by iterating a digital chaotic map.A weaker version applies the same scrambling vector to every row and column of the binary matrix.
- Paper contribution: The paper finds that the simpler ISEA version consists of two cascaded scrambling algorithms with domains of sizes M and 8N, rather than one domain of size M × 8N.This domain decomposition motivates efficient known-plaintext and general chosen-plaintext attacks.
- Paper contribution: The paper also reports that important visual information can be observed from a single cipher image encrypted by ISEA.The study re-evaluates ciphertext-only as well as known- and chosen-plaintext security using experimental results.
2. Description of ISEA
ISEA converts a grayscale image into a binary matrix, then applies vertical and horizontal permutations derived from chaotic-map-generated scrambling vectors. Repeated rounds and reversed operations define encryption and decryption, while the paper studies only the simpler version rather than the full ISEA.
- Image representation: ISEA encrypts a grayscale image of size M × N by representing it as an M × 8N binary matrix.The binary matrix records the eight bits associated with each grayscale pixel.
- Key and initialization: The secret key contains three positive integers, a Logistic-map initial condition, and a control parameter.The control parameter lies in (3.569945672, 4), and the map generates the sequence used during initialization.
- Key and initialization: Initialization derives a length-M vector TM and a 1 × 8N matrix TN by ranking selected Logistic-map sequence values.TM and TN define the scrambling relations used in the two directions.
- Encryption procedure: The encryption procedure performs vertical permutation, horizontal permutation, and repetition across multiple rounds.The intermediate binary matrix is first generated by vertical permutation, followed by horizontal permutation and repeated rounds.
- Decryption: Decryption reverses the encryption rounds, executes the horizontal step first, and swaps the corresponding equation parts.These modifications invert the order and direction of the encryption operations.
- Scope: The study examines only the simpler ISEA version; the full version uses an M × 8N matrix TN with a distinct row vector for each binary-matrix row.The full version had already been comprehensively cryptanalyzed elsewhere.
3. Cryptanalysis of ISEA
The analysis shows that ISEA leaks visual information under ciphertext-only attack and is vulnerable to efficient plaintext attacks because its scrambling decomposes into independent row and column permutations.
- Ciphertext-only attack: ISEA fails the basic requirement of robustness against ciphertext-only attacks.The attack reconstructs an approximate binary image from correlations preserved between neighboring rows and columns of the cipher-image.
- Ciphertext-only attack: Neighboring vectors are identified by correlation-based searching, using the ratio of equal bits as a similarity measure for binary template matching.Iterative horizontal and vertical searches produce an approximate version of the scrambled binary image, from which visible blocks can be detected.
- Known-plaintext attack: Known-plaintext recovery expands row and column candidate sets iteratively by matching unique row or column counts and vectors across plaintext-ciphertext pairs.Additional known image pairs can further expand the sets and reduce ambiguity in the recovered permutation positions.
- Known-plaintext attack: Three known image pairs empirically recover all 256 row positions and 1921 of 2048 column positions during the reported attack.The corresponding ratios in Figure 5 confirm the reported performance of the known-plaintext attack.
- Chosen-plaintext attack: Chosen plaintexts can break both orthogonal scrambling directions simultaneously, reducing the number of required images and attack complexity.The proposed complexity is O(n*·MN), and the required number of chosen plaintexts is smaller than an earlier estimate under the stated size conditions.
4. Conclusion
The paper’s comprehensive cryptanalysis of ISEA shows broader lessons for multimedia encryption: data correlation can aid attacks, scrambling domains matter, and permutation-only encryption preserves histograms.
- Correlation in multimedia data may support specific attacks and improve breaking performance.
- The size of each independent scrambling domain should be checked carefully against the intended security requirement.
- Permutation-only encryption algorithms do not change the histogram of the permuted elements.
- A multimedia encryption algorithm’s security level should match its application scenario.