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Breaking a novel image encryption scheme based on improved hyperchaotic sequences
Chengqing Li, Yuansheng Liu, Tao Xie, Michael Z. Q. Chen
TL;DR
The paper addresses whether a proposed hyperchaotic image encryption scheme is secure against known-plaintext analysis and changes in plaintext or secret key. It re-evaluates the scheme mathematically and experimentally, finding effective attacks and additional security defects. The results show that one known plaintext can break the scheme, while two improve attack performance.
Problem
The security of a hyperchaotic image encryption scheme, including its resistance to known-plaintext attacks and key or plaintext changes, required re-evaluation.
Method
The paper analyzes the encryption scheme's key and pixel operations, derives known-plaintext attacks, and supports them with mathematical proofs and experiments.
Results
One known plaintext can narrow the equivalent-key search, while two known plaintexts make the attack more effective; the scheme also has low sensitivity to secret-key and plaintext changes.
Takeaways & Limitations
The scheme is effectively breakable with known plaintexts, and its reported security properties are undermined by equivalent keys and insensitivity defects.
Takeaways & Limitations
The prior attack's required number of known or chosen plaintexts is difficult to estimate, and its complexity is high for very large images.
Abstract
from arXiv · showhide
Recently, a novel image encryption scheme based on improved hyperchaotic sequences was proposed. A pseudo-random number sequence, generated by a hyper-chaos system, is used to determine two involved encryption functions, bitwise exclusive or (XOR) operation and modulo addition. It was reported that the scheme can be broken with some pairs of chosen plain-images and the corresponding cipherimages. This paper re-evaluates the security of the encryption scheme and finds that the encryption scheme can be broken with only one known plain-image. The performance of the known-plaintext attack, in terms of success probability and computation load, become even much better when two known plain-images are available. In addition, security defects on insensitivity of the encryption result with respect to changes of secret key and plain-image are also reported.
1 Introduction
Image security is increasingly important as capture and transmission expand, but conventional text encryption is inefficient for images. This paper re-evaluates a hyperchaotic image encryption scheme and identifies multiple security weaknesses.
- Image security has become increasingly important with the spread of image capture devices and faster networks.
- Traditional text encryption techniques cannot efficiently protect images because images differ substantially from text.
- The studied scheme uses a four-dimensional hyperchaos-generated pseudo-random sequence to control modulo addition and bitwise XOR operations.
- Earlier work reported that equivalent secret-key information could be obtained by brute force from some chosen plaintext–ciphertext pairs.
- The present paper narrows the equivalent-key search with one known plaintext, confirms it with two, and reports insensitivity to plaintext and secret-key changes.
2 The image encryption scheme under study
The studied scheme encrypts grayscale images represented as raster-scanned 8-bit sequences. It initializes a hyperchaotic system to generate a four-dimensional pseudo-random sequence, then applies two confusion rounds controlled by that sequence.
- The plaintext is a grayscale image represented as a one-dimensional 8-bit sequence, with pixels scanned in raster order.The sequence length L is assumed to be a multiple of 4.
- The secret key is the initial state of the specified four-dimensional hyperchaotic system.The initial state is given by (x(0), y(0), z(0), w(0)).
- Initialization iterates the hyperchaotic system with fourth-order Runge–Kutta integration using step length h = 0.001 and discards more than 500 initial iterations.
- The resulting states are quantized into a four-dimensional pseudo-random sequence whose components are assigned through functions of x(l), y(l), z(l), and w(l).
- Encryption performs two confusion rounds over the pixel sequence, while decryption reverses their order and the operations within each round.The cipher begins with a predefined c(0) in [1, 255].
3 Cryptanalysis
The paper re-evaluates the scheme’s known-plaintext security and develops attacks using one or two known plain-images. It also identifies equivalent secret keys and low sensitivity to changes in the secret key or plain-image.
- 3.1 Attack proposed by Fatih et al.: The reviewed earlier attack searches candidate values and has complexity O(2^20L), making it costly for large images.Its success also depends on an uncertain number of known or chosen plain-images.
- 3.2 Attack with one known plain-image: One known plain-image is sufficient to break the scheme by searching candidate values of k(L−1) and k(L) and verifying them through the encryption relations.These values determine the equivalent secret-key sequence used by the attack.
- 3.2 Attack with one known plain-image: 60.13% of pixels were correctly recovered using a wrong candidate key, while the one-image attack has complexity O(2^17L).This shows that even an incorrect surviving candidate can reveal image information.
- 3.3 Attack with two known plain-images: With two known plain-images, L−2 independent conditions greatly improve the success probability and reduce the attack computation.The resulting key recovery has extremely high probability when L ≥5 and complexity O(2^21 + 6L), much smaller than Fatih et al.’s attack.
- 3.3 Attack with two known plain-images: An equivalent secret key recovered from the second known plain-image decrypts the target cipher-image identically to the original version.The experiment uses the known image “Babarra” and decrypts the cipher-image associated with “Lenna.”
- 3.4 Two other security defects: For each secret key, at least 2^L equivalent keys exist for the least 7 significant bit planes, and plaintext changes affect only higher bit planes of corresponding cipher-image pixels.The paper attributes the latter defect to the absence of nonlinear operations and carry propagation toward lower bit levels.
4 Conclusion
The paper re-evaluates the scheme’s security, showing it can be effectively broken with two known plain-images and exposing additional security defects.
- The encryption scheme can be effectively broken with only two known plain-images.Mathematical proofs and experimental results support the proposed attack.
- The paper also identifies other security defects in the encryption scheme.
- The analysis provides an example framework for security analysis of chaotic cryptosystems.