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Breaking a modified substitution-diffusion image cipher based on chaotic standard and logistic maps
Chengqing Li, Shujun Li, Kwok-Tung Lo
TL;DR
The paper examines whether modifying a chaotic image cipher protects it from a known/chosen-plaintext attack. It shows that the attack still breaks the modified scheme and reports further security weaknesses in both versions.
Problem
A modified chaotic image-encryption scheme was claimed to resist an attack that had recovered an equivalent key from one known/chosen plaintext and its ciphertext, leaving its security in question.
Source: §1 · p. 2Method
The paper re-evaluates the modified scheme by analyzing its key-dependent diffusion and examines weaknesses shared by the original and modified schemes.
Source: §3 · p. 4, §3.1 · p. 5Results
The same known/chosen-plaintext attack breaks the modified scheme, and both versions have insufficient PRNS randomness and insufficient sensitivity to plaintext changes.
Source: §4 · pp. 7–8Takeaways & Limitations
The authors recommend not using either scheme unless its security is further enhanced with more complicated countermeasures.
Source: §4 · p. 8The scheme description assumes plaintexts are RGB true-color images of size H × W.
Source: §2 · p. 2
Abstract
from arXiv · showhide
Recently, an image encryption scheme based on chaotic standard and logistic maps was proposed by Patidar et al. It was later reported by Rhouma et al. that an equivalent secret key can be reconstructed with only one known/chosen-plaintext and the corresponding ciphertext. Patidar et al. soon modified the original scheme and claimed that the modified scheme is secure against Rhouma et al.'s attack. In this paper, we point out that the modified scheme is still insecure against the same known/chosen-plaintext attack. In addition, some other security defects existing in both the original and the modified schemes are also reported.
1. Introduction
The paper situates chaos-based multimedia encryption amid security concerns and prior cryptanalytic weaknesses. It re-examines a modified image cipher, finding that the earlier attack still applies and that both versions have additional security defects.
1. Introduction
- Multimedia encryption has been studied as a response to application requirements that traditional text encryption may not meet efficiently.The introduction notes that chaos-based multimedia schemes have been proposed in large numbers, while many have been found to have cryptographic security problems.Source: §1 · p. 1
- The modified scheme remains vulnerable to the known/chosen-plaintext attack that broke the original, and both versions have additional security defects.The paper also identifies insufficient PRNS randomness and insufficient sensitivity to plaintext changes.Source: §1 · p. 2
- The paper is organized to introduce the schemes and earlier attack, present cryptanalysis, and then conclude.Source: §1 · p. 2
2. The image encryption schemes under study and Rhouma et al.’s attack
This section describes the two image-encryption schemes and the earlier attack. The original scheme combines key-derived masking, diffusion, and chaotic streams; the modified scheme makes its diffusion key-dependent, but the attack can still recover an equivalent key.
2. The image encryption schemes under study and Rhouma et al.’s attack
- For the schemes’ description, the plaintext is assumed to be an RGB true-color image of size H × W, and the original and modified schemes are named PPS09 and mPPS09.Source: §2 · p. 2
2.1. The original image encryption scheme PPS09 [15]
- PPS09 uses four concatenated encryption operations, including XOR masking, horizontal and vertical diffusion, and a chaotic-stream mask.Its diffusion steps scan pixels in different directions and mask each pixel using its predecessor in the scan.Source: §2.1 · p. 3
2.2. Rhouma et al.’s attack [19]
- Because PPS09’s diffusion operations commute with XOR and do not depend on the key, Rhouma et al. showed that one known/chosen plaintext and its ciphertext yield an equivalent key usable on same-sized images.The equivalent key is independent of plaintext and ciphertext.Source: §2.2 · pp. 3–4
2.3. The modified image encryption scheme mPPS09 [20]
- mPPS09 modifies horizontal and vertical diffusion to depend on 16 diffusion keys derived from the secret key’s parameters.The scheme replaces the original diffusion equations with key-dependent forms.Source: §2.3 · p. 4
3. Cryptanalysis
The cryptanalysis shows that mPPS09’s key-dependent diffusion does not stop the known/chosen-plaintext attack, and reports insufficient PRNS randomness and plaintext sensitivity in the schemes under study.
3.1. Insecurity of mPPS09 against Rhouma et al.’s attack
- mHD and mVD equal ordinary diffusion plus their respective zero-input outputs, rendering their key dependence ineffective against the attack.The paper uses these equivalent forms to show that the modified scheme retains the same attack vulnerability.Source: §3.1 · pp. 5–6
- One known/chosen plaintext–ciphertext pair yields an equivalent key for mPPS09, which successfully decrypts another ciphertext.The reported experiment recovered the plain-image “Peppers” from a cipher-image encrypted with the same key.Source: §3.1 · pp. 5–6, Figure 1 · p. 6
3.2.1. Insufficient randomness of the PRNS {BCKS(i, j)}
- Tests of 100 PRNSs found that the logistic-map sequence was not random enough.The sequences had length 512 × 512, and the reported NIST tests used a 0.01 significance level.Source: §3.2.1 · pp. 6–7, Table 1 · p. 7
3.2.2. Insufficient sensitivity with respect to change of plaintext
- Changing one plaintext bitplane leaves other cipher-image bitplanes unchanged, while the resulting change pattern is far from random and balanced.In the reported one-bit red-channel experiment, only some bits on the same bitplane changed.Source: §3.2.2 · p. 7
4. Conclusion
The modified image cipher remains vulnerable to the known/chosen-plaintext attack that breaks the original scheme. Both schemes also have other reported security weaknesses.
4. Conclusion
- The modified scheme remains vulnerable to the same known/chosen-plaintext attack that breaks the original scheme.The paper re-evaluates the modified scheme and reports that the attack still applies.Source: §4 · pp. 7–8
- Both schemes have insufficient PRNS randomness and insufficient sensitivity to plaintext changes; Figure 2 depicts the differential cipher image and its color channels after an MSB change.Source: §4 · p. 8, Figure 2 · p. 8
- The authors recommend avoiding these schemes unless their security is further enhanced with more complicated countermeasures.Source: §4 · p. 8