Source-linked AI summary
Breaking a novel colour image encryption algorithm based on chaos
Chengqing Li, Yu Zhang, Rong Ou, Kwok-Wo Wong
TL;DR
Security analysis of chaos-based image encryption schemes lagged scheme design, and some schemes were vulnerable to conventional attacks. This paper analyzes the algorithm in [17] with a divide-and-conquer chosen-plaintext attack, finding it can be broken efficiently and is not suggested for serious applications requiring high security.
Problem
Security analysis of chaos-based image-encryption schemes was relatively scarce compared with scheme design, leaving the security of many schemes under-scrutinized.
Source: §1 · p. 1Method
Results
The algorithm can be broken efficiently with chosen-plaintext attack, with required images proportional to the logarithm of plaintext size and attack complexity proportional to image size.
Source: §4 · pp. 4–5Takeaways & Limitations
The authors do not suggest the algorithm for serious applications requiring a high level of security.
Source: §4 · p. 5
Abstract
from arXiv · showhide
Recently, a colour image encryption algorithm based on chaos was proposed by cascading two position permutation operations and one substitution operation, which are all determined by some pseudo-random number sequences generated by iterating the Logistic map. This paper evaluates the security level of the encryption algorithm and finds that the position permutation-only part and the substitution part can be separately broken with only $\lceil (\log_2(3MN))/8 \rceil$ and 2 chosen plain-images, respectively, where $MN$ is the size of the plain-image. Concise theoretical analyses are provided to support the chosen-plaintext attack, which are verified by experimental results also.
1. Introduction
The introduction notes that security analysis of chaos-based image encryption has lagged scheme design, despite multimedia security concerns and vulnerabilities to conventional attacks. It presents a chosen-plaintext analysis of the algorithm in [17], supported by theoretical analysis and experiments.
1. Introduction
- Chaos-based encryption uses similarities between chaotic-system properties and cryptographic diffusion and confusion to motivate encryption designs.Image data is commonly used as the encryption object because it represents multimedia data and helps demonstrate claimed performance.Source: §1 · p. 1
- More than 400 chaos-based image-encryption design papers, but no more than 150 security-analysis papers, appeared from 1997 through 2011.The introduction connects limited scrutiny with schemes vulnerable to conventional attacks.Source: §1 · p. 1
- The paper finds that the three operations in the algorithm proposed in are key-invertible and can be broken separately with a few chosen plaintexts.The authors support the chosen-plaintext attack with theoretical analyses and experimental results.Source: §1 · p. 1
2. The colour image encryption algorithm under study
The algorithm encrypts an M×N RGB image through row permutation, column permutation, and substitution, with operations controlled by sequences generated from Logistic-map iterations. Its key and initialization procedures generate sequences used by these operations.
2. The colour image encryption algorithm under study
- The plaintext is an M×N RGB image represented as an M×N×3 matrix of pixel values.The corresponding cipher-image is also represented as a matrix of pixel values.Source: §2 · p. 2
- The secret key includes two positive integers and two Logistic-map initial-condition and control-parameter sets.The initial conditions lie in (0, 1), and the control parameters lie in (3.5699456, 4).Source: §2 · p. 2
- Initialization iterates the logistic map m1 times from x0 under fixed µ0, then 3M times to obtain chaotic states and their sorted version; from x*0 under fixed µ*0, it iterates m2 then 3MN times.Source: §2 · p. 2
- Encryption concatenates row permutation, column permutation, and substitution, while decryption reverses the operation order and uses inverse permutation sequences.The decryption substitution equations also differ from the encryption equations.Source: §2 · pp. 2–3
- Substitution selects pixels iteratively from the intermediate image and encrypts each using the previous selected pixel, its corresponding cipher-pixel, and a pseudo-random number.The encryption procedure also specifies a first-pixel substitution rule.Source: §2 · p. 2
3. Chosen-plaintext attack
The attack exploits the encryption operations’ independence to break substitution and position permutation separately with chosen plaintexts. The analysis derives high-probability substitution recovery and a low-complexity permutation attack, then verifies recovery experimentally.
3. Chosen-plaintext attack
- Because the three encryption operations are independent, divide-and-conquer lets the attack break the position-permutation and substitution parts separately.The paper challenges the earlier claim that key-sensitive PRNSs and substitution feedback make the algorithm robust against chosen-plaintext attack.Source: §3 · p. 3
- With two available chosen plain-images of fixed values d1 and d2, both row and column permutations cancel, leaving only the substitution, whose breaking can be implemented successfully with extremely high probability.Source: §3 · pp. 3–4
- At T = 128, Prob(2272 · 1704) ≈ 1.1173·10^-16; the upper-bound probability Prob(MN) increases strictly with MN.For smaller images, the attack success probability is much greater than 1−1.12·10^-16.Source: §3 · p. 4
- ⌈(log2(3MN))/8⌉ chosen-plaintext pairs recover the equivalent position-permutation key, with attack complexity O(3MN).The plaintext values need ⌈log2(3MN)⌉ bits to distinguish all 3MN possible pixel positions; each channel has 8 bits.Source: §3 · p. 4
- On 512 × 512 images, two fixed-value plaintexts recovered the PRNS and three further pairs recovered permutation subkeys, yielding a decryption identical to the original image.The fixed-value plaintexts used pixel values 127 and 0.Source: §3 · p. 4
4. Conclusion
The studied chaos-based colour image encryption algorithm can be broken efficiently with a chosen-plaintext attack. The authors conclude it is not suggested for serious applications requiring high security.
4. Conclusion
- The chosen-plaintext attack breaks the studied algorithm, with required images scaling logarithmically with plain-image size and attack complexity scaling with image size.The paper studies the algorithm proposed in.Source: §4 · pp. 4–5
- Figure 1 shows the chosen constant-value inputs, the Baboon ciphertext, and the recovered image.Source: Figure 1 · p. 5
- The algorithm is not suggested for serious applications requiring a high level of security.Source: §4 · p. 5