The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index; none of the 10 sources its claims cite is checked for support yet.
Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks
Open accessAbstract
In [Pattern Recognition Letters, in press, doi:10.1016/j.patrec.2009.11.008], an image scrambling encryption algorithm of pixel bit based on chaos map was proposed. Considering the algorithm as a typical binary image scrambling/permutation algorithm exerting on plaintext of size M � (8N), this paper proposes a novel optimal method to break it with some known/chosen-plaintexts. The spatial complexity and computational complexity of the attack are only O(32 � MN) and O(16 � n0 � MN) respectively, where n0 is the number of known/chosen-plaintexts used. The method can be easily
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper gives an optimal known/chosen-plaintext cryptanalysis of a chaos-based pixel-bit image permutation cipher and extends it to any permutation-only multimedia cipher. It recovers the equivalent permutation matrix with low spatial and computational complexity and reports experimental recovery on 256×256 images.
Key findings
- For the binary image permutation algorithm on plaintext size \(M \times (8N)\), the attack needs only \(O(32 \cdot MN)\) spatial complexity and \(O(16 \cdot n_0 \cdot MN)\) computational complexity, where \(n_0\) is the number of known/chosen plaintexts.
- For any permutation-only scheme on size \(M \times N\) with \(L\) value levels, the attack achieves \(O(MN)\) spatial complexity and \(O(\lceil \log_L(MN)\rceil \cdot MN)\) computational complexity.
- For 256×256 images, the known-plaintext threshold becomes \(n_0 > \lceil \log_2(2^{19}-1)\rceil = 19\); with 20 known plain-images, the recovered “Peppers” image had \(23509/65536 \approx 35.8\%\) correct pixels but most visual information recovered, and performance was good when \(n_0 \ge 20\).
- Exact chosen-plaintext recovery requires \(n_c = \lceil \log_2(8MN)\rceil = 3 + \lceil \log_2(MN)\rceil\) chosen plain-images; the paper also notes weaknesses including weak Logistic-map randomness, failure on all-zero/all-255 images, plaintext insensitivity, equivalent subkeys \(x_0\) and \(1-x_0\), unchanged bit histogram, and low efficiency.
Methods
- The cipher is represented as an \(M \times (8N)\) permutation matrix \(W\); the attack constructs a binary tree from known/chosen plaintext–ciphertext pairs to recover \(W\), then extends this to a multi-branch tree for general \(L\)-level permutation-only schemes.
- Experiments use randomly selected natural images of size 256×256, with an illustrated key \((x_0,\mu,m,n,T)=(0.2009,3.98,20,51,4)\) and recovered “Peppers” images using estimates \(W_{20}\) and \(W_{25}\), plus a \(3\times3\) median filter.
- The analysis derives recovery thresholds under a uniform independent-bit assumption and reports spatial/computational complexity for the binary and general cases.
Limitations
- The paper states no explicit limitations section.
- Evident from the text: the known-plaintext threshold analysis assumes each bit is uniformly distributed over \(\{0,1\}\) and independent; the authors note natural-image redundancy causes flat performance slopes for \(n_0 \ge 25\) and has two opposite influences on breaking.
- Evident from the text: experimental validation is mainly on 256×256 natural images with one illustrated secret key, and the attack inherently requires known or chosen plaintext–ciphertext pairs.
Model-written summary. Check it against the paper before relying on it.
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Claims the paper makes
25 Own interpretation · 9 No full text of the sources · 9 No basis given · 2 Own result · 1 Sources not found
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The corresponding spatial complexity and computational complexity are only O ( MN ) and O ( ⌈ log L ( MN ) ⌉ · MN ) respectively.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The attacker can obtain some known or chosen plaintexts together with their corresponding ciphertexts encrypted under the same secret key.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It is found that most visual information contained in the original plain-image has been recovered in Fig. 2c), although only 23509 / 65536 ≈ 35 . 8% of plain pixels are correct in value.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“spatial complexity and computational complexity of the attack are O ( MN ) and O ( n 0 · MN ), respectively.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The corresponding spatial complexity and computational complexity are only O ( MN ) and O ( ⌈ log L ( MN ) ⌉ · MN ) respectively.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The attacker can obtain some known or chosen plaintexts together with their corresponding ciphertexts encrypted under the same secret key.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“One can see that the breaking performance is good when n 0 ≥ 20.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The spatial complexity and computational complexity of the attack are only O (32 · MN ) and O (16 · n 0 · MN ) respectively, where n 0 is the number of known/chosenplaintexts used.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The attacker can obtain some known or chosen plaintexts together with their corresponding ciphertexts encrypted under the same secret key.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It is found that the complex intersection operations can be avoided by extending the idea proposed in Sec. 3.1, namely constructing a multi-branch tree”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The spatial complexity and computational complexity of the attack are only O (32 · MN ) and O (16 · n 0 · MN ) respectively, where n 0 is the number of known/chosenplaintexts used.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The attacker can obtain some known or chosen plaintexts together with their corresponding ciphertexts encrypted under the same secret key.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It can also be observed that the slopes of the three lines shown in Fig. 5 are very flat when n 0 ≥ 25.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“spatial complexity and computational complexity of the attack are O ( MN ) and O ( n 0 · MN ), respectively.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- It may state two separate claims as one. 7
- Probably not a substantial claim. 2
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Fail to encrypt images of fixed value zero or 255”
- Also stated in: § 3.2. Chosen-plaintext attack · p. 7 · plain
“For both the two images, all elements of the corresponding intermediate matrix B ∗ are the same, which make all the encryption procedures do nothing.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Also stated in: § 3.2. Chosen-plaintext attack · p. 7 · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Insensitivity with respect to changes of plaintext”
- Also stated in: § 3.2. Chosen-plaintext attack · p. 8 · plain
“Unfortunately, the image permutation algorithm under study does not consider this property at all.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Also stated in: § 3.2. Chosen-plaintext attack · p. 8 · plain
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although the histogram on plain-byte is changed by the image permutation algorithm under study, the one on plain-bit keep unchanged, which make the cipher-image still reveal some information of the plain-image.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“Since that the secret permutation does not change the values of the permuted elements, a general algorithm was proposed in [20] for obtaining the permutation matrix by comparing the values of the elements of some plaintexts and the corresponding ciphertexts.”
What the sources say
- Not checked — no full text of the sourcecites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
In the paper
“Substitute n 0 with ⌈ log L ( MN ) ⌉ , the complexity becomes O ( ⌈ log L ( MN ) ⌉· MN ), which is lower much than O ( ⌈ log L ( MN ) ⌉ · MN 2 ), the whole attack complexity estimated in [20].”
What the sources say
- Not checked — no full text of the sourcecites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Obviously, the spatial complexity and the computational complexity of the proposed knownplaintext attack are only O (32 · MN ) and O (16 · n 0 · MN ), respectively.”
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“due to strong redundancy in natural images, two pixel values are close to each other with a probability larger than the average one, hence many incorrectly recovered pixels are close to their true values with a probability larger than the average one also.”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The generation method of permutation matrixes T M and T N make the computational complexity of the image permutation algorithm under study is O ( M · (8 N ) 2 ), which is even much larger than that of DES.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since that the secret permutation does not change the values of the permuted elements, a general algorithm was proposed in [20] for obtaining the permutation matrix by comparing the values of the elements of some plaintexts and the corresponding ciphertexts.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
The authors state this as an assumption.
The attacker can obtain some known or chosen plaintexts together with their corresponding ciphertexts encrypted under the same secret key.
“The known-plaintext attack is an attack model for cryptanalysis where the attacker has some samples of both the plaintext and the corresponding ciphertext and make use of them to reveal secret information, such as secret keys and/or its equivalent ones.”
“this paper proposes a novel optimal method to break it with some known/chosen-plaintexts.”
The authors state this as an assumption.
Each element in B is uniformly distributed over {0,1}.
“To simplify the analyses, we assume that each element in B distributes uniformly over { 0 , 1 } , and any two elements are independent of each other.”
The authors state this as an assumption.
Any two elements in B are independent of each other.
“To simplify the analyses, we assume that each element in B distributes uniformly over { 0 , 1 } , and any two elements are independent of each other.”
The paper relies on this without support.
Decryption is acceptable when every bit is correctly determined with probability greater than 0.5.
“Generally speaking, when every bit is determined correctly with a probability larger than a half, namely p b > 0 . 5, the decryption will be acceptable.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 3.1. Known-plaintext attack · p. 4
“Search for all nodes whose third item is greater than one, namely, both the corresponding two sets have more than one elements;”
§ 3.1. Known-plaintext attack · p. 3
“every node includes five components in order: a pointer holding address of the left child node, PT L ; two sets containing some entry positions of plain-image and cipher-image, respectively; cardinality of one of the two sets; a pointer holding address of the right child node, PT R .”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 3.1. Known-plaintext attack · p. 5
“The results of two images shown in Figs. 2c) and d) with a 3 × 3 median filter are shown in Figs. 4a) and b), respectively.”
§ 3.1. Known-plaintext attack · p. 6
“Figure 4: The enhanced results of applying a 3 × 3 median filter to the two recovered plain-images: a) the image shown in Fig. 2c); b) the image shown in Fig. 2b).”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 3.1. Known-plaintext attack · p. 4
“where p b = 1 1+(8 MN -1) / 2 n 0 , i = 0 ∼ 8. Generally speaking, when every bit is determined correctly with a probability larger than a half, namely p b > 0 . 5, the decryption will be acceptable.”
§ 3.1. Known-plaintext attack · p. 4
“In this case, Eq. (5) become n 0 > ⌈ log 2 (2 19 -1) ⌉ = 19.”
Citations
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Background
Cited by
Sorted by citations
Image encryption using 2D Logistic-adjusted-Sine map
Hua, Z., & Zhou, Y. (2016) · Information Sciences · doi:10.1016/j.ins.2016.01.017 · Cited by 745
“Many successful cryptanalysis cases using the chosen-plaintext or chosen-ciphertext attack were reported in [22,23,30].”
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Kaur, M., & Kumar, V. (2018) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-018-9298-8 · Cited by 409
A novel image encryption scheme based on DNA sequence operations and chaotic systems
Chai, X., Gan, Z., Yuan, K., Chen, Y., & Liu, X. (2017) · Neural Computing and Applications · doi:10.1007/s00521-017-2993-9 · Cited by 323
Chen, J., Zhu, Z.-L., Zhang, L.-B., Zhang, Y., & Yang, B.-Q. (2018) · Signal Processing · doi:10.1016/j.sigpro.2017.07.034 · Cited by 320
“However, as pixel values remain unchanged after image permutation, an adversary can easily launch chosen-plaintext attack to recover the permutation matrix and hence crack the permutation-only ciphers [33-35].”
BackgroundOn the cryptanalysis of Fridrich’s chaotic image encryption scheme
Xie, E. Y., Li, C., Yu, S., & Lü, J. (2017) · Signal Processing · doi:10.1016/j.sigpro.2016.10.002 · Cited by 268
“As quantitatively analyzed in [18, 19], any position permutation-only encryption scheme can be efficiently broken with only O(dlogL(H · W)e) known/chosen plaintexts and the computational complexity of magnitude O(H ·W · dlogL(H · W)e), where L denotes the number of different gray-values of the plaintexts, and H × W (h…”
BackgroundSelf-citation
Metadata
- Authors
- Li, C., & Lo, K.-T.
- Affiliations
- Hong Kong Polytechnic University (HK)
- Corresponding author
- Li, Chengqing
- Venue
- Signal Processing
- Publisher
- Elsevier BV
- Published
- 2011-04
- Volume
- 91
- Issue
- 4
- Pages
- 949-954
- ISSN
- 0165-1684 (ISSN-L)
- OpenAlex
- W4252343056
- Semantic Scholar
- 0de6e37101946ad2f13be6c1af186eaa87525cf3
- Cited by
- 213
- References
- 26
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 12 · 2023: 7 · 2022: 11 · 2021: 16 · 2020: 20 · 2019: 14 · 2018: 21 · 2017: 27 · 2016: 15 · 2015: 20 · 2014: 22 · 2013: 11 · 2012: 8
- FWCI
- 7.72
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Signal Processing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- PolyU Institutional Research Archive (Hong Kong Polytechnic University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
- Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
- Keywords
- chaotic maps, cryptanalysis, known-plaintext attack, chosen-plaintext attack, attack complexity, multimedia encryption
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