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
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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
0 of 10 cited sources checked · 0 supported · 0 flagged
- Findingreasoning§ Abstract · p. 1
For the extended attack on any permutation-only scheme with plaintext size M × N and L value levels, the computational complexity is O(⌈log_L(MN)⌉ · MN).
“The corresponding spatial complexity and computational complexity are only O ( MN ) and O ( ⌈ log L ( MN ) ⌉ · MN ) respectively.”
Quote in the paperSubstantial claim- 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.
- Findingown data§ 3.1. Known-plaintext attack · p. 4
With 20 known plain-images, the recovered Peppers image contains most visual information despite only 23509/65536 ≈ 35.8% of plain pixels being correct.
“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.”
Quote in the paperSubstantial claim - Findingreasoning§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9
The spatial complexity of the proposed attack is O(MN).
“spatial complexity and computational complexity of the attack are O ( MN ) and O ( n 0 · MN ), respectively.”
Quote in the paperSubstantial claim - Findingreasoning§ Abstract · p. 1
For the extended attack on any permutation-only scheme with plaintext size M × N and L value levels, the spatial complexity is O(MN).
“The corresponding spatial complexity and computational complexity are only O ( MN ) and O ( ⌈ log L ( MN ) ⌉ · MN ) respectively.”
Quote in the paperSubstantial claim- 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.
- Findingown data§ 3.1. Known-plaintext attack · p. 5
Breaking performance is good when n0 ≥ 20.
“One can see that the breaking performance is good when n 0 ≥ 20.”
Quote in the paperSubstantial claim
- Findingnone given§ Abstract · p. 1
The computational complexity of the proposed attack on the binary image permutation algorithm is O(16 · n0 · MN), where n0 is the number of known/chosen plaintexts used.
“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.”
Quote in the paperSubstantial claim- 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.
- Findingreasoning§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9
The complex intersection operations of the prior attack can be avoided by extending the earlier idea to construct a multi-branch tree.
“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”
Quote in the paperSubstantial claim - Findingnone given§ Abstract · p. 1
The spatial complexity of the proposed attack on the binary image permutation algorithm is O(32 · MN).
“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.”
Quote in the paperSubstantial claim- 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.
- Findingreasoning§ 3.1. Known-plaintext attack · p. 5
The slopes of the three lines in Fig. 5 are very flat when n0 ≥ 25.
“It can also be observed that the slopes of the three lines shown in Fig. 5 are very flat when n 0 ≥ 25.”
Quote in the paperNot a substantial claim - Findingreasoning§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9
The computational complexity of the proposed attack is O(n0·MN).
“spatial complexity and computational complexity of the attack are O ( MN ) and O ( n 0 · MN ), respectively.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1. Known-plaintext attack · p. 3
The cardinalities of the two sets in the two child nodes are always the same.
“Since the secret permutation does not change the values of the permuted elements, the cardinalities of the two sets in the two child nodes are always the same.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
A smaller value of the product over leaf nodes of (|B_i|!) means a more accurate estimation of the permutation matrix.
“The less value of Π P i =1 ( | B i | !) means more accurate estimation of the permutation matrix.”
Quote in the paperSubstantial claim - Interpretationnone given§ 5. Conclusion · p. 9
The proposed method can be extended to break any permutation-only multimedia encryption scheme with optimal performance.
“Furthermore, the method can be extended to break any permutation-only multimedia encryption schemes with an optimal performance also.”
Quote in the paperNot a substantial claim - Interpretationcitation§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9
Any permutation-only multimedia encryption scheme acting on a plaintext of size M×N can be efficiently broken with O(⌈log_L(MN)⌉) known/chosen plaintexts.
“we can conclude that any permutation-only multimedia encryption schemes exerting on plaintext of size M × N can be efficiently broken with O ( ⌈ log L ( MN ) ⌉ ) known/chosen-plaintexts”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
- Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
For 256×256 images, Eq. (5) gives n0 > ceil(log2(2^19-1)) = 19.
“In this case, Eq. (5) become n 0 > ⌈ log 2 (2 19 -1) ⌉ = 19.”
Quote in the paperSubstantial claim- Rests on an assumption: Decryption is acceptable when every bit is correctly determined with probability greater than 0.5.
- Interpretationnone given§ 3.2. Chosen-plaintext attack · p. 8
Since f(x)=f(1-x), x0 and 1-x0 are equivalent sub-keys for decryption.
“Since f ( x ) = f (1 -x ), x 0 and (1 -x 0 ) are equivalent sub-keys for decryption.”
Quote in the paperNot a substantial claim - Interpretationnone given§ Abstract · p. 1
The proposed method can be extended to break any permutation-only encryption scheme that acts on plaintext of size M × N and has L different levels of values.
“The method can be easily extended to break any permutation-only encryption scheme exerting on plaintext of size M × N and with L different levels of values.”
Quote in the paperNot a substantial claim- 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.
- Premisecitation§ 3.2. Chosen-plaintext attack · p. 7
Logistic maps cannot serve as a good random number generator.
“As shown in [22, Sec. 3.1], Logistic maps cannot serve as a good random number generator.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [22, Sec. 3.1]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationown data§ 3.1. Known-plaintext attack · p. 5
The non-uniform distribution of most natural images has two opposite influences on the final breaking.
“Now, one can see that the non-uniform distribution of most natural images has two opposite influences on the final breaking.”
Quote in the paperSubstantial claim - Interpretationcitation§ 3.1. Known-plaintext attack · p. 5
The flat slopes for n0 ≥ 25 are due to the negative impact of strong redundancy in natural images, such as neighboring pixels' MSBs being the same with high probability.
“This is due to the negative impact incurred by the strong redundancy in natural images such as the MSBs of neighboring pixels are the same with a high probability.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
- Interpretationreasoning§ 3.1. Known-plaintext attack · p. 3
The combination of multiple rounds of the encryption procedure can be represented by an M × (8N) permutation matrix W.
“Apparently, the combination of multiple rounds of the operations in the encryption procedure can be represented by an M × (8 N ) permutation matrix W = [ w ( i, l )] M, 8 N i =0 ,l =0 , where w ( i, l ) = ( i ′ , l ′ ) denotes the secret position of the plain bit B ( i, j ) in B ′ .”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
The number of error bits n8 in a recovered pixel follows the stated binomial distribution Prob(n8=i)=C(8,i)(1-p_b)^i(p_b)^(8-i), with p_b=1/(1+(8MN-1)/2^n0).
“Prob ( n 8 = i ) = ( 8 i ) · (1 -p b ) i · ( p b ) 8 -i , where p b = 1 1+(8 MN -1) / 2 n 0 , i = 0 ∼ 8.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Each element in B is uniformly distributed over {0,1}.
- The authors state this as an assumption: Any two elements in B are independent of each other.
- Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
For the whole permutation matrix, the number of possible cases is the product over leaf nodes of (|B_i|!), where P is the number of leaf nodes in the binary tree.
“For the whole permutation matrix, there are Π P i =1 ( | B i | !) possible cases, where P is the number of leaf nodes in the binary tree.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
Under the uniform independent-bit assumption, each fake position in B_i occurs with probability 1/2^n0 because one condition in Eq. (4) is satisfied consecutively n0 times.
“other fake positions , each of which occurs in B i with a probability of 1 / 2 n 0 , since one condition in Eq. (4) is satisfied consecutively for n 0 times.”
Quote in the paperSubstantial claim- The authors state this as an assumption: Each element in B is uniformly distributed over {0,1}.
- The authors state this as an assumption: Any two elements in B are independent of each other.
- Premisecitation§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9
The intersection operations of Step 2 in the prior attack make its computational complexity O(n0·MN2).
“The operations in Step 2 make the computational complexity of the above attack become O ( n 0 · MN 2 ).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
- Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
The product over leaf nodes of (|B_i|!) decreases rapidly as the number of known images n0 increases.
“Roughly speaking, Π P i =1 ( | B i | !) rapidly decrease when the number of known-images, n 0 , is increased.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 5. Conclusion · p. 9
An optimal method, in terms of spatial complexity and computational complexity, is proposed to break the binary image permutation algorithm.
“An optimal method, in term of spatial complexity and computational complexity, is proposed to break the binary image permutation algorithm.”
Quote in the paperSubstantial claim - Premisecitation§ 1. Introduction · p. 1
The image permutation algorithm proposed in [19] is a permutation-only algorithm that acts on a binary image of size M × (8N).
“In [19], an image permutation algorithm was proposed by scrambling/permuting binary bit of every pixel with pseudo-random number sequence generated by chaotic logistic map. Essentially, it is a permutation-only algorithm exerting on a binary image of size M × (8 N ).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19] Ye, 2010, Image scrambling encryption algorithm of pixel bit based on chaos map, Pattern Recognition Letters source
- Interpretationown data§ 3.1. Known-plaintext attack · p. 5
The analysis result obtained under the uniform-distribution assumption also holds for ordinary natural images.
“The experiments have shown that the above analysis result obtained under the assumption of uniform distribution also holds for the case of ordinary natural images.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.2. Chosen-plaintext attack · p. 7
For the image permutation algorithm, at least n_c = ceil(log2(8MN)) = 3 + ceil(log2(MN)) chosen plain-images are needed to make every leaf-node set cardinality one, so every permutation-matrix element can be recovered exactly.
“at least n c = ⌈ log 2 (8 MN ) ⌉ = 3 + ⌈ log 2 ( MN ) ⌉ chosen plain-images are needed to make cardinality of the set in every leaf node of the binary tree for breaking is equal to one, namely, every element of the permutation matrix can be recovered exactly.”
Quote in the paperSubstantial claim - Premisecitation§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 8
Every permutation-only multimedia encryption scheme acting on a plaintext of size M×N can be represented as a permutation matrix W over the M×N position grid, regardless of the permuted element values.
“no matter what the permuted elements of multimedia data are, all permutationonly multimedia encryption schemes on a plaintext of size M × N can be represented as”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
- Premisecitation§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 8
Permutation-only multimedia encryption can be broken with only O(⌈log_L(MN)⌉) known/chosen plaintexts, where L is the number of different elements in the plaintext.
“Then it was analyzed that permutation-only multimedia encryption can be broken with only O ( ⌈ log L ( MN ) ⌉ ) known/chosen plaintexts, where L is the number of different elements in the plaintext.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
- Interpretationreasoning§ 3.1. Known-plaintext attack · p. 3
Once the attacker recovers W and its inverse W−1, the attacker can use it as an equivalent key to decrypt any cipher-image encrypted with the same secret key.
“Once the attacker recovers the permutation matrix W and then obtains its inverse W -1 , he can use it as an equivalent key to decrypt any cipher-image encrypted with the same secret key.”
Quote in the paperSubstantial claim- 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.
- Premisecitation§ 3.2. Chosen-plaintext attack · p. 7
The distribution of the Logistic map trajectory is mainly determined by the control parameter.
“This point can also be guessed by observing distribution of the trajectory of Logistic map, which is mainly determined by the control parameter [23].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [23] Wang, 2009, Symbolic dynamics approach to parameter estimation without initial value, Physics Letters A source
- Interpretationnone given§ Abstract · p. 1
The proposed known/chosen-plaintext attack is an optimal method for breaking the image permutation algorithm under study.
“this paper proposes a novel optimal method to break it with some known/chosen-plaintexts.”
- Also stated in: § 1. Introduction · p. 1 · plain
“an optimal method is proposed to break the image permutation algorithm under study with some known/chosen plaintexts;”
Quote in the paperSubstantial claim- 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.
- Also stated in: § 1. Introduction · p. 1 · plain
- Interpretationnone given§ 3.2. Chosen-plaintext attack · p. 7
The randomness of vectors T_M and T_N depends on the randomness of the sequences generated by iterating the Logistic map.
“Obviously, randomness of vectors T M and T N depends on randomness of the sequences generated by iterating Logistic map.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1. Known-plaintext attack · p. 4
In the binary-tree attack, a permutation-matrix entry w(i,l) is uniquely determined if and only if the corresponding leaf-node set B_i has cardinality 1.
“Apparently, w ( i, l ) can be uniquely determined if and only if | B i | = 1.”
Quote in the paperSubstantial claim
- May combine two claims. 7
- Classified as probably not a substantial claim. 2
May combine two claims.
Interpretationown data§ 3.2. Chosen-plaintext attack · p. 7The image permutation algorithm fails to encrypt images of fixed value zero or 255 because all elements of the intermediate matrix B* are the same, making all encryption procedures do nothing.
“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.”
Quote in the paperSubstantial claim- Also stated in: § 3.2. Chosen-plaintext attack · p. 7 · plain
May combine two claims.
Interpretationnone given§ 3.2. Chosen-plaintext attack · p. 7The image permutation algorithm is insensitive to changes of plaintext and does not consider the property that changing any single plaintext bit should change every ciphertext bit with probability one half.
“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.”
Quote in the paperSubstantial claim- Also stated in: § 3.2. Chosen-plaintext attack · p. 8 · plain
May combine two claims.
Interpretationnone given§ 3.2. Chosen-plaintext attack · p. 8Although the algorithm changes the plain-byte histogram, it leaves the plain-bit histogram unchanged, so the cipher-image still reveals some plain-image information.
“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.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
Premisecitation§ 3.1. Known-plaintext attack · p. 3A general algorithm for obtaining the permutation matrix by comparing the values of elements of some plaintexts and corresponding ciphertexts was proposed in [20].
“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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
May combine two claims.
Interpretationreasoning§ 4. Known/chosen-plaintext attack on any permutation-only multimedia encryption schemes · p. 9Substituting n0 with ⌈log_L(MN)⌉, the attack complexity becomes O(⌈log_L(MN)⌉·MN), which is much lower than the O(⌈log_L(MN)⌉·MN2) estimated in [20].
“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].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [20] Li, 2008, A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks, Signal Processing: Image Communication source
May combine two claims.
Interpretationnone given§ 3.1. Known-plaintext attack · p. 6The proposed known-plaintext attack has spatial complexity O(32·MN) and computational complexity O(16·n0·MN).
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationreasoning§ 3.1. Known-plaintext attack · p. 5The recovery of most visual information despite low pixel correctness is due to strong redundancy in natural images, which makes two pixel values close with probability larger than average and many incorrectly recovered pixels close to their true values.
“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.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationnone given§ 3.2. Chosen-plaintext attack · p. 8The generation method of permutation matrices T_M and T_N makes the computational complexity of the image permutation algorithm O(M·(8N)^2), which is much larger than that of DES.
“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.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S4 (based).
Premisenone given§ 3.1. Known-plaintext attack · p. 3A secret permutation does not change the values of the permuted elements.
“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.”
Quote in the paperNot a substantial claim
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.
Binary-tree search tests the wrong component
MinorThe node definition places a set in the third component and its cardinality in the fourth. The later search tests whether the third item is greater than one, although that test applies to the cardinality.
“Search for all nodes whose third item is greater than one, namely, both the corresponding two sets have more than one elements;”
“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 .”
Figure 4b identifies the wrong source image
MinorThe text says Figure 4b is the median-filtered result of Figure 2d, but the Figure 4 caption says it is the result of Figure 2b.
“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.”
“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).”
Threshold excludes a value satisfying its stated criterion
MinorFor the stated 256 × 256 case, 8MN − 1 = 219 − 1. At n0 = 19, the paper's formula gives p_b = 1/(1 + (219 − 1)/219) > 0.5, yet its reported inequality requires n0 > 19.
“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.”
“In this case, Eq. (5) become n 0 > ⌈ log 2 (2 19 -1) ⌉ = 19.”
Cites
SOME BASIC CRYPTOGRAPHIC REQUIREMENTS FOR CHAOS-BASED CRYPTOSYSTEMS
ALVAREZ, G., & LI, S. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015970 · Cited by 2,119 · cited 1× · see citing works
“unately, most of them have been found to be insecure to dierent extents from the viewpoint of modern cryptography [8{16]. For more discussion on chaos-based image encryption schemes, please refer to [17, 18]. In [19], an image permutation algorithm was proposed by scrambling/permuting binary bit of every pixel with ps…”
BackgroundA symmetric image encryption scheme based on 3D chaotic cat maps
Chen, G., Mao, Y., & Chui, C. K. (2004) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2003.12.022 · Cited by 2,092 · cited 1× · see citing works
“Due to the subtle similarities between cryptography and chaos, a great number of image encryption schemes based on chaos have been proposed in the paste decade [1, 2, 3, 4, 5].”
BackgroundRukhin, A., Sota, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., et al. (2000) · doi:10.6028/nist.sp.800-22 · Cited by 1,867 · see citing works
Partial encryption of compressed images and videos
Cheng, H., & Li, X. (2000) · IEEE Transactions on Signal Processing · doi:10.1109/78.852023 · Cited by 517 · cited 1× · see citing works
“Again, this cryptanalysis paper proves that the security of a good image encryption scheme should rely on well combination of traditional cryptography and special properties of image data, like the schemes proposed in [22, 23, 24].”
BackgroundLi, S., Li, C., Chen, G., Bourbakis, N. G., & Lo, K.-T. (2008) · Signal Processing: Image Communication · doi:10.1016/j.image.2008.01.003 · Cited by 324 · cited 5× · see citing works
“Depending on the fact that the secret permutation does not change the values of the permuted elements, a general algorithm was proposed in [18] for obtaining the permutation matrix by comparing the values of the elements of some plaintexts and the corresponding ciphertexts.”
BackgroundMethodInfluentialSelf-citationImage scrambling encryption algorithm of pixel bit based on chaos map
Ye, G. (2010) · Pattern Recognition Letters · doi:10.1016/j.patrec.2009.11.008 · Cited by 302 · cited 1× · see citing works
“In [17], an image permutation algorithm was proposed by scrambling/permuting binary bit of every pixel with pseudo-random number sequence generated by chaotic logistic map.”
MethodA new encryption algorithm for image cryptosystems
Chang, C., Hwang, M.-S., & Chen, T.-S. (2001) · Journal of Systems and Software · doi:10.1016/s0164-1212(01)00029-2 · Cited by 269 · cited 1× · see citing works
“Again, this cryptanalysis paper proves that the security of a good image encryption scheme should rely on well combination of traditional cryptography and special properties of image data, like the schemes proposed in [22, 23, 24].”
Background(2004) · CRC Press eBooks · doi:10.1201/9781420038262 · Cited by 246 · see citing works
A novel image encryption algorithm based on self-adaptive wave transmission
Liao, X., Lai, S., & Zhou, Q. (2010) · Signal Processing · doi:10.1016/j.sigpro.2010.03.022 · Cited by 235 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundImage encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator
Tong, X., & Cui, M. (2009) · Signal Processing · doi:10.1016/j.sigpro.2008.09.011 · Cited by 196 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundOn the security defects of an image encryption scheme
Li, C., Li, S., Asim, M., Nunez, J., Álvarez, G., & Chen, G. (2009) · Image and Vision Computing · doi:10.1016/j.imavis.2008.12.008 · Cited by 179 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundSelf-citationOn the security of 3D Cat map based symmetric image encryption scheme
Wang, K., Pei, P., Zou, L., Song, A., & He, Z. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.05.040 · Cited by 167 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundEncryption and decryption of images with chaotic map lattices
Pisarchik, A. N., Flores-Carmona, N. J., & Carpio, M. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2242052 · Cited by 162 · cited 1× · see citing works
“e data specially become an urgent task. Due to the subtle similarities between cryptography and chaos, a great number of image encryption schemes based on chaos have been proposed in the paste decade [1, 2, 3, 4, 5]. Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of m…”
BackgroundOn the security of a new image encryption scheme based on chaotic map lattices
Arroyo, D., Rhouma, R., Álvarez, G., Li, S., & Fernández, V. (2008) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2959102 · Cited by 147 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundCryptanalyzing a nonlinear chaotic algorithm (NCA) for image encryption
Álvarez, G., & Li, S. (2009) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2009.02.033 · Cited by 101 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundCryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations
Li, C., Li, S., Álvarez, G., Chen, G., & Lo, K. (2007) · Physics Letters A · doi:10.1016/j.physleta.2007.04.023 · Cited by 98 · cited 1× · see citing works
“As shown in [20, Sec.”
Self-citationChaos-Based Encryption for Digital Images and Videos
Li, S., Chen, G., & Zheng, X. (2004) · Internet and communications · doi:10.1201/9781420038262.ch4 · Cited by 90 · see citing works
Large encrypting binary images with higher security
Chung, K., & Chang, L.-C. (1998) · Pattern Recognition Letters · doi:10.1016/s0167-8655(98)00017-8 · Cited by 85 · cited 1× · see citing works
“Due to the subtle similarities between cryptography and chaos, a great number of image encryption schemes based on chaos have been proposed in the paste decade [1, 2, 3, 4, 5].”
BackgroundCryptanalysis of the RCES/RSES image encryption scheme
Li, S., Li, C., Chen, G., & Lo, K. (2007) · Journal of Systems and Software · doi:10.1016/j.jss.2007.07.037 · Cited by 73 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundSelf-citationCryptanalysis of a spatiotemporal chaotic image/video cryptosystem
Rhouma, R., & Belghith, S. M. (2008) · Physics Letters A · doi:10.1016/j.physleta.2008.07.042 · Cited by 64 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundOn the security of a class of image encryption schemes
Li, C., & Chen, G. (2008) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2008.4542161 · Cited by 56 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundSelf-citationA new cryptography system and its VLSI realization
Chen, H., & Yen, J.-C. (2003) · Journal of Systems Architecture · doi:10.1016/s1383-7621(03)00087-0 · Cited by 45 · cited 1× · see citing works
“Due to the subtle similarities between cryptography and chaos, a great number of image encryption schemes based on chaos have been proposed in the paste decade [1, 2, 3, 4, 5].”
BackgroundCryptanalysis of an encryption scheme for binary images
Chang, C., & Yu, T.-X. (2002) · Pattern Recognition Letters · doi:10.1016/s0167-8655(02)00157-5 · Cited by 43 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundChaos-Based Encryption for Digital Images and Videos
Li, S., Chen, G., & Zheng, X. (2004) · Multimedia Security Handbook · doi:10.1201/9781420038262-4 · Cited by 34 · see citing works
Self-synchronizing chaotic stream ciphers
Kurian, A. P., & Puthusserypady, S. K. (2008) · Signal Processing · doi:10.1016/j.sigpro.2008.04.003 · Cited by 22 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundCryptanalysis of a spatiotemporal chaotic cryptosystem
Rhouma, R., & Belghith, S. M. (2008) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2008.07.016 · Cited by 22 · see citing works
On the security of the Yen–Guo’s domino signal encryption algorithm (DSEA)
Li, C., Li, S., Lou, D., & Zhang, D. (2005) · Journal of Systems and Software · doi:10.1016/j.jss.2005.04.021 · Cited by 19 · cited 1× · see citing works
“Unfortunately, most of them have been found to be insecure of different extents from the viewpoint of modern cryptography [6, 7, 8, 9, 10, 11, 12, 13, 14].”
BackgroundSelf-citationSymbolic dynamics approach to parameter estimation without initial value
Wang, K., Pei, W., Hou, X., Shen, Y., & He, Z. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.10.021 · Cited by 10 · cited 1× · see citing works
“This point can also be guessed by observing distribution of the trajectory of Logistic map, which is mainly determined by the control parameter [21].”
Background
Flagged first, then by citations
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 737 · see citing works
“Many successful cryptanalysis cases using the chosen-plaintext or chosen-ciphertext attack were reported in [22,23,30].”
BackgroundA Comprehensive Review on Image Encryption Techniques
Kaur, M., & Kumar, V. (2018) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-018-9298-8 · Cited by 392 · see citing works
A novel image encryption scheme based on DNA sequence operations and chaotic systems
Chai, X.-L., Gan, Z.-H., Yuan, K., Chen, Y.-R., & Liu, X.-X. (2017) · Neural computing & applications (Print) · doi:10.1007/s00521-017-2993-9 · Cited by 279 · see citing works
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 · see citing works
“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 · see citing works
“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-citationZhou, N., Li, H., Wang, D., Pan, S., & Zhou, Z. (2015) · Optics Communications · doi:10.1016/j.optcom.2014.12.084 · Cited by 270 · see citing works
Brief review on application of nonlinear dynamics in image encryption
Özkaynak, F. (2018) · Nonlinear Dynamics · doi:10.1007/s11071-018-4056-x · Cited by 262 · see citing works
Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits
Li, C., Lin, D., & Lü, J. (2017) · IEEE Multimedia · doi:10.1109/mmul.2017.3051512 · Cited by 219 · see citing works
“As the full version of ISEA was cryptanalyzed comprehensively in [9], only the simpler version is studied in the remainder of this paper.”
BackgroundMethodInfluentialSelf-citationOn the Security of Permutation-Only Image Encryption Schemes
Jolfaei, A., Wu, X.-W., & Muthukkumarasamy, V. (2015) · IEEE Transactions on Information Forensics and Security · doi:10.1109/tifs.2015.2489178 · Cited by 216 · see citing works
“To verify the feasibility of the proposed attack, experiments were performed on the recently proposed permutation-only image ciphers by Rahman et al. [16] and Fu et al. [17].”
BackgroundMethodAn image encryption scheme based on rotation matrix bit-level permutation and block diffusion
Zhang, Y., & Xiao, D. (2013) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2013.06.031 · Cited by 200 · see citing works
Design of image cipher using block-based scrambling and image filtering
Hua, Z., & Zhou, Y. (2017) · Information Sciences · doi:10.1016/j.ins.2017.02.036 · Cited by 195 · see citing works
Medical image encryption using edge maps
Cao, W., Zhou, Y., Chen, C. L. P., & Xia, L. (2016) · Signal Processing · doi:10.1016/j.sigpro.2016.10.003 · Cited by 187 · see citing works
Cryptanalysis of a DNA-based image encryption scheme
Chen, J., Chen, L., & Zhou, Y. (2020) · Information Sciences · doi:10.1016/j.ins.2020.02.024 · Cited by 195 · see citing works
Cracking a hierarchical chaotic image encryption algorithm based on permutation
Li, C. (2016) · Signal Processing · doi:10.1016/j.sigpro.2015.07.008 · Cited by 173 · see citing works
“In [11], the computational complexity of the attack is further reduced to O(n · (M ·N)) by replacing the set intersection operations of quadratic complexity with linear element access operations.”
BackgroundSelf-citationChen, J., Zhang, Y., Qi, L., Fu, C., & Xu, L. (2017) · Optics & Laser Technology · doi:10.1016/j.optlastec.2017.09.008 · Cited by 172 · see citing works
Zhang, Y., Xiao, D., Shu, Y., & Li, J. (2013) · Signal Processing Image Communication · doi:10.1016/j.image.2012.12.009 · Cited by 150 · see citing works
Designing permutation–substitution image encryption networks with Henon map
Ping, P., Xu, F., Mao, Y., & Wang, Z. (2017) · Neurocomputing · doi:10.1016/j.neucom.2017.12.048 · Cited by 149 · see citing works
An efficient image encryption scheme using lookup table-based confusion and diffusion
Chen, J., Zhu, Z., Fu, C., Zhang, L., & Zhang, Y. (2015) · Nonlinear Dynamics · doi:10.1007/s11071-015-2057-6 · Cited by 120 · see citing works
“In other words, we can directly construct the permutation matrix ( PM ) [39,40] as Eq.”
BackgroundMethodA novel chaotic map application in image encryption algorithm
Li, L. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.124316 · Cited by 121 · see citing works
Breaking a novel colour image encryption algorithm based on chaos
Li, C., Zhang, L. Y., Ou, R., Wong, K., & Shu, S. (2012) · Nonlinear Dynamics · doi:10.1007/s11071-012-0626-5 · Cited by 115 · see citing works
“Referring to quantitative cryptanalysis of permutation-only encryption algorithms in [19, 20], the complexity of breaking the position permutation part is only O(3MN).”
BackgroundSelf-citationA chaotic image encryption scheme owning temp-value feedback
Zhang, L. Y., Hu, X., Liu, Y., Wong, K., & Gan, J. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.03.016 · Cited by 113 · see citing works
“Thus makes this kind of permutation tough for the known/chosen plaintext attack proposed in [13, 17].”
BackgroundA fuzzy based ROI selection for encryption and watermarking in medical image using DWT and SVD
Balasamy, K., & Suganyadevi, S. (2020) · Multimedia Tools and Applications · doi:10.1007/s11042-020-09981-5 · Cited by 111 · see citing works
“Apply 2-level DWT on W, W = [LL2,HL2, LH2,HH2] 7.”
MethodInfluentialCryptanalysis of a one round chaos-based Substitution Permutation Network
Arroyo, D., Díaz, J. A., & Rodrı́guez, F. B. (2012) · Signal Processing · doi:10.1016/j.sigpro.2012.11.019 · Cited by 108 · see citing works
“As it is commented in [21], the fact that Eq.”
BackgroundMethodSecurity measurement of a medical communication scheme based on chaos and DNA coding
Chen, L., Li, C., & Li, C. (2022) · Journal of Visual Communication and Image Representation · doi:10.1016/j.jvcir.2021.103424 · Cited by 108 · see citing works
“In this process, MPPS is degenerated to a position permutation-only encryption scheme, whose security performance has been studied in depth in [22, 21].”
MethodSelf-citationLuo, Y., Zhou, R., Liu, J., Cao, Y., & Ding, X. (2018) · Nonlinear Dynamics · doi:10.1007/s11071-018-4251-9 · Cited by 112 · see citing works
“Specifically, several chaotic cryptosystems have been proposed for image security [23,30].”
BackgroundA novel bit permutation-based image encryption algorithm
Raza, S. F., & Satpute, V. (2019) · Nonlinear Dynamics · doi:10.1007/s11071-018-4600-8 · Cited by 99 · see citing works
Differential cryptanalysis of a novel image encryption algorithm based on chaos and Line map
Chen, L., Ma, B., Zhao, X., et al. (2016) · Nonlinear Dynamics · doi:10.1007/s11071-016-3153-y · Cited by 98 · see citing works
“In [20], Li et al. optimize the analysis above by a binary tree clas-sification method and a multi-branch tree classification method, and the corresponding spatial complexity and the computational complexity are reduced to only O ( M N ) and O ( M N log L ( M N )) ,respectively.”
MethodA Content-Adaptive Joint Image Compression and Encryption Scheme
Li, P., & Lo, K. (2017) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2017.2786860 · Cited by 94 · see citing works
Self-citationTPE2: Three-Pixel Exact Thumbnail-Preserving Image Encryption
Zhao, R., Zhang, Y., Xiao, X., Ye, X., & Lan, R. (2021) · Signal Processing · doi:10.1016/j.sigpro.2021.108019 · Cited by 91 · see citing works
Counteracting Dynamical Degradation of Digital Chaotic Chebyshev Map via Perturbation
Liu, Y., Luo, Y., Song, S., Cao, L., Liu, J., & Harkin, J. (2017) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812741750033x · Cited by 88 · see citing works
Zhou, N., Yang, J., Tan, C., et al. (2015) · Optics Communications · doi:10.1016/j.optcom.2015.05.043 · Cited by 86 · see citing works
An efficient image encryption scheme using gray code based permutation approach
Chen, J., Zhu, Z., Fu, C., Yu, H., & Zhang, L. (2014) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2014.11.017 · Cited by 85 · see citing works
Plaintext-related image encryption algorithm based on perceptron-like network
Zhang, Y., Chen, A., Tang, Y., Dang, J., & Wang, G. (2020) · Information Sciences · doi:10.1016/j.ins.2020.03.054 · Cited by 84 · see citing works
Design of an image encryption scheme based on a multiple chaotic map
Tong, X. (2012) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2012.11.002 · Cited by 83 · see citing works
Breaking an Image Encryption Algorithm Based on DNA Encoding and Spatiotemporal Chaos
Wen, H., Yu, S., & Lü, J. (2019) · Entropy · doi:10.3390/e21030246 · Cited by 78 · see citing works
“Whereas, in 2017, Dou et al. [30] used the chosen-plaintext attack method to break the algorithm proposed in Reference [29].”
BackgroundMethodInfluentialCryptanalysis of image encryption scheme based on a new 1D chaotic system
Dhall, S., Pal, S. K., & Sharma, K. (2018) · Signal Processing · doi:10.1016/j.sigpro.2017.12.021 · Cited by 77 · see citing works
Zhang, Y., Xiao, D., Wen, W., et al. (2013) · Optics Letters · doi:10.1364/ol.38.004506 · Cited by 75 · see citing works
Zhang, Y., Wen, W., Su, M., & Li, M. (2013) · Optik · doi:10.1016/j.ijleo.2013.09.018 · Cited by 74 · see citing works
Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion
Hu, G., Xiao, D., Wang, Y., & Li, X. (2017) · Nonlinear Dynamics · doi:10.1007/s11071-016-3311-2 · Cited by 74 · see citing works
“What is more, the optimal quantitative cryptanalysis of permutation-only cipher has been thoroughly and systematically discussed in [20], in which only few known/chosen plain images are sufficient to achieve a good attack performance.”
BackgroundImproved known-plaintext attack to permutation-only multimedia ciphers
Zhang, L. Y., Liu, Y., Wang, C., Zhou, J., Zhang, Y., & Chen, G. (2018) · Information Sciences · doi:10.1016/j.ins.2017.11.021 · Cited by 75 · see citing works
A new image encryption algorithm based on two-dimensional spatiotemporal chaotic system
He, Y., Zhang, Y., & Wang, X. (2018) · Neural Computing and Applications · doi:10.1007/s00521-018-3577-z · Cited by 71 · see citing works
Cryptanalysis and improvement in a chaotic image cipher using two-round permutation and diffusion
Li, M., Lu, D., Xiang, Y., Zhang, Y., & Ren, H. (2019) · Nonlinear Dynamics · doi:10.1007/s11071-019-04771-7 · Cited by 71 · see citing works
“Meanwhile, some encryption meth-ods with only permutation or diffusion have also been cracked [21–24].”
BackgroundCryptanalysis of Image Ciphers With Permutation-Substitution Network and Chaos
Chen, J., Chen, L., & Zhou, Y. (2020) · IEEE transactions on circuits and systems for video technology (Print) · doi:10.1109/tcsvt.2020.3021908 · Cited by 56 · see citing works
Hanif, M., Naqvi, R. A., Abbas, S., Khan, M. A., & Iqbal, N. (2020) · IEEE Access · doi:10.1109/access.2020.3004536 · Cited by 68 · see citing works
“In the literature, one can easily find encryption schemes that only perform the permutation (confusion/scrambling) [19]–[22].”
BackgroundZhang, Y., Xiao, D., Wen, W., & Li, M. (2014) · Nonlinear Dynamics · doi:10.1007/s11071-014-1235-2 · Cited by 67 · see citing works
“Moreover, some works [9–13] to evaluate the security of chaos-based image cryptosystems are of vital significance for its advancement.”
BackgroundIqbal, N., Hanif, M., Abbas, S., Khan, M. A., & Rehman, Z. U. (2021) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2021.102809 · Cited by 68 · see citing works
A Chaos Based Image Encryption Scheme Using Digit-Level Permutation and Block Diffusion
Ping, P., Fan, J., Mao, Y., Xu, F., & Gao, J. Z. (2018) · IEEE Access · doi:10.1109/access.2018.2879565 · Cited by 68 · see citing works
“Such pixel-level permutations are vulnerable to histogram attacks and chosen/known-plaintext attacks if they have no diffusions or bad diffusions [25], [26].”
BackgroundCryptanalysis of an image encryption algorithm using Chebyshev generator
Wang, X., Luan, D., & Bao, X.-M. (2013) · Digital Signal Processing · doi:10.1016/j.dsp.2013.10.020 · Cited by 66 · see citing works
Security analysis and enhancements of an image cryptosystem based on hyperchaotic system
Ahmad, M., Doja, M. N., & Beg, M. M. S. (2018) · Journal of King Saud University - Computer and Information Sciences · doi:10.1016/j.jksuci.2018.02.002 · Cited by 66 · see citing works
“…have been successfully cracked by security experts and attackers and were found insecure (Hermassi et al., 2012; Li, 2016; Bechikh et al., 2015; Li and Lo, 2011; Rhouma and Belghith, 2009; Ahmad, 2011; Jeng et al., 2015; Özkaynak et al., 2012; Özkaynak and Özer, 2016; Chen et al., 2017; Fan et…”
Universal Chosen-Ciphertext Attack for a Family of Image Encryption Schemes
Chen, J., Chen, L., & Zhou, Y. (2020) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2020.3011315 · Cited by 66 · see citing works
Parallel strength Pareto evolutionary algorithm‐II based image encryption
Kaur, M., Singh, D., & Uppal, R. S. (2019) · IET Image Processing · doi:10.1049/iet-ipr.2019.0587 · Cited by 65 · see citing works
“From Tables 10 and 12, it can be seen that the proposed approach has minimum horizontal, diagonal, and vertical correlations in most of the cases.”
BackgroundCryptanalyzing Two Image Encryption Algorithms Based on a First-Order Time-Delay System
Liu, S., Li, C., & Hu, Q. (2021) · IEEE Multimedia · doi:10.1109/mmul.2021.3114589 · Cited by 65 · see citing works
“As discussed in [17, 18], some minor error elements in permutation matrix have no much influence on the decryption performance.”
BackgroundMethodSelf-citationCryptanalysis of a DNA and chaos based image encryption algorithm
Dou, Y., Liu, X., Fan, H., & Li, M. (2017) · Optik · doi:10.1016/j.ijleo.2017.08.050 · Cited by 66 · see citing works
SPRING: a novel parallel chaos-based image encryption scheme
Lee, W.-K., Phan, R. C.-W., Yap, W.-S., & Goi, B.-M. (2018) · Nonlinear Dynamics · doi:10.1007/s11071-018-4076-6 · Cited by 65 · see citing works
Chaotic image encryption using pseudo-random masks and pixel mapping
Li, X., Li, C., & Lee, I. (2015) · Signal Processing · doi:10.1016/j.sigpro.2015.11.017 · Cited by 64 · see citing works
Self-citationEfficient Chaos-Based Substitution-Box and Its Application to Image Encryption
El‐Latif, A. A. A., Abd-El-Atty, B., Belazi, A., & Iliyasu, A. M. (2021) · Electronics · doi:10.3390/electronics10121392 · Cited by 68 · see citing works
Khelifi, F. (2018) · Signal Processing · doi:10.1016/j.sigpro.2017.09.020 · Cited by 63 · see citing works
“It has also been successful in breaking a number of permutation-only image encryption systems [28, 29] though its performance remains clearly lower than that of the known-plaintext attack and the chosen-plaintext attack [30, 31, 32].”
BackgroundCryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map
Chen, J., Han, F., Qian, W., Yao, Y.-D., & Zhu, Z.-L. (2018) · Nonlinear Dynamics · doi:10.1007/s11071-018-4332-9 · Cited by 62 · see citing works
Cryptanalyzing a chaos-based image encryption algorithm using alternate structure
Zhang, L. Y., Li, C., Wong, K., Shu, S., & Chen, G. (2012) · Journal of Systems and Software · doi:10.1016/j.jss.2012.04.002 · Cited by 60 · see citing works
“Keywords: image, chaos, cryptanalysis, differential attack, encryption”
Self-citationFeng, W., & He, Y.-G. (2018) · IEEE Photonics Journal · doi:10.1109/jphot.2018.2880590 · Cited by 60 · see citing works
“An attacker can degrade the encryption algorithm into a permutation-only one by using the chosen plaintext attack, whereas permutation-only algorithms have been proved to be unsafe in many literatures [25]–[27].”
MethodError-free holographic frames encryption with CA pixel-permutation encoding algorithm
Li, X., Xiao, D., & Wang, Q. (2017) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2017.08.018 · Cited by 59 · see citing works
Cryptanalysis of Reversible Data Hiding in Encrypted Images by Block Permutation and Co-Modulation
Qu, L., Chen, F., Shanjun, Z., et al. (2021) · IEEE Transactions on Multimedia · doi:10.1109/tmm.2021.3090588 · Cited by 59 · see citing works
Hanif, M., Iqbal, N., Rahman, F. U., Khan, M. A., Ghazal, T. M., Abbas, S., Ahmad, M., Hamadi, H. A., & Yeun, C. Y. (2022) · Sensors · doi:10.3390/s22166243 · Cited by 62 · see citing works
Wen, H., & Yu, S.-M. (2019) · The European Physical Journal Plus · doi:10.1140/epjp/i2019-12797-4 · Cited by 58 · see citing works
Feature Extraction-based Medical Image Watermarking Using Fuzzy-based Median Filter
Balasamy, K., & Shamia, D. (2021) · IETE Journal of Research · doi:10.1080/03772063.2021.1893231 · Cited by 57 · see citing works
Luo, Y., Liu, Y., Liu, J., et al. (2020) · Information Sciences · doi:10.1016/j.ins.2020.12.065 · Cited by 56 · see citing works
Cryptanalysis of a new image encryption algorithm based on chaos
Özkaynak, F., & Özer, A. B. (2016) · Optik · doi:10.1016/j.ijleo.2016.03.018 · Cited by 56 · see citing works
Zhao, L., Adhikari, A., Xiao, D., & Sakurai, K. (2011) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2011.12.015 · Cited by 55 · see citing works
On the security of block scrambling-based ETC systems against jigsaw puzzle solver attacks
Chuman, T., Kurihara, K., & Kiya, H. (2017) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2017.7952538 · Cited by 53 · see citing works
“Several efficient attacks on the permutation-only encryption have been studied [9,10], but they are not available for the block scrambling-based encryption.”
BackgroundXie, T., Liu, Y., & Tang, J. (2014) · Optik · doi:10.1016/j.ijleo.2014.07.111 · Cited by 52 · see citing works
Breaking a novel image encryption scheme based on Brownian motion and PWLCM chaotic system
Zhu, C., Xu, S., Hu, Y., & Sun, K. (2014) · Nonlinear Dynamics · doi:10.1007/s11071-014-1757-7 · Cited by 51 · see citing works
“In this case, suppose the 3×3 cipher image to be recovered in 1D form is C = [196, 179, 18, 219, 157, 93, 62, 58, 105]; M = 3, N = 3, and L = M × N = 9.”
BackgroundA novel gray scale image encryption scheme based on pixels’ swapping operations
Bashir, Z., Iqbal, N., & Hanif, M. (2020) · Multimedia Tools and Applications · doi:10.1007/s11042-020-09695-8 · Cited by 49 · see citing works
“Some encryption schemes were developed by permutation-only [18, 19, 28], for instance.”
MethodA block chaotic image encryption scheme based on self-adaptive modelling
Ye, G., & Zhou, J. (2014) · Applied Soft Computing · doi:10.1016/j.asoc.2014.05.025 · Cited by 49 · see citing works
Performance study of selective encryption in comparison to full encryption for still visual images
Khashan, O. A., Zın, A. M., & Sundararajan, E. A. (2014) · Frontiers of Information Technology & Electronic Engineering · doi:10.1631/jzus.c1300262 · Cited by 48 · see citing works
“Furthermore, several random position permutation algorithms (Li et al., 2008; Li and Lo, 2011; Zhang et © Zhejiang University and Springer-Verlag Berlin Heidelberg 2014 al., 2013a) and chaotic based cryptosystems (Liu and Wang, 2010; Bhatnagar and Wu, 2012; Zhang et al., 2013b) have been used to…”
MethodJoint SPIHT compression and selective encryption
Xiang, T., Qu, J., & Xiao, D. (2014) · Applied Soft Computing · doi:10.1016/j.asoc.2014.03.009 · Cited by 47 · see citing works
An Image Encryption Algorithm Utilizing Julia Sets and Hilbert Curves
Sun, Y., Chen, L., Xu, R., et al. (2014) · PLoS ONE · doi:10.1371/journal.pone.0084655 · Cited by 47 · see citing works
“For some shortcomings in encryption algorithms, Li et al. made the optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks [13] [14].”
MethodCryptanalysis of an image block encryption algorithm based on chaotic maps
Ma, Y., Li, C., & Ou, B. (2020) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2020.102566 · Cited by 100 · see citing works
Self-citationA Novel Image Encryption Scheme Using the Composite Discrete Chaotic System
Zhu, H., Zhang, X., Yu, H., Zhao, C., & Zhu, Z. (2016) · Entropy · doi:10.3390/e18080276 · Cited by 46 · see citing works
Differential attack on a hyper-chaos-based image cryptosystem with a classic bi-modular architecture
Wen, W., Zhang, Y., Su, M., Zhang, R., Chen, J., & Li, M. (2016) · Nonlinear Dynamics · doi:10.1007/s11071-016-3049-x · Cited by 46 · see citing works
“Once this diffusion algorithm is broken, the algorithm to be cryptanalyzed is equivalent to a permutation-only cipher, which has been thoroughly studied in [18,19].”
BackgroundMethodOn the Security of Block Scrambling-Based EtC Systems against Extended Jigsaw Puzzle Solver Attacks
Chuman, T., Kurihara, K., & Kiya, H. (2017) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2017mup0001 · Cited by 45 · see citing works
“Several efficient attacks on the permutation-only encryption have been studied [11], [12], but they are not available for the block scrambling-based encryption.”
BackgroundSurvey on JPEG compatible joint image compression and encryption algorithms
Li, P., & Lo, K. (2020) · IET Signal Processing · doi:10.1049/iet-spr.2019.0276 · Cited by 45 · see citing works
Self-citationChosen plaintext attack on JPEG image encryption with adaptive key and run consistency
He, H., Yuan, Y., Ye, Y., et al. (2022) · Journal of Visual Communication and Image Representation · doi:10.1016/j.jvcir.2022.103733 · Cited by 44 · see citing works
Differential cryptanalysis of a medical image cryptosystem with multiple rounds
Chen, L., & Wang, S. (2015) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2015.07.024 · Cited by 44 · see citing works
“Li et al and Li and Lo [12,13] have demonstrated that the permutation-only schemes are insecure, but their cryptanalysises cannot apply to the permutation–diffusion (permutation–substitution) encryption type [1].”
BackgroundMethodImage encryption based on a new 2D logistic adjusted logistic map
Sharma, M. J. (2019) · Multimedia Tools and Applications · doi:10.1007/s11042-019-08079-x · Cited by 44 · see citing works
Cryptanalysis and Improvement of an Efficient and Secure Medical Image Protection Scheme
Zhang, L., Zhu, Z., Yang, B.-Q., Liu, W., Zhu, H., & Zou, M. (2015) · Mathematical Problems in Engineering · doi:10.1155/2015/913476 · Cited by 41 · see citing works
“After the substitution key stream elements have been recovered, there are various types of methods for the attackers to go back to retrieve the permutationmatrix [24, 31], and then thewhole cryptosystem is completely broken.”
MethodChuman, T., Kurihara, K., & Kiya, H. (2017) · IEEE International Conference on Multimedia and Expo (ICME) · doi:10.1109/icme.2017.8019487 · Cited by 42 · see citing works
“Several efficient attacks on the permutation-only encryption have been studied [9,10], but they are not available for the block scrambling-based encryption.”
BackgroundOutsourcing chaotic selective image encryption to the cloud with steganography
Xiang, T., Hu, J., & Sun, J. (2015) · Digital Signal Processing · doi:10.1016/j.dsp.2015.05.006 · Cited by 42 · see citing works
A chaos-based image encryption scheme using 2D rectangular transform and dependent substitution
Zhang, X., Fan, X. P., Wang, J., & Zhao, Z. (2014) · Multimedia Tools and Applications · doi:10.1007/s11042-014-2372-9 · Cited by 42 · see citing works
“Since the permutation only shuffles the pixel positions but remains the pixel values unchanged, it can be easily cryptanalyzed[14, 15].”
BackgroundAn Enhanced Image Encryption Algorithm Using Fractional Chaotic Systems
Ahmad, M., Shamsi, U., & Khan, I. R. (2015) · Procedia Computer Science · doi:10.1016/j.procs.2015.07.494 · Cited by 40 · see citing works
Azoug, S. E., & Bouguezel, S. (2015) · Optics Communications · doi:10.1016/j.optcom.2015.09.054 · Cited by 40 · see citing works
Cryptanalyzing a class of image encryption schemes based on Chinese remainder theorem
Li, C., Liu, Y., Zhang, L. Y., & Wong, K. (2014) · Signal Processing Image Communication · doi:10.1016/j.image.2014.06.011 · Cited by 39 · see citing works
“So, the complexity required in recovering equivalent version of the permutation part is O(L) [28].”
BackgroundMethodResultSelf-citationLightweight Selective Encryption for Social Data Protection Based on EBCOT Coding
Qiu, H., Meikang Qiu, A., Liu, M., & Ming, Z. (2019) · IEEE Transactions on Computational Social Systems · doi:10.1109/tcss.2019.2952553 · Cited by 39 · see citing works
“Since the attacker may recover the permutation rule if the K is not related to the plaintext and is reused [31].”
BackgroundOn The Security of Block Permutation and Co-XOR in Reversible Data Hiding
Qu, L., He, H., & Chen, F. (2021) · IEEE Transactions on Circuits and Systems for Video Technology · doi:10.1109/tcsvt.2021.3069811 · Cited by 37 · see citing works
On the novel image encryption based on chaotic system and DNA computing
Iqbal, N., Hanif, M., Rehman, Z. U., & Zohaib, M. (2022) · Multimedia Tools and Applications · doi:10.1007/s11042-022-11912-5 · Cited by 37 · see citing works
“In the literature, one may find the ciphers based only on the permutation operations [23, 24, 33].”
BackgroundSecurity analysis of image cryptosystems only or partially based on a chaotic permutation
Hermassi, H., Rhouma, R., & Belghith, S. M. (2012) · Journal of Systems and Software · doi:10.1016/j.jss.2012.04.031 · Cited by 36 · see citing works
“This version of the cryptosystem under study was also analyzed by Li and Lo in [28], their attacks consist on constructing a binary tree to reveal the permutation matrix W of size M × 8N by applying a known plaintext attack and a chosen plaintext attack.”
MethodCryptanalysis of image scrambling based on chaotic sequences and Vigenère cipher
Zhang, Y., Xiao, D., Wen, W., & Nan, H. (2014) · Nonlinear Dynamics · doi:10.1007/s11071-014-1435-9 · Cited by 36 · see citing works
A Pseudorandom Number Generator Based on the Chaotic Map and Quantum Random Walks
Zhao, W., Chang, Z., Ma, C., et al. (2023) · Entropy · doi:10.3390/e25010166 · Cited by 35 · see citing works
“; thus, a cryptosystem based on the original chaotic map may be successfully attacked [4,13,14].”
BackgroundSecure image cryptosystem with unique key streams via hyper-chaotic system
Diab, H., & El-semary, A. M. (2018) · Signal Processing · doi:10.1016/j.sigpro.2017.06.028 · Cited by 35 · see citing works
Security enhancement of double random phase encoding using rear-mounted phase masking
Chen, J., Zhang, L. Y., Jin-chang, L., & Zhang, L. (2017) · Optics and Lasers in Engineering · doi:10.1016/j.optlaseng.2017.09.019 · Cited by 35 · see citing works
Deciphering an image cipher based on 3-cell chaotic map and biological operations
Zhang, Y., Li, Y., Wen, W., Wu, Y., & Chen, J. (2015) · Nonlinear Dynamics · doi:10.1007/s11071-015-2280-1 · Cited by 34 · see citing works
“If there needs to be a blurry or rough image through the crypt-analysis, the number of the images when deciphering the scrambling phase can be further optimized by the methods [34,35], in which the scrambling-only image ciphers have been thoroughly and systematically cryptanalyzed.”
Method
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-18.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-18.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
