Cipher Image Damage: An Application of Filters
Open accessAbstract
In this paper, color images are encrypted and subsequently damage occlusion is made to the encrypted figures, with different sizes; the intention is to simulate an attack.In this research, two aspects are discussed, namely: the first is to encrypt images with quality; that is, the figures encrypted pass randomness tests proposed in this paper.The second aspect deals with the problem of recovering the encrypted figure information when it has been damaged.To retrieve information from encrypted images, the enryption of images is carried out in two steps: in the first a permutation is applied to the entire image and the second uses the AES cryptosystem with variable permutations.To perform this task an algorithm is used that utilizes the pi number to generate the permutations.To improve the sharpness of the deciphered figures with damage two filters are applied; median and average.To measure the degree of improvement in the damaged images two tests are proposed; the first is the correlation coefficient between adjacent pixels in the horizontal, vertical and diagonal directions.The second is based on the information entropy.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper encrypts color images with a whole-image pi-based permutation followed by AES with per-block variable permutations, then simulates occlusion damage on ciphertexts and applies median/average filters after decryption. It reports that encrypted images pass randomness tests and that filtering improves damaged decrypted images, though recovery degrades as damage grows.
Key findings
- Encrypted images passed the proposed randomness tests at α = 0.01; entropy values were near 8, e.g. for the proposed image red 7.99934, green 7.99925, blue 7.99934, with similar values for Peppers, Baboon, Barbara and Lena.
- Adjacent-pixel correlations dropped from high values in original images (e.g. red horizontal 0.60–0.99) to near zero in cipher images (Table VII values 0.000–0.061). Sensitivity analysis between keys k and k+1 gave correlations of red 0.0313, green 0.0133, blue 0.0098.
- For damaged decrypted image (a) Figure 4, filters improved correlation: red horizontal at 35% damage was 0.392, rising to 0.957 with median 3×3, 0.964 with median 5×5, and 0.957 with average. Entropy decreased from 7.851 to 7.655, 7.614, and 7.551 respectively.
- Larger damage reduced filter effectiveness; the paper states damage greater than 50% makes recovery very difficult, and around 80% or 90% is very difficult. Encryption time was about 85 milliseconds in C++ on an Intel Core i7.
Methods
- Two-step encryption: first a permutation over all image pixels generated using pi and the AES key, then AES-128 in ECB mode with a different permutation for each 128-bit block after the XOR operation in the first round; no compression is used.
- Images encrypted were Peppers, Baboon, Barbara, Lena, and a proposed image of poetry by Octavio Paz. Damage was occlusion by concentric rectangles at sizes 35%, 40% and 45% (the text also mentions 30%, 40% and 45%). Filters applied were median 3×3, median 5×5, and average 3×3.
- Analysis used DFT, entropy, a proposed chi-square goodness-of-fit test, adjacent-pixel correlation in horizontal, vertical and diagonal directions, and sensitivity between keys k and k+1. Improvement after filtering was measured by entropy and correlation, using random samples of 3000 pixel pairs.
Limitations
- Stated: only occlusion noise is used; additive and multiplicative noise are left for future work. Only median and mean filters are used; other filters, including mathematical morphology, are left for further research. Compression is not used. Larger damage, especially >50% and around 80–90%, makes recovery very difficult.
- Evident: the damage sizes are inconsistently reported as 35/40/45% and 30/40/45%. The paper states it does not aim to compare filters, and results are limited to a small set of images plus one proposed image.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
0 of 33 cited sources checked · 0 supported · 0 flagged
- Findingreasoning
For an image of dimensions 960 × 540, the time spent constructing the permutation is less than ten milliseconds using software.
“Actually, the time spent on the construction of the switch from one image of dimensions 960 × 540 is less than ten milliseconds using software.”
Quote in the paperNot a substantial claim - Findingreasoning
The permutation generation algorithm has complexity O(l).
“Regarding the complexity to perform this algorithm is O(l), since in each step removal and replacement of an element is carried out, the others remaining unchanged.”
Quote in the paperNot a substantial claim - Findingcitation
Applying median and average filters to decrypted damaged images improves their sharpness.
“To improve the sharpness of the deciphered figures with damage two filters are applied; median and average.”
- Also stated in: § I. INTRODUCTION · plain
“this is not the objective of this research which shows the improvement in the decrypted figures when some of the aforementioned filters are applied.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § I. INTRODUCTION · plain
- Findingreasoning
For an image of about 500,000 pixels (960 × 540), the permutation problem can be resolved speedily.
“If the figure is about 500,000 pixels, 960 × 540, the size of the problem to be solved is O(500, 000) for this particular case, which means it can be resolved speedily.”
Quote in the paperNot a substantial claim - Findingown data
The encrypted images pass all the randomness tests proposed in this research.
“Encrypted image passes all the aforementioned tests of randomness and also the proposal.”
- Also stated in: § VIII. DISCUSSION OF THE RESULTS · plain
“encrypted images pass all the randomness tests proposed in this research.”
Quote in the paperSubstantial claim - Also stated in: § VIII. DISCUSSION OF THE RESULTS · plain
- Findingreasoning
For bigger damage, the filters are less efficient.
“in general it can be said that for bigger damage, the filters are less efficient, i.e. both measuring instruments may be inaccurate.”
Quote in the paperSubstantial claim - Findingown data
Sensitivity testing shows there is no relationship between encrypted images and keys in close proximity.
“Sensitivity testing was also performed in order to show that there is no relationship between encrypted images and keys in close proximity.”
Quote in the paperSubstantial claim - Findingnone given
Noise reduction is significant when the correlation coefficient is used as a measuring instrument.
“Noise reduction is significant as can be seen, when the Correlation as an instrument of measure is used.”
Quote in the paperSubstantial claim - Findingnone given
The entropy results for the encrypted images in Table 4 are better than those shown in other studies [5].
“Entropy results presented in Table 4 are better than those shown in other studies [5].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [5]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Premisenone given
When ECB mode is used to encrypt images with low randomness and without variable permutations, using the same key for all 128-bit blocks, the encrypted image may reveal information, with the distribution of basic color shades following a pattern.
“However, when the ECB protocol is used to encrypt figures that have low randomness degree in their bits and does not apply the variable permutations process, and also uses the same key for all 128 bit blocks of the image, it may be that the encrypted figure could give us information; i.e, the distribution of the different shades of basic colors follows a certain pattern; see Figure 2.”
Quote in the paperSubstantial claim - Premisecitation
For an encrypted image of good quality, the correlation coefficient between adjacent pixels in horizontal, vertical, and diagonal directions is expected to be close to zero.
“With respect to the Correlation between adjacent pixels of an encrypted image with “quality,” it is expected that there is a Correlation coefficient close to zero between adjacent pixels, that is, the linear relationship between them must be very weak [39].”
- Also stated in: § II. PRELIMINARIES · plain
“if the encryption figure has good “quality”; then it is expected that the Correlation coefficient between adjacent pixels horizontal, vertical and diagonal is a number close to zero.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [39]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § II. PRELIMINARIES · plain
- Premisecitation
If the distribution of bits is totally random, the entropy is 8.
“In this vein, it is said that if the distribution of bits is totally random the Entropy is 8.”
- Also stated in: § II. PRELIMINARIES · plain
“if a particular primary color has uniform distribution; i.e, all points are equally likely, the entropy value is 8 [31].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [31]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Also stated in: § II. PRELIMINARIES · plain
- Interpretationnone given
Generally, if damage is greater than 50%, it is very difficult to gather the information of the original image again.
“Generally, if the damage is large, say greater than 50%, it can be said that it is very difficult to gather the information of the original image again.”
Quote in the paperNot a substantial claim - Interpretationreasoning
When an image is decrypted with damage, the result is less sharp than the original due to noise introduced in the decoded image.
“Clearly, when the figure is decrypted with failure the result is less sharp than the original image.This is due to noise which is introduced in the decoded image.”
Quote in the paperSubstantial claim - Premisecitation
Chosen-plaintext attacks such as linear or differential are not addressed in prior works.
“The chosen-plaintext attacks as linear [8] or differential [9] are not addressed.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [8]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [9]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationreasoning
There are many relatively small images with χ2 that can be applied directly to the AES cryptosystem without a random permutation after the x-or operation in the first round for each 128-bit block of plaintext.
“there are many relatively small images with χ 2 which can be applied directly to the AES cryptosystem, see Figure 5; i.e. it is not necessary to use a random permutation after the x-or operation in the first round for each 128-bits block of plaintext.”
Quote in the paperSubstantial claim - Interpretationreasoning
If damage is around 80% or 90%, it is very difficult to recover the original image.
“if the damage is around 80% or 90% it is very difficult with this information to recover the original image.”
Quote in the paperSubstantial claim - Premisecitation
In all NIST 800-22 tests, the randomness of the tone distribution of the basic colors is not measured.
“In all NIST 800-22 tests, to determine the degree of randomness of the bits in a string, this type of proof does not appear, that is, the tone distribution randomness of the basic colors is not measured, so, it is a different situation.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites NIST 800-22
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- May combine two claims. 18
- Classified as probably not a substantial claim. 24
May combine two claims.
FindingcitationThe algorithm defines a bijective function from the set of integers to the set of permutations, so two different sets of constants C_i have two different permutations.
“the algorithm described in the previous section defines a Bijective function [33], from the integers set to the permutations set, which is denoted as I m , thus, if I m is a Bijective function, it follows that it is a one to one function.This is important, since two different sets of constants C i have associated two different permutations”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [33]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Findingown dataThe proposed encryption method (initial permutation over the entire image followed by AES with variable permutations) produces encrypted images that pass the proposed randomness tests: horizontal, vertical, and diagonal correlation, Discrete Fourier Transform, entropy, and the proposed Goodness-of-fit test.
“It is shown later that the images encrypted by this method pass the tests of randomness proposed, which are: horizontal, vertical and diagonal correlation [19]; Discrete Fourier Transform (DTF) [20]; entropy; and the proposed “Goodness-of-fit test” [19].”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [19]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [20]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
Findingnone givenThe chosen image has χ2 r = 56,638,911.17, χ2 g = 56,555,658.91, and χ2 b = 55,396,932.18.
“In this investigation a figure with the following chi-square for the primary colors red, green and blue is used: χ 2 r = 56,638,911.17,χ 2 g = 56, 555, 658.91 and χ 2 b = 55, 396, 932.18.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataWhen figures are encrypted and then decoded with damage, they can be improved by using filters; both median and average filters decreased noise.
“it is shown that when these figures were encrypted and then decoded with damage, they can be improved by using filters.The filters used were: median and average and in both cases the noise decreased.”
- Also stated in: § VIII. DISCUSSION OF THE RESULTS · hedged
“In all cases it was possible to reduce noise as illustrated in Tables 8 to 11.”
Quote in the paperSubstantial claim- Also stated in: § VIII. DISCUSSION OF THE RESULTS · hedged
May combine two claims.
Findingown dataThe measuring instruments show that there is a reduction in noise: entropy decreased and correlation coefficient increased.
“The measuring instruments to determine the degree of improvement in the decoded images show that there is a reduction in noise, i.e. the Entropy amount was reduced and the Correlations coefficient value increased.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationAES is a symmetric algorithm, which makes it very fast to encrypt information.
“It is also noted that AES is a symmetric algorithm [7], which makes it very fast to encrypt information.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [7]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisereasoningWhen entropy is near 8, the string of zeros and ones is understood to be random; otherwise it is not.
“When Entropy is near 8 it understands that the string of zeros and ones is random; otherwise it would mean that it is not.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisenone givenThe Discrete Fourier Transform measures the degree of randomness of a zeros and ones string by detecting absence of periodicity or repetitive patterns.
“The Discrete Fourier Transform measures the degree of randomness of zeros and ones string, that is, there is no periodicity -repetitive patterns-one followed by another.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
PremisecitationNo efficient method for breaking AES has yet been found.
“On the other hand, an efficient method for breaking it has not yet been found [26].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [26]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisenone givenThe keys set of the AES cryptosystem can be up to 2^256 elements.
“It also shows that the keys set of AES cryptosystem can be up to 2 256 elements.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningApplying the variable permutation in the first round gives more opportunity to scramble information, so at the end of encryption the ones and zeros appear randomly.
“Furthermore, why in the first round?Given that the information is mixed in each round, then any changes made in the first round there is more opportunity to scramble information, and at the end of the encryption process the ones and zeros will appear randomly.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningApplying the variable permutation after the x-or operation in the first round modifies bit strings even when the image has areas of the same color, whereas a permutation applied before the x-or would not modify strings of all ones or zeros.
“Regarding the first question, the reason it is not used at the entrance of the first round as with Triple-DES or Triple DES-96 [34], is because some images have areas of the same color; for example, black or white.In this situation a permutation applied to ones or zeros strings does not make any modifications to them.But, when it is used after the x-or operation, this allows modifying the bit str”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [34]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim. May combine two claims.
PremisecitationAES is a recent symmetric encryption system and the international standard at this time, making it the most studied algorithm in the world.
“The algorithm used for image encryption is AES [25] for the following reasons: because it is a recent symmetric encryption system and as the international standard at this time, it makes this algorithm the most studied in the world.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [25]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationIn a prior research, the original image is modified when the figure is decrypted.
“There is an interesting research in this field [14], however, the original image is modified when the figure is decrypted.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [14]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationIn prior optics encryption investigations, the number of keys is not noted.
“Also, there are investigations in optics [11], [12], [13] where the number of keys is also not noted.”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites [11]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [12]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [13]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe average filter is classified as linear.
“This filter is classified as linear [17].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
InterpretationreasoningFor significance level α = 0.01, the threshold is 307.61; for α = 0.001, the threshold is 324.78.
“So, the threshold for significance level α = 0.01 is 307.61 and for α = 0.001 is 324.78.”
Quote in the paperSubstantial claim- The authors state this as an assumption: The χ2 statistic for each primary color can be approximated by a normal distribution via the central limit theorem.
Classified as probably not a substantial claim.
PremisecitationFor encrypted damage figures, the proposal is to use filters to improve the sharpness of images with decrypted damage.
“As for encrypted damage figures [16], the proposal is to use filters [17] in order to improve the sharpness of images with decrypted damage.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [16]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim.
Premisenone givenA correlation coefficient close to 0 means there is no linear relationship between adjacent pixels in the same three directions.
“This means that there is no linear relationship between adjacent pixels for the same three directions.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe pi number is the transcendental employed because it has been well studied.
“The pi number is the transcendent to be employed in this article because it has been well studied [29].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [29]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S4 (based).
Premisenone givenThe product of an integer representing the AES key and pi is a transcendental number.
“Then the product m × pi is also a transcendental number and from it is possible to get the constants that are used to generate permutations”
Quote in the paperNot a substantial claimMay combine two claims.
Premisenone givenIf the tones distribution in each of the three basic colors is totally random, χ2 = 0, meaning each color histogram is a uniform distribution.
“if the tones distribution in each of the three basic colors was totally random χ 2 = 0.In fact, this means that each color histogram is a uniform distribution.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe median filter is a statistical non-linear type.
“It starts with the median filter which is a statistical non-linear type [17].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [17]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Classified as probably not a substantial claim.
InterpretationreasoningThe initial permutation over all image pixels spreads the figure data so that when an encrypted figure suffers damage, it does not appear focused on the deciphered image.
“Therefore, applying an initial permutation over all image pixels, randomly constructed is recommended.The intention is to spread the figure data, so that the pixels remain randomly distributed.In this sense, when an encrypted figure suffers damage, it does not appear focused on the deciphered image.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationThe proposed proof uses the Goodness-of-fit test with the χ2 statistic, which has a Chi-square probability distribution with n-1 degrees of freedom.
“the proposal proof uses the Goodness-of-fit test, utilizing the statistical, χ 2 , which has a probability distribution of Chi-square with n -1 degrees of freedom.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationA prior color image encryption work does not use any NIST Special Publication 800-22 proposal as proof of encryption quality.
“This work does not use as proof of the encryption quality any of the proposals in NIST Special Publication 800-22.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [15]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationIn a prior color image encryption research, the set size of the keys is not specified.
“In addition, there is a research of color image encryption [10], where the set size of the keys is not specified.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [10]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S4 (based).
Premisenone givenAn image is well encrypted if the entropy of each basic color is closer to eight.
“an image is”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationTranscendental numbers have the property that the decimal point to the right does not follow any regularity, so they are good candidates for generating pseudo-random numbers.
“Transcendental numbers are utilized, which have the characteristic of not being a solution of any polynomial with the form a n x n + a (n-1) x (n-1) + . . .+ a 0 with a i ∈ Z [28], but also have the property that the decimal point to the right does not follow any regularity, so they are good candidates for use in generating pseudo-random numbers.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [28]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
May combine two claims.
InterpretationreasoningWhen χ2 has a very large value for each primary color, AES with variable permutations should be applied; otherwise encryption is not efficient.
“when χ 2 has a very large value for each of the primary colors AES with variable permutations should be applied, otherwise the encryption is not efficient, see Figure 2.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenDamage to the figure does not necessarily achieve greater sharpness.
“The damage of the figure does not necessarily achieve greater sharpness.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationIn prior Hilbert transform and Chaos image encryption methods, the size of the keys set is not known specifically.
“In the Hilbert transform and Chaos cases, there is the difficulty of not knowing specifically, the size of the keys set.”
Quote in the paperNot a substantial claim0 of 3 sources checked- cites [2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- cites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S4 (based).
Premisenone givenFor a well-coded image, the correlation coefficient between adjacent pixels in horizontal, vertical, or diagonal directions is expected to be close to 0.
“If an image is”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationFor an image, the shades of each color can be represented as a histogram with 256 divisions, so the degrees of freedom are 255.
“the shades of each color of an image can be represented as a histogram whose abscissa has 256 divisions.Then, the degrees of freedom are 255 [19].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S2 (checkable), S4 (based).
Premisenone givenIn any image encryption it is important that the distribution of its bits should be random, in order to avoid bias that might lead to attacks to discover the key or plaintext.
“In any image encryption it is important that the distribution of its bits should be random, in order to avoid bias that might lead to attacks to discover the key or plaintext.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationIn prior Hyper-chaos encryption, the keys set is 2^167 and only brute force attack is mentioned.
“In the case of Hyper-chaos, the keys set is 2 167 and only the brute force attack is mentioned.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [5]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S4 (based).
PremisereasoningThe generating of permutations is dependent on the AES key.
“The generating of permutations is dependent on the AES key.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe proposed method does not use compression because some countries' safety areas do not allow compression in encryption images.
“It is important to clarify that this article does not use the compression process in the encryption image, because there are some countries whose safety areas do not allow the compression process in encryption images [23].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [23]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
The paper relies on this without support.
The occlusion damage model using concentric rectangles with 35%, 40%, and 45% area adequately simulates an attack on encrypted images.
“Damage to the encrypted images is carried out by concentric rectangles, see Figure 6, and the fault sizes are 35%, 40% and 45% of the total figure area.”
“the intention is to simulate an attack.”
The paper relies on this without support.
Many current images do not exceed 2^24 bits in spatial resolution, so 24-bit chains are sufficient for whole-image permutation.
“This, since many current images do not exceed 2 24 bits in the spatial resolution.”
The paper relies on this without support.
The selected test images (Peppers, Baboon, Barbara, Lena, and a fifth) are representative for evaluating the proposed encryption and damage recovery method.
“The images encrypted in this work appear in many other investigations.These figures are: Peppers, Baboon, Barbara and Lena.A fifth figure is proposed according to the criteria described below.”
The authors state this as an assumption.
The χ2 statistic for each primary color can be approximated by a normal distribution via the central limit theorem.
“if it is considered that the random variable χ 2 approaches the normal distribution according to the center limit theorem, it follows that the mean and variance of χ 2 statistical are: µ = 255 and σ = 2(255) = 22.5831 for each basic color.”
The paper relies on this without support.
An image with a very large χ2 for each primary color is a suitable test case to demonstrate the effectiveness of the proposed encryption method.
“in this research, it is proposed to choose an image that has a χ 2 as large as possible for each of the basic colors in order to show that the proposed method is effective for encrypt images.”
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.
Average filter does not reduce entropy in every case
MajorThe conclusion says entropy was reduced, but Table IX reports green entropy rising from 7.829 to 7.959 after average filtering at 45% damage. Thus the stated improvement does not hold in all cases.
“Green color Entropy 35% 7.756 7.068 40% 7.795 7.011 45% 7.829 7.959”
“In all cases it was possible to reduce noise as illustrated in Tables 8 to 11.”
Damage sizes disagree
MinorThe introduction specifies 35%, 40%, and 45% damage, but Section VII lists 30%, 40%, and 45%. The results tables also use 35%, not 30%.
“the fault sizes are 35%, 40% and 45% of the total figure area.”
“Damage sizes used in this article are shown hereunder: 30%, 40% and 45%.”
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Self-citationThe triple-DES-96 cryptographic system
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Self-citationLong-range dependencies in quick-sort algorithm
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Flagged first, then by citations
- Authors
- Flores-Carapia, R., Silva-García, V. M., Luna-Benoso, B., & Rentería-Márquez, C.
- Affiliations
- Instituto Politécnico Nacional (MX)
- ORCID
- Venue
- Polibits
- Published
- 2015-07-31
- Volume
- 52
- Pages
- 67-78
- ISSN
- 1870-9044 (ISSN-L)
- 2395-8618
- OpenAlex
- W2378912908
- Semantic Scholar
- 53f92790ecdd5578d97fc794b22f1040d4db8c04
- Cited by
- 1
- References
- 39
- Citations by year
- 2015: 1
- FWCI
- 0.29
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Polibits (publishedVersion)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion)
- Funders
- Instituto Politécnico Nacional
- Comisión de Operación y Fomento de Actividades Académicas, Instituto Politécnico Nacional
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
- Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
- Keywords
- image encryption, occlusion attack, image restoration, permutation-based encryption, AES, median filter, moving average filter, Shannon entropy, randomness testing
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 2026-10-23.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-23.
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 ›
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