A design of multiple color image encryption scheme based on finite algebraic structures
Open accessAbstract
This article introduces an innovative method for constructing substitution and permutation boxes and their application in image encryption. In encryption, the essential component that creates confusion is the substitution box(S-box). S-boxes can be constructed using different mathematical structures. An S-box with high nonlinearity enhances confusion in encryption. The nonlinearity of the S-box depends on its mathematical structure; the more nonlinear the structure, the higher the quality of the S-box. Quality can be measured using differential, linear, and statistical attacks. Another main component in image encryption is the permutation box(P-box), which creates confusion by scrambling the image pixels. The proposed scheme is based on the algebraic structure of the Galois field. In this scheme, we utilize the group action over an 8-bit finite field and then apply a bi-linear transformation to construct S-boxes and P-boxes. The proposed encryption scheme satisfies standard cryptographic requirements. Experimental results show that, in comparison with other well-known existing schemes, the method successfully generates many unique, uncorrelated, and secure S-boxes. A security study of the proposed scheme indicates that multiple color-encrypted images can swiftly and effectively mitigate numerous risks, rendering them suitable for real-time applications with stringent security demands.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper constructs S-boxes and P-boxes over GF(2^8) using group actions, inversion, and linear fractional transformations, then applies them in a multiple color-image encryption scheme with permutation, substitution, and XOR. It reports standard cryptographic metrics near ideal and NIST test passes, claiming suitability for real-time secure image encryption.
Key findings
- The proposed S-box has nonlinearity 112, SAC average 0.504, LAP max 0.0664, and DAP 0.0234 in Table 2; the text reports BIC values of 0.5000034, 0.49998, and 0.50456, while Table 2 lists BIC average as 112.
- The encryption scheme reports a key space of 2^240, encrypted-image entropy of 7.9976–7.9987, near-zero correlation values, NPCR above 99.1%, and UACI around 33.1–33.7%.
- PSNR between plain and ciphered images is 9.38–10.36 dB; under cropping from 5% to 45%, decrypted-image PSNR ranges from 10.36 to 8.23 dB.
- NIST SP 800-22 tests are reported as passed for a 4×4 image block, and the scheme takes 8 seconds to encrypt an image on a standard PC.
Methods
- S-box/P-box construction: build GF(2^8) with primitive polynomial \(y^8+y^4+y^3+y^2+1\), apply group actions of GF(2^8) on itself via addition and multiplication, then an inversion map and linear fractional transformation \(\Phi(y)=\frac{a y+b}{c y+d}\) to generate S-boxes and P-boxes.
- Image encryption: split an RGB image into R, G, and B channels; permute each channel with a P-box; substitute each permuted channel with a separate S-box; XOR with a P-box-generated random sequence; concatenate the encrypted channels. Multiple images are handled as blocks of sizes \(2^n,3^n,\ldots\), including 2×2, 3×3, and 4×4 blocks.
- Evaluation: standard S-box metrics (NL, LAP, DAP, SAC, BIC), image-security metrics (key space, entropy, histogram, correlation, NPCR/UACI, PSNR, occlusion, computation), and NIST SP 800-22 randomness tests; test images include Butterfly, Baboon, and Peppers at 256×256×3.
Limitations
- Stated limitations: the paper does not state explicit limitations; it proposes future work in audio/video encryption and hardware implementation.
- Evident from the text: the key-space arithmetic is inconsistent—each S-P box is said to have \(2^{48}\) configurations, but the total keyspace is written as \((2^{45})^5=2^{240}\) for five boxes.
- Evident from the text: Table 2 lists BIC average as 112 while the text and Table 6 report BIC values near 0.5; security claims rely on standard statistical tests and comparisons without a formal cryptanalytic proof or broader attack model.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
- Findingreasoning
The desired S-boxes are from step 5, which exhibits high nonlinearity.
“The desired S-boxes are from step 5, which exhibits high nonlinearity.”
Quote in the paperSubstantial claim - Findingown data
The proposed S-boxes satisfy the SAC test.
“The numerical values indicate that S-boxes satisfy the SAC test.”
Quote in the paperSubstantial claim - Findingown data
The proposed S-boxes have DAP values closer to the ideal range.
“The DAP values of the proposed S-boxes are provided in Table 4, showing values closer to the ideal range.”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has nonlinearity values of 112 for all eight output bits.
“| Proposed Scheme | 112 | 112 | 112 | 112 | 112 | 112 | 112 | 112 | 112 |”
Quote in the paperSubstantial claim - Findingown data
In comparison with other well-known existing schemes, the proposed method successfully generates many unique, uncorrelated, and secure S-boxes.
“Experimental results show that, in comparison with other well-known existing schemes, the method successfully generates many unique, uncorrelated, and secure S-boxes.”
Quote in the paperSubstantial claim
- Findingnone given
The SAC values of the newly constructed S-boxes are equal to those of other well-known existing S-boxes listed in comparison Table 2.
“Furthermore, the SAC values of the newly constructed S-boxes are equal to those of other well-known existing S-boxes listed in comparison Table 2.”
Quote in the paperNot a substantial claim - Findingown data
The proposed S-boxes have lower DAP values than S-boxes from published work.
“Additionally, Table 2 compares S-boxes from the proposed scheme with those from published work, demonstrating that the suggested S-boxes have lower DAP values.”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has an average BIC value of 112.
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has a minimum nonlinearity value of 112.
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
Quote in the paperSubstantial claim - Findingown data
The BIC values of the newly suggested S-boxes are very close to the optimal value.
“Table 2 shows that the BIC values of the newly suggested S-boxes are 0.5000034, 0.49998, and 0.50456, which is very close to an optimal value.”
Quote in the paperSubstantial claim - Findingown data
The BIC values of the newly suggested S-boxes are 0.5000034, 0.49998, and 0.50456.
“Table 2 shows that the BIC values of the newly suggested S-boxes are 0.5000034, 0.49998, and 0.50456, which is very close to an optimal value.”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has a DAP value of 0.0234.
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has a maximum LAP value of 0.0664.
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has an average SAC value of 0.504.
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
Quote in the paperSubstantial claim - Findingown data
The proposed S-box has an average nonlinearity value of 112.
“The S-box S_{1} has an average NL value of 112.”
- Also stated in: § Nonlinearity(NL) · plain
“| Proposed Scheme | 112 | 112 | 112 | 112 | 112 | 112 | 112 | 112 | 112 |”
Quote in the paperSubstantial claim - Also stated in: § Nonlinearity(NL) · plain
- Findingreasoning
The space complexity of the proposed method is about O(M + 5m + n + 2l + r + 2s).
“About O(M + 5m + n + 2l + r + 2s) is the space complexity”
Quote in the paperNot a substantial claim - Findingown data
The newly built S-boxes have good resistance against well-known attacks.
“The newly built S-boxes have good resistance against well-known attacks.”
Quote in the paperSubstantial claim - Findingreasoning
Following the proposed scheme, hundreds of S-boxes of nonlinearity 112 can be obtained.
“Following our proposed scheme, we obtain hundreds of S-boxes of nonlinearity 112.”
Quote in the paperSubstantial claim - Findingown data
The numerical values of the linear, differential, and statistical analysis are very close to optimal values.
“The numerical values of the linear, differential, and statistical analysis are very close to optimal values.”
Quote in the paperSubstantial claim - Findingown data
The ciphered images in the proposed method have an entropy of approximately 8.
“The ciphered images in our recently proposed method have an entropy of approximately 8, which suggests that they are resilient to statistical attacks.”
Quote in the paperSubstantial claim - Findingreasoning
The overall time complexity of the proposed method is O(M + 3m + 3n + 3l + r + 3s).
“the overall time complexity of the operations is O(M + 3m + 3n + 3l + r + 3s).”
Quote in the paperSubstantial claim - Findingown data
The proposed approach for digital image encryption successfully passes the NIST tests.
“Considering these findings, it can be concluded that our proposed approach for digital image encryption successfully passes the NIST tests.”
- Also stated in: § Computation analysis · plain
“We can determine that our predicted digital image encryption tool’s efficiency passes the NIST test by analyzing these results.”
Quote in the paperSubstantial claim - Also stated in: § Computation analysis · plain
- Findingown data
The proposed scheme could recover the original data when data was cropped from various parts of the images on decryption.
“When we cropped data from various parts of the images on decryption, the results demonstrated that the proposed scheme could recover the original data.”
Quote in the paperSubstantial claim - Findingown data
The recently suggested scheme can generate hundreds of S-boxes.
“The comparison Tables 2, 3, 4, 5, and 6 show that the recently suggested scheme can generate hundreds of S-boxes”
Quote in the paperSubstantial claim - Findingnone given
The nonlinearity of the proposed S-box is 112.
“The nonlinearity of the proposed s-box is 112, which is the minimum.”
Quote in the paperSubstantial claim - Findingnone given
The suggested scheme takes 8 seconds to encrypt the image on a standard PC.
“Moreover, the suggested scheme takes 8 seconds to encrypt the image on a standard PC”
Quote in the paperNot a substantial claim - Findingnone given
The proposed S-P-boxes have confusion and diffusion properties.
“These S-P-boxes have confusion and diffusion properties.”
- Also stated in: § Conclusion · plain
“These S-P-boxes create confusion and diffusion in data encryption.”
Quote in the paperSubstantial claim - Also stated in: § Conclusion · plain
- Interpretationown data
The proposed encryption scheme satisfies standard cryptographic requirements.
“The proposed encryption scheme satisfies standard cryptographic requirements.”
Quote in the paperSubstantial claim - Interpretationreasoning
The inversion map and linear fractional transformation create randomness in the elements of GF due to their non-linear behavior.
“The inversion map and linear fractional transformation create randomness in the elements of GF due to their non-linear behavior.”
Quote in the paperNot a substantial claim - Interpretationown data
The suggested S-boxes can resist common attacks.
“The numerical values of BIC ensure that the suggested S-boxes can resist common attacks.”
Quote in the paperSubstantial claim - Interpretationreasoning
The generation of S-boxes, P-boxes, and a random number key in the proposed scheme solely relies on Galois field structures.
“The generation of S-boxes, P-boxes, and a random number key in the proposed scheme solely relies on Galois field structures.”
Quote in the paperSubstantial claim - Study design and conductnone given
The proposed S-boxes undergo Strict Avalanche Criteria (SAC) to ensure the slight change in the input bit results in a bigger change in the output.
“The proposed S-boxes also undergo Strict Avalanche Criteria (SAC) to ensure the slight change in the input bit results in a bigger change in the output.”
Quote in the paperNot a substantial claim - Interpretationown data
The proposed S-boxes are resistant to differential attacks.
“Hence, we can conclude that the proposed S-boxes are resistant to differential attacks.”
Quote in the paperSubstantial claim - Interpretationown data
The proposed scheme demonstrates robust resistance to differential attacks, as indicated by its NPCR and UACI values.
“Table 9 presents the NPCR and UACI values pixels wise of the newly suggested method, demonstrating robust resistance to differential attacks.”
Quote in the paperSubstantial claim- Rests on an assumption: NPCR and UACI are valid metrics for assessing resistance to differential attacks in image encryption.
- Interpretationown data
The ciphered images in the proposed method are resilient to statistical attacks.
“The ciphered images in our recently proposed method have an entropy of approximately 8, which suggests that they are resilient to statistical attacks.”
Quote in the paperSubstantial claim - Interpretationown data
The proposed work is resilient to a cropping attack.
“We can conclude that the proposed work is resilient to a cropping attack.”
Quote in the paperSubstantial claim - Interpretationreasoning
The proposed scheme has enough key space to protect confidential data from adversaries.
“In other words, we have enough key space to protect confidential data from adversaries.”
Quote in the paperSubstantial claim - Interpretationown data
The proposed encryption system can transmit images with enhanced security, as suggested by PSNR values.
“This suggests that the proposed encryption system can transmit images with enhanced security.”
Quote in the paperSubstantial claim- Rests on an assumption: PSNR is a valid metric for assessing image quality and security in image encryption.
- Interpretationnone given
The proposed image encryption technique is based on S-boxes generated through the action of groups on the Galois field GF(256).
“The entire innovative technique of image encryption is based on S-Boxes generated through the action of groups on the Galois field GF(256).”
Quote in the paperSubstantial claim - Interpretationown data
The proposed scheme is fast.
“According to Section 6, the proposed scheme is secure, fast, and suitable for real-time applications.”
Quote in the paperSubstantial claim- Rests on an assumption: The standard PC used for timing is representative of typical hardware for real-time applications.
- Interpretationown data
The proposed scheme is suitable for real-time applications.
“According to Section 6, the proposed scheme is secure, fast, and suitable for real-time applications.”
Quote in the paperSubstantial claim- Rests on an assumption: The standard PC used for timing is representative of typical hardware for real-time applications.
- Interpretationown data
The proposed scheme is secure.
“According to Section 6, the proposed scheme is secure, fast, and suitable for real-time applications.”
Quote in the paperSubstantial claim- Rests on an assumption: NPCR and UACI are valid metrics for assessing resistance to differential attacks in image encryption.
- Rests on an assumption: PSNR is a valid metric for assessing image quality and security in image encryption.
- Rests on an assumption: The comparison with existing methods in Tables 9 and 10 is fair and uses equivalent conditions.
- Interpretationown data
The suggested method is quite resistant to statistical attacks.
“As a result, it becomes clear that the suggested method is quite resistant to statistical attacks.”
Quote in the paperSubstantial claim - Interpretationown data
The proposed scheme for S-P-boxes can generate several highly secure S-boxes.
“Further, the proposed scheme for S-P-boxes can generate several highly secure S-boxes.”
Quote in the paperSubstantial claim - Interpretationown data
The recently suggested scheme has greater security against linear, differential, and statistical attacks.
“and have greater security against linear, differential, and statistical attacks.”
Quote in the paperSubstantial claim - Interpretationown data
The nonlinearity of the newly generated S-boxes is the same as that of well-known S-boxes like AES and Gray.
“The non-linearity of the newly generated S-boxes is the same as that of well-known S-boxes like AES and gray.”
Quote in the paperSubstantial claim
- May combine two claims. 7
- Classified as probably not a substantial claim. 7
May combine two claims.
Findingown dataThe proposed S-box has a maximum SAC value of 0.545 and a minimum of 0.43.
“The maximum and minimum values of the suggested S-box are 0.545 and 0.43, respectively.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataThe histograms of the ciphered images are substantially different from those of the matching original images, with an essentially uniform distribution.
“The histograms of the ciphered images are substantially different from those of the matching original images, with an essentially uniform distribution.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningThe proposed scheme uses two P-boxes and three S-boxes, and the total keyspace is 2^240.
“We used two P-boxes and three S-boxes in the entire proposed scheme, so the total keyspace is (2^{45})^5=2^{240}.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable). May combine two claims.
InterpretationreasoningA security study of the proposed scheme indicates that multiple color-encrypted images can swiftly and effectively mitigate numerous risks, rendering them suitable for real-time applications with stringent security demands.
“A security study of the proposed scheme indicates that multiple color-encrypted images can swiftly and effectively mitigate numerous risks, rendering them suitable for real-time applications with stringent security demands.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Study design and conductnone givenTo ensure the resistance and cryptographic strength of the proposed S-boxes, S-boxes undergo numerous cryptographic analyses.
“To ensure the resistance and cryptographic strength of the proposed S-boxes, S-boxes undergo numerous cryptographic analyses that are explained in detail in the following sections (Table 2).”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe suggested technique is distinctive as it treats Galois fields (GF) as a group and operates on GF independently.
“The suggested technique is distinctive as it treats Galois fields (GF) as a group and operates on GF independently.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe proposed S-box is resistant to linear attacks, as demonstrated by its LAP value in Table 2.
“Table 2 provides the LAP value of the suggested scheme along with a comparison to other published studies, demonstrating the proposed S-box’s resistance to linear attacks.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Premisenone givenThe group action of GF(2^8) on itself through addition and multiplication represents a linear transformation.
“The group action of GF(2^{8}) on itself through addition and multiplication represents a linear transformation.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S2 (checkable).
InterpretationreasoningThe recommended image encryption technique ensures the secure transfer of digital images.
“The recommended image encryption technique ensures the secure transfer of digital images.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenThe confusion component of the proposed scheme enhanced the security of the multiple images.
“The confusion component of the scheme enhanced the security of the multiple images.”
Quote in the paperNot a substantial claimMay combine two claims.
Interpretationown dataThe proposed scheme withstands various attacks, including key space analysis, differential attacks, linear attacks, and statistical attacks.
“The proposed scheme withstands various attacks, including key space analysis, differential attacks, linear attacks, and statistical attacks.”
Quote in the paperSubstantial claim- Rests on an assumption: NPCR and UACI are valid metrics for assessing resistance to differential attacks in image encryption.
- Rests on an assumption: PSNR is a valid metric for assessing image quality and security in image encryption.
Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
Interpretationnone givenThe suggested method can encrypt images containing any type of digital data.
“The suggested method can encrypt images containing any type of digital data.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing), S4 (based).
InterpretationreasoningThe suggested scheme should take less time on more advanced systems.
“it should take less time on more advanced systems.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
Existing multiple-image encryption techniques solely rely on chaotic structures and encrypt grayscale images.
“The numerous existing multiple-image encryption techniques, which solely rely on chaotic structures, encrypt grayscale images.”
The paper relies on this without support.
The nonlinearity of an S-box depends on its mathematical structure; the more nonlinear the structure, the higher the quality of the S-box.
“The nonlinearity of the S-box depends on its mathematical structure; the more nonlinear the structure, the higher the quality of the S-box.”
The paper relies on this without support.
An S-box with high nonlinearity enhances confusion in encryption.
“An S-box with high nonlinearity enhances confusion in encryption.”
The paper relies on this without support.
The optimal nonlinearity value for an S-box is 120 over GF(2^8).
“For an S-box, the optimal nonlinearity value is 120 over GF(2^{8}).”
The paper relies on this without support.
Existing image encryption methods that encrypt only one image approximate the original image rather than exactly recovering it, resulting in poor image quality.
“The drawback of these methods is that, instead of providing a mathematically exact recovery, the reconstruction approach theoretically approximates the original image, resulting in poor image quality.”
The paper relies on this without support.
The random iterative method requires a high number of projections, which increases imaging time.
“Specifically, the random iterative method necessitates a high number of projections, which increases the imaging time.”
The paper relies on this without support.
NPCR and UACI are valid metrics for assessing resistance to differential attacks in image encryption.
“The NPCR (Normalized Pixel Change Rate) and UACI (Unified Average Changing Intensity) are important metrics for evaluating image encryption techniques.”
The paper relies on this without support.
PSNR is a valid metric for assessing image quality and security in image encryption.
“Peak Signal-to-Noise Ratio (PSNR) is a commonly used metric in data compression and transmission to assess the quality of encrypted or reconstructed images.”
The paper relies on this without support.
The test images (Baboon, Pepper, Butterfly, Block of 4x4) are representative for evaluating the proposed scheme's security.
“While conducting all of the NIST tests, we used the ciphered Baboon 24-bit digital image.”
The paper relies on this without support.
The standard PC used for timing is representative of typical hardware for real-time applications.
“Moreover, the suggested scheme takes 8 seconds to encrypt the image on a standard PC; it should take less time on more advanced systems.”
The paper relies on this without support.
The comparison with existing methods in Tables 9 and 10 is fair and uses equivalent conditions.
“Table 9 Comparison of NPCR and UACI Metrics Between the Proposed Scheme and Existing Methods.”
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.
Total key-space exponent is miscalculated
MajorFive boxes with 2^45 configurations each give (2^45)^5 = 2^225, not 2^240. The preceding description instead assigns 2^48 configurations to each box, which would yield 2^240.
Reported 240 · recomputed 225
“We used two P-boxes and three S-boxes in the entire proposed scheme, so the total keyspace is (2^{45})^5=2^{240}.”
Claim of lower differential probability conflicts with comparison table
MajorThe paper says the proposed S-boxes have lower DAP values than published alternatives. Table 2 gives the proposed scheme 0.0234, higher than the AES value of 0.0156.
“Additionally, Table 2 compares S-boxes from the proposed scheme with those from published work, demonstrating that the suggested S-boxes have lower DAP values.”
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 | | AES Standard | 112 | 0.453 | 112 | 0.0625 | 0.0156 |”
Stated maximum SAC is below a tabulated value
MinorThe text gives a maximum SAC of 0.545, but Table 5 includes 0.562500.
“The maximum and minimum values of the suggested S-box are 0.545 and 0.43, respectively.”
“| 0.515625 | 0.484375 | 0.531250 | 0.468750 | 0.546875 | 0.484375 | 0.562500 | 0.484375 |”
Optical-encryption citation points to different authors
MinorThe text attributes the cited optical multiple-image method to Gao et al., while reference 28 lists Sahasrabuddhe and Laiphrakpam and describes a 3D-scrambling method.
“The methodology employed by Gao et al. utilized optical methods to encrypt multiple images; however, optical encryption is costly and presents specific obstacles and limitations in practical applications28.”
“28. Sahasrabuddhe, A. & Laiphrakpam, D. S. Multiple images encryption based on 3D scrambling and hyper-chaotic system. Inf. Sci. 550, 252–267 (2021).”
Stated minimum SAC is below every tabulated value
MinorThe text gives a minimum SAC of 0.43, whereas the lowest value in Table 5 is 0.453125.
“The maximum and minimum values of the suggested S-box are 0.545 and 0.43, respectively.”
“| 0.531250 | 0.453125 | 0.468750 | 0.468750 | 0.500000 | 0.453125 | 0.531250 | 0.453125 |”
Citation 25 does not name Zhang et al.
MinorThe description attributes reference 25 to Zhang et al., but the listed authors of reference 25 are Li, Mou, Xiong, Wang, and Xu.
“In25, Zhang et al. developed an MIE algorithm employing the SIE approach to consolidate all images into one extensive image.”
“25. Li, X., Mou, J., Xiong, L., Wang, Z. & Xu, J. Fractional-order double-ring erbium-doped fiber laser chaotic system and its application on image encryption. Opt. Laser Technol. 140, 107074 (2021).”
Table 2 does not contain the claimed BIC values
MinorThe text attributes three near-0.5 BIC values to Table 2, but its proposed-scheme row reports a single BIC average of 112.
“Table 2 shows that the BIC values of the newly suggested S-boxes are 0.5000034, 0.49998, and 0.50456, which is very close to an optimal value.”
“| Proposed Scheme | 112 | 0.504 | 112 | 0.0664 | 0.0234 |”
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Farwa, S., Shah, T., & Idrees, L. (2016) · SpringerPlus · doi:10.1186/s40064-016-3298-7 · Cited by 76 · cited 1× · see citing works
“The comparison Tables 2, 3, 4, 5, and 6 show that the recently suggested scheme can generate hundreds of S-boxes and have greater security against linear, differential, and statistical attacks.”
Self-citationImproved Cryptanalysis and Enhancements of an Image Encryption Scheme Using Combined 1D Chaotic Maps
Zhu, C., Wang, G., & Sun, K. (2018) · Entropy · doi:10.3390/e20110843 · Cited by 76 · see citing works
Designing S-Box Based on 4D-4Wing Hyperchaotic System
Islam, F. U., & Liu, G. (2017) · 3D Research · doi:10.1007/s13319-017-0119-x · Cited by 72 · see citing works
Statistical analysis of S-box in image encryption applications based on majority logic criterion
Shah, T., Hussain, I., Gondal, M. A., & Mahmood, H. (2011) · International Journal of the Physical Sciences · doi:10.5897/ijps11.531 · Cited by 70 · see citing works
Self-citationConstruction of S8 Liu J S-boxes and their applications
Hussain, I., Shah, T., Mahmood, H., & Gondal, M. A. (2012) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2012.05.017 · Cited by 67 · see citing works
Self-citationNovel SCAN-CA-based image security system using SCAN and 2-D von Neumann cellular automata
Chen, R., & Horng, S. (2010) · Signal Processing Image Communication · doi:10.1016/j.image.2010.03.002 · Cited by 65 · see citing works
A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map
Razaq, A., Yousaf, A., Shuaib, U., Siddiqui, N., Ullah, A., & Waheed, A. (2017) · Security and Communication Networks · doi:10.1155/2017/5101934 · Cited by 65 · see citing works
Multiple-image encryption and hiding with an optical diffractive neural network
Gao, Y., Jiao, S., Fang, J., Lei, T., Xie, Z., & Yuan, X. (2020) · Optics Communications · doi:10.1016/j.optcom.2020.125476 · Cited by 61 · see citing works
Meta: A Memory-Efficient Tri-Stage Polynomial Multiplication Accelerator Using 2D Coupled-BFUs
Xu, Y., Ding, L., He, P., Lu, Z., & Zhang, J. (2024) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2024.3461736 · Cited by 58 · see citing works
WiShield: Privacy Against Wi-Fi Human Tracking
Hu, J., Jiang, H., Chen, S., et al. (2024) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2024.3414597 · Cited by 57 · see citing works
Two-Factor Authentication for Keyless Entry System via Finger-Induced Vibrations
Jiang, H., Ji, P., Zhang, T., Cao, H., & Liu, D. (2024) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2024.3368331 · Cited by 56 · see citing works
Advanced Differential-Style Cryptanalysis of the NSA's Skipjack Block Cipher
Kim, J., & Phan, R. C. ‐. (2009) · Cryptologia · doi:10.1080/01611190802653228 · Cited by 55 · cited 1× · see citing works
“The comparison Tables 2, 3, 4, 5, and 6 show that the recently suggested scheme can generate hundreds of S-boxes and have greater security against linear, differential, and statistical attacks.”
A novel approach to improve multimedia security utilizing 3D mixed chaotic map
Naseer, Y., Shah, D., & Shah, T. (2018) · Microprocessors and Microsystems · doi:10.1016/j.micpro.2018.12.003 · Cited by 55 · see citing works
Self-citationPermutation based Image Encryption Technique
Indrakanti, S. P., & Avadhani, P. S. (2011) · International Journal of Computer Applications · doi:10.5120/3404-4748 · Cited by 53 · see citing works
Altaleb, A., Saeed, M. S., Hussain, I., & Aslam, M. (2017) · AIP Advances · doi:10.1063/1.4978264 · Cited by 51 · see citing works
Chaos based adaptive double-image encryption scheme using hash function and S-boxes
Liu, H., Kadir, A., Sun, X., & Li, Y. (2017) · Multimedia Tools and Applications · doi:10.1007/s11042-016-4288-z · Cited by 50 · see citing works
Khan, M. A., Ali, A., Jeoti, V., & Manzoor, S. (2018) · Iranian Journal of Science and Technology Transactions of Electrical Engineering · doi:10.1007/s40998-018-0061-9 · Cited by 50 · see citing works
A Novel Algebraic Technique for the Construction of Strong Substitution Box
Attaullah, A., Jamal, S. S., & Shah, T. (2017) · Wireless Personal Communications · doi:10.1007/s11277-017-5054-x · Cited by 48 · see citing works
Self-citation4D mixed chaotic system and its application to RGB image encryption using substitution-diffusion
Haq, T. U., & Shah, T. (2021) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2021.102931 · Cited by 46 · see citing works
Self-citationA Deniable Encryption Method for Modulation-Based DNA Storage
Chu, L., Su, Y., Zan, X., Lin, W., Yao, X., Xu, P., & Liu, W. (2024) · Interdisciplinary Sciences Computational Life Sciences · doi:10.1007/s12539-024-00648-5 · Cited by 46 · cited 1× · see citing works
“through deniable encryption 50,51 .”
Construction of highly nonlinear S-boxes for degree 8 primitive irreducible polynomials over ℤ2
Shah, T., & Shah, D. (2018) · Multimedia Tools and Applications · doi:10.1007/s11042-018-6250-8 · Cited by 43 · see citing works
Self-citationAlgebra-chaos amalgam and DNA transform based multiple digital image encryption
Haq, T. U., & Shah, T. (2020) · Journal of Information Security and Applications · doi:10.1016/j.jisa.2020.102592 · Cited by 43 · see citing works
Self-citationA New Dynamic Substitution Box for Data Security Using an Innovative Chaotic Map
Manzoor, A., Zahid, A. H., & Hassan, M. T. (2022) · IEEE Access · doi:10.1109/access.2022.3184012 · Cited by 42 · see citing works
A Novel Algorithm of Constructing Highly Nonlinear S-p-boxes
Naseer, Y., Shah, T., Shah, D., et al. (2019) · Cryptography · doi:10.3390/cryptography3010006 · Cited by 39 · see citing works
Self-citationA novel design for the construction of safe S-boxes based on TDERC sequence
AlKhaldi, A. H., Hussain, I., & Gondal, M. A. (2015) · Alexandria Engineering Journal · doi:10.1016/j.aej.2015.01.003 · Cited by 37 · see citing works
Fuzzy Logic-Based Substitution-Box for Robust Medical Image Encryption in Telemedicine
Razaq, A., Maghrabi, L. A., Ahmad, M., Aslam, F., & Feng, W. (2024) · IEEE Access · doi:10.1109/access.2024.3351794 · Cited by 36 · see citing works
Echoes of Fingertip: Unveiling POS Terminal Passwords Through Wi-Fi Beamforming Feedback
Chen, S., Jiang, H., Hu, J., et al. (2024) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2024.3465564 · Cited by 33 · cited 1× · see citing works
“through deniable encryption 50,51 .”
Multiple image encryption techniques: Strategies, challenges, and potential future directions
Eltoukhy, M. M., Alsubaei, F. S., Elnabawy, Y. M., et al. (2025) · Alexandria Engineering Journal · doi:10.1016/j.aej.2025.04.006 · Cited by 28 · cited 1× · see citing works
“In 52 , a multiple image encryption(MIE) scheme based on 2D and 3D representation challenges to guide future research in MIE; also, MIE is a scheme based on S-boxes and DNA sequences discussed in 53 .”
Dynamic S-Box Generation Using Novel Chaotic Map with Nonlinearity Tweaking
Zahid, A. H., Arshad, M. J., Ahmad, M., Soliman, N. F., & El‐Shafai, W. (2023) · Computers, materials & continua/Computers, materials & continua (Print) · doi:10.32604/cmc.2023.037516 · Cited by 26 · see citing works
Li, Z., Zhang, S., Tan, W., & Wu, X. (2025) · Nonlinear Dynamics · doi:10.1007/s11071-025-11110-6 · Cited by 24 · see citing works
Secure S-box construction with 1D chaotic maps and finite field theory for block cipher encryption
Jamal, S. S., Ali, R., Jamil, M. K., et al. (2025) · Alexandria Engineering Journal · doi:10.1016/j.aej.2025.03.109 · Cited by 23 · see citing works
Üstün, D., & Şahinkaya, S. (2025) · Mathematics and Computers in Simulation · doi:10.1016/j.matcom.2025.03.019 · Cited by 22 · see citing works
Quaternion and multiple chaotic systems based pseudo-random number generator
Li, L., Abd-El-Atty, B., Elseuofi, S., et al. (2019) · International Conference on Computer Applications & Information Security (ICCAIS) · doi:10.1109/cais.2019.8769495 · Cited by 19 · see citing works
Razzaque, A., Razaq, A., Farooq, S. M., Masmali, I. A. H., & Faraz, M. I. (2023) · Electronic Research Archive · doi:10.3934/era.2023137 · Cited by 18 · see citing works
A two-parameter extended logistic chaotic map for modern image cryptosystems
Latoui, A., & Daachi, M. E. H. (2024) · Digital Signal Processing · doi:10.1016/j.dsp.2024.104463 · Cited by 16 · see citing works
Multiple-image encryption algorithm based on S-boxes and DNA sequences
Safdar, M. U., Shah, T., & Ali, A. (2025) · Signal Processing Image Communication · doi:10.1016/j.image.2025.117353 · Cited by 16 · cited 1× · see citing works
“In 52 , a multiple image encryption(MIE) scheme based on 2D and 3D representation challenges to guide future research in MIE; also, MIE is a scheme based on S-boxes and DNA sequences discussed in 53 .”
Self-citationRazaq, A., Maghrabi, L. A., Ahmad, M., et al. (2024) · AIMS Mathematics · doi:10.3934/math.2024303 · Cited by 13 · see citing works
A novel one-dimensional chaotic map, novel diffusion and DNA encoding-based image encryption scheme
Dua, M., Kumar, R., Dua, S., & Chakravarty, N. (2025) · International Journal of Dynamics and Control · doi:10.1007/s40435-025-01653-2 · Cited by 13 · see citing works
A combinatory approach of non-chain ring and henon map for image encryption application
Din, S. M. U., Shah, T., Alblehai, F., Nooh, S. A., & Jamal, S. S. (2025) · Scientific Reports · doi:10.1038/s41598-025-85814-5 · Cited by 12 · see citing works
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The class of bivariate non-chain rings and its application to data security
Safdar, M. U., Shah, T., & Ali, A. (2025) · Cluster Computing · doi:10.1007/s10586-024-05030-0 · Cited by 6 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 3
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Cited by
Sorted by citations
SCD-CHAOS: dynamic S-box and chaotic hybrid adaptive image encryption using multi-map diffusion
Yogi, B., Majumdar, R., Ghosh, P., et al. (2026) · Scientific Reports · doi:10.1038/s41598-026-43981-z · Cited by 3 · see citing works
Color image encryption algorithm inspired by the Japanese game Amidakuji
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“…et al. 2024; Alawida 2024), elliptic curve cryptography (ECC) (Murtaza and Hayat 2025; Pandey and Sharma 2025; Hanchate and Anandan 2024; Yadav et al. 2026), and algebraic methods based on finite fields (Jamal et al. 2025; Broumandnia 2020; Qayyum et al. 2025; Wang et al. 2025; Arshad et al. 2022).”
Lv, S., Rauf, A., Tasleem, D., et al. (2026) · IET Image Processing · doi:10.1049/ipr2.70466
- Authors
- Qayyum, T., Shah, T., Khan, I., & Popa, I.-L.
- Affiliations
- Quaid-i-Azam University (PK)
- Al-Ahliyya Amman University (JO)
- Transylvania University of Brașov (RO)
- Corresponding author
- Qayyum, Tanveer
- Popa, Ioan-Lucian
- Venue
- Scientific Reports
- Published
- 2025-11-28
- Volume
- 15
- Issue
- 1
- Pages
- 42571-42571
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC12663366
- OpenAlex
- W4416781182
- Semantic Scholar
- 81ed8d3ae6557ac8a5b1f763aaf84c88fd234fa8
- Cited by
- 4
- References
- 55
- Citations by year
- 2026: 4
- FWCI
- 1.50
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Scientific Reports (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (submittedVersion, cc-by-nc-nd)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- 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
- image encryption, substitution boxes, S-box design, finite fields, Möbius transformations, nonlinearity, confusion and diffusion, cryptanalysis resistance
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