Chaos-Based Image Encryption: Review, Application, and Challenges

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Chen system has a chaotic attractor and two unstable equilibrium points.

“Moreover, the Chen system has a chaotic attractor and two unstable equilibrium points.”

• cites [19] Chen, 1999, Yet another chaotic attractor, Int. J. Bifurc. Chaos sourcePartly supported

  Section 1, “The New Attractor,” reports a chaotic attractor for the Chen system. It says the system has three equilibria, but does not say that two are unstable. The paper’s copy therefore supports the attractor but not the stated number of unstable equilibrium points. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

May combine two claims.

An image-encryption scheme based on a chaotic system with a small LE can reduce decryption error by using a chaotic system with low numerical solution error, and experiments on an XOR encryption scheme proved its positive effect.

“However, an image-encryption scheme based on chaotic systems with a small LE was proposed in [53].The authors utilized a chaotic system with a low numerical solution error to reduce the decryption error and proved its positive effect by conducting experiments on an XOR encryption scheme.”

• cites [53] Santos, T.A., Magalhães, E.P., Basílio, N.P., Nepomuceno, E.G., Karimov, T.I., and Butusov, D.N. (2020, January 11–13). Improving Chaotic Image Encryption Using Maps with Small Lyapunov Exponents. Proceedings of the 2020 Moscow Workshop on Electronic and Networking Technologies (MWENT), Moscow, Russia. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

Liu and Miao's Logistic-map-based method with varying parameters can change parameters randomly to improve robustness to phase space reconstruction attacks.

“Their approach can make the parameters change in a random way to improve robustness to the phase space reconstruction attack.”

• cites [50] Liu, 2016, A new image encryption algorithm based on logistic chaotic map with varying parameter, SpringerPlus sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

In the NIST statistical tests, the significance level is set at 0.01.

“In the NIST statistical tests, the significance level is set at 0.01.”

• cites [24] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Booz-Allen and Hamilton Inc. sourcePartly supported

  The “No error” section says that the significance level can be chosen and is typically in the range 0.001–0.01. It sets 0.01 for the document’s examples, but does not say that all NIST statistical tests have a fixed significance level of 0.01. (LLM, conf=0.90)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

The NIST Statistical Suite uses 16 separate statistical verification tests when verifying the randomness of binary sequences.

“The NIST Statistical Suite [24] uses 16 separate statistical verification tests when verifying the randomness of binary sequences.”

• cites [24] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Booz-Allen and Hamilton Inc. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

When the p-value of the sequence to be tested is ≥0.01, the sequence is considered to pass the statistical test.

“When the p-value of the sequence to be tested is ≥0.01, the sequence is considered to pass the statistical test.”

• cites [24] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Booz-Allen and Hamilton Inc. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Nardo and G's scheme takes finite accuracy error as the source of randomness and solves the problem of finite-accuracy-induced degradation in image encryption.

“Lucas G. Nardoa and Erivelton G [52] took finite accuracy error as the source of randomness and proposed a new image-encryption scheme to solve this problem.”

• cites [52] Nardo, 2019, Image encryption using finite-precision error, Chaos Solitons Fractals sourcePartly supported

  The Conclusion (p. 9) confirms that the authors proposed an image-encryption scheme exploiting finite-precision computer error as a source of randomness. It explicitly says they did so instead of attempting to mitigate finite-precision degradation, so the claim that the scheme solves that degradation problem overstates the paper. (LLM, conf=0.88)

  Experimental — accuracy not yet measured

• AssumptionRests on an assumption: The limited accuracy of computers degrades the chaotic characteristics of a chaotic system.

Probably not a substantial claim: may not pass S3 (load-bearing).

Currently NIST statistical tests are considered the current criteria for random testing.

“Currently NIST statistical tests are considered the current criteria for random testing.”

• cites [24] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., and Barker, E. (2001). A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications, Booz-Allen and Hamilton Inc. sourcePartly supported

  The ‘Random Number Generation Tests’ section describes the NIST suite as 16 tests developed to assess the randomness of binary sequences, supporting its use for random testing. The Introduction calls the procedures useful, but our copy does not establish that they are the currently accepted criteria for random testing. (LLM, conf=0.81)

  Experimental — accuracy not yet measured

May combine two claims.

Behnia and Akhshani's mixture of the Logistic map with a coupled map has large key space and high-level security, although its speed is only acceptable.

“S. Behnia and A. Akhshani [55] were the first to mix the Logistic map with a coupled map based on [56,57] for image encryption.This mixture scheme has large key space and high-level security, although its speed is only acceptable.”

• cites [55] Behnia, 2008, A novel algorithm for image encryption based on mixture of chaotic maps, Chaos Solitons Fractals sourceNot checked — no full text of the source
• cites [56] Jafarizadeh, 2001, Hierarchy of chaotic maps with an invariant measure and their coupling, Phys. D Nonlinear Phenom. sourcePartly supported

  Section 2 (p. 4) defines a family of chaotic maps, supporting the citation’s use as background for the maps on which the encryption scheme is said to be based. Our copy does not describe Behnia and Akhshani’s image-encryption mixture or assess its key space, security, or speed; those claims cannot be established from this source. (LLM, conf=0.78)

  Experimental — accuracy not yet measured
• cites [57] Jafarizadeh, 2001, Hierarchy of chaotic maps with an invariant measure, J. Stat. Phys. sourcePartly supported

  The Introduction (p. 3) describes a family of chaotic maps constructed by composition, supporting the citation's use as a basis for a map-based scheme. It does not describe Behnia and Akhshani's Logistic-map image-encryption scheme or assess its key space, security, or speed. (LLM, conf=0.84)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

The algorithm of [121] is secure enough to resist chosen-plaintext attack (CPA).

“Furthermore, it is secure enough to resist chosen-plaintext attack (CPA).”

• cites [121] Shakiba, 2021, A randomized CPA-secure asymmetric-key chaotic color image encryption scheme based on the Chebyshev mappings and one-time pad, J. King Saud Univ.-Comput. Inf. Sci. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

The algorithms in [110,111] have high effectiveness, safety, and robustness.

“these algorithms have high effectiveness, safety, and robustness.”

• cites [110] Jiao, 2020, Image encryption scheme based on a generalized Arnold map and RSA algorithm, Secur. Commun. Netw. sourceSupported
• cites [111] Xu, 2020, A visually secure asymmetric image encryption scheme based on RSA algorithm and hyperchaotic map, Phys. Scr. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The key space of the algorithm of [121] was greatly expanded.

“The key space of this algorithm was greatly expanded.”

• cites [121] Shakiba, 2021, A randomized CPA-secure asymmetric-key chaotic color image encryption scheme based on the Chebyshev mappings and one-time pad, J. King Saud Univ.-Comput. Inf. Sci. sourcePartly supported

  The Keyspace section says the algorithm’s key space depends on the chosen key length and can be made arbitrarily large; the Conclusion also calls it large. Neither passage establishes that it was greatly expanded relative to an earlier algorithm or baseline. Page numbers are not available in our copy. (LLM, conf=0.82)

  Experimental — accuracy not yet measured

May combine two claims.

Zhenlong Man and Jinqing Li [130] first tried to combine a convolutional neural network (CONN) and plaintext correlation scrambling mechanism and proposed double image encryption with a CONN and dynamic adaptive diffusion.

“Zhenlong Man and Jinqing Li [130] first tried to combine a convolutional neural network (CONN) and plaintext correlation scrambling mechanism and proposed double image encryption with a CONN and dynamic adaptive diffusion.”

• cites [130] Man, 2021, Double image encryption algorithm based on neural network and chaos, Chaos Solitons Fractals sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

CA can be used in cryptosystems or to generate random sequences.

“Thus, CA can be used in cryptosystems [142,143] or to generate random sequences [144].”

• cites [142] Sen, S., Shaw, C., Chowdhuri, D.R., Ganguly, N., and Chaudhuri, P.P. (2002, January 9–12). Cellular automata based cryptosystem (CAC). Proceedings of the Information and Communications Security: 4th International Conference, ICICS, Singapore. sourceNot checked — no full text of the source
• cites [143] Abdo, 2013, A cryptosystem based on elementary cellular automata, Commun. Nonlinear Sci. Numer. Simul. sourceNot checked — no full text of the source
• cites [144] Wolfram, 1986, Random sequence generation by cellular automata, Adv. Appl. Math. sourceSupported

May combine two claims.

The chaotic image-encryption and compression algorithm [187] has shorter fractal compression time and faster encryption efficiency than some other algorithms.

“Besides its fractal compression time being shorter and its encryption efficiency being faster than those of some other algorithms”

• cites [187] Wang, 2022, A chaos-based image compression and encryption scheme using fractal coding and adaptive-thresholding sparsification, Phys. Scr. sourceSupported

May combine two claims.

Zhang [203] developed a novel two-dimensional chaotic system by combining logistic and sine functions and employed it in a thumbnail-preserving encryption technique that produced highly secure ciphertext images even under known-plaintext attacks, data-loss attacks, and noise attacks.

“Zhang [203] developed a novel two-dimensional chaotic system by combining logistic and sine functions and employed it in the creation of a thumbnail-preserving encryption technique that produced highly secure ciphertext images, even in the wake of known-plaintext attacks, data-loss attacks, and noise attacks.”

• cites [203] Zhang, 2022, High-efficiency and visual-usability image encryption based on thumbnail preserving and chaotic system, J. King Saud Univ.-Comput. Inf. Sci. sourcePartly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

The algorithm [187] has an image reconstruction function that has yet to be perfected.

“However, its image reconstruction function has yet to be perfected.”

• cites [187] Wang, 2022, A chaos-based image compression and encryption scheme using fractal coding and adaptive-thresholding sparsification, Phys. Scr. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

The algorithm [187] can process gray and color images of different sizes.

“it can also process gray and color images of different sizes”

• cites [187] Wang, 2022, A chaos-based image compression and encryption scheme using fractal coding and adaptive-thresholding sparsification, Phys. Scr. sourceSupported

May combine two claims.

Qing Zhang and Yong Yan [192] combined chaos-based image encryption with a deep learning model and realized safe retrieval of images while effectively hiding the content information of the original image using a fusion method of a feature vector and ciphertext.

“Recently, Qing Zhang and Yong Yan [192] combined chaos-based image encryption with a deep learning model and realized the safe retrieval of images while effectively hiding the content information of the original image using a fusion method of a feature vector and ciphertext.”

• cites [192] Zhang, 2022, Image Security Retrieval Based on Chaotic Algorithm and Deep Learning, IEEE Access sourceSupported

May combine two claims.

An image-encryption algorithm based on mixed linear-nonlinear coupled map lattices has fewer periodic windows and a larger range of parameters.

“The algorithm with this kind of spatiotemporal system has less periodic windows and a larger range of parameters.”

• cites [94] Zhang, 2014, A symmetric image encryption algorithm based on mixed linear–nonlinear coupled map lattice, Inf. Sci. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A 2D CML-based chaotic image-encryption scheme takes only one operation cycle and renders the image indistinguishable.

“Fuyan Sun and Shutang Liu [93] proposed 2D CML-based chaotic image encryption, which takes only one operation cycle and renders the image indistinguishable.”

• cites [93] Sun, 2008, A novel image encryption scheme based on spatial chaos map, Chaos Solitons Fractals sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Kanso and Ghebleh's three-dimensional Arnold Cat map color image-encryption algorithm is valid for color images of any size.

“The algorithm can be valid for color images of any size.”

• cites [78] Kanso, 2012, A novel image encryption algorithm based on a 3D chaotic map, Commun. Nonlinear Sci. Numer. Simul. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

A binary-image encryption algorithm using chaotic mapping based on a modified sine function can quickly encrypt binary images in real time.

“The algorithm can quickly encrypt binary images in real time.”

• cites [96] Belkhouche, F., and Qidwai, U. (2003, January 11). Binary image encoding using 1D chaotic maps. Proceedings of the Annual Technical Conference IEEE Region 5, New Orleans, LA, USA. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The Chaotic Key-Based Algorithm (CKBA) is weak against the known-plaintext attack.

“However, Shujun Li and Xuan Zheng [83] estimated its security and pointed out that this algorithm is weak for the known-plaintext attack, which implies that the security of the algorithm needs to be improved.”

• cites [83] Li, S., and Zheng, X. (2002, January 26–29). Cryptanalysis of a chaotic image encryption method. Proceedings of the 2002 IEEE International Symposium on Circuits and Systems (ISCAS), Phoenix-Scottsdale, AZ, USA. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The investigation shows that chaos-based image-encryption technology is mainly applied in the following three fields: medicine, the Internet of Things, and satellites.

“The investigation shows that chaos-based image-encryption technology is mainly applied in the following three fields: medicine, the Internet of Things, and satellites.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In 1976, Robert M. May proposed the Logistic map in an article, which was studied in depth by M.J. Feigenbaum, who proposed the universality of this map in 1978.

“In 1976, Robert M. May [3] proposed the Logistic map in an article, which was studied in depth by M.J. Feigenbaum, who proposed the universality of this map in 1978.”

• cites [3] May, 1976, Simple mathematical models with very complicated dynamics, Nature sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The advantage of a discrete chaos map is that the mathematical model is relatively simple and easy to implement and compute.

“The advantage of a discrete chaos map is that the mathematical model is relatively simple and easy to implement and compute; however, the disadvantage is that the parameter range is usually not large enough and the wrong selection of parameters can lead to rapid degradation of the dynamic characteristics of the system.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The disadvantage of a discrete chaos map is that the parameter range is usually not large enough and the wrong selection of parameters can lead to rapid degradation of the dynamic characteristics of the system.

“The advantage of a discrete chaos map is that the mathematical model is relatively simple and easy to implement and compute; however, the disadvantage is that the parameter range is usually not large enough and the wrong selection of parameters can lead to rapid degradation of the dynamic characteristics of the system.”

Probably not a substantial claim: may not pass S3 (load-bearing).

LE is a tool used to visualize the separation of trajectories from two initial values with minimal error over time.

“When two initial values with minimal error are applied to the same chaotic system, the trajectories they generate will be separated exponentially over time.LE is a tool used to visualize this phenomenon [21].”

• cites [21] Wolf, 1985, Determining Lyapunov exponents from a time series, Phys. D Nonlinear Phenom. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The strange attractors of chaotic systems usually exhibit fractal characteristics, i.e., they have similar structure and morphology at different scales.

“The strange attractors of chaotic systems usually exhibit fractal characteristics, i.e., they have similar structure and morphology at different scales.”

Probably not a substantial claim: may not pass S4 (based).

Small changes in the system to critical parameters can cause the system to exhibit completely different dynamical states.

“Small changes in the system to critical parameters can cause the system to exhibit completely different dynamical states.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Henon map is a nonlinear and dissipative system that exhibits complex dynamical behavior.

“The Henon map is a nonlinear and dissipative system that exhibits complex dynamical behavior.”

• cites [17] Liu, 2015, Asymmetric color image encryption scheme using 2D discrete-time map, Signal Process. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The term chaos was first used by Tienyien Li and James A. Yorke in their 1975 paper Period Three Implies Chaos to describe this phenomenon.

“The term “chaos” was first used by Tienyien Li and James A. Yorke [2] in their 1975 paper “Period Three Implies Chaos” to describe this phenomenon.”

• cites [2] Li, T.-Y., and Yorke, J.A. (2004). The Theory of Chaotic Attractors, Springer.Not checked yet

  Not checked in the free run.

Probably not a substantial claim: may not pass S3 (load-bearing).

Robert Matthews explicitly proposed the chaotic encryption algorithm in 1989.

“Robert Matthews [6] explicitly proposed the “chaotic encryption” algorithm in 1989.”

• cites [6] Matthews, 1989, On the derivation of a “chaotic” encryption algorithm, Cryptologia sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Continuous chaotic systems have the advantage of providing richer dynamical behavior and greater flexibility.

“Continuous chaotic systems have the advantage of providing richer dynamical behavior and greater flexibility, but have the disadvantage of requiring higher computational power and more complex mathematical models, as well as the need for discretization to suit practical applications.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

The unique attributes of chaos, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, are conducive to cross-referencing with other disciplines and improving image-encryption methods.

“The unique attributes of chaos, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, are conducive to cross-referencing with other disciplines and improving image-encryption methods.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Continuous chaotic systems have the disadvantage of requiring higher computational power and more complex mathematical models, as well as the need for discretization to suit practical applications.

“Continuous chaotic systems have the advantage of providing richer dynamical behavior and greater flexibility, but have the disadvantage of requiring higher computational power and more complex mathematical models, as well as the need for discretization to suit practical applications.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Lorenz equation is characterized by having a chaotic attractor with a shape that resembles a butterfly, and it is particularly known for its sensitivity to initial conditions.

“The Lorenz equation is characterized by having a chaotic attractor with a shape that resembles a butterfly, and it is particularly known for its sensitivity to initial conditions.”

• cites [3] May, 1976, Simple mathematical models with very complicated dynamics, Nature sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

Chaotic systems have features including high ergodicity, determination, and pseudo-randomness, which are crucial for image encryption.

“Additionally, chaotic systems have other features, including high ergodicity, determination, and pseudo-randomness, which are crucial for image encryption.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

A strange attractor corresponds to a single trajectory.

“A strange attractor corresponds to a single trajectory.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Image data has special characteristics, such as a large capacity, high redundancy, and high correlation between pixels; therefore, image encryption has special structural requirements.

“The data of an image has special characteristics, such as a large capacity, high redundancy, and high correlation between pixels; therefore, image encryption has special structural requirements.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Discrete chaotic maps are suitable for applications such as digital signal processing and modulators in communication systems, and for image encryption and compression.

“Discrete chaotic maps are suitable for applications such as digital signal processing and modulators in communication systems, and for image encryption and compression.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The Rössler system typically shows spiral-like structures known as Rössler attractors in their state trajectories.

“The Rössler system typically shows spiral-like structures known as Rössler attractors in their state trajectories.”

• cites [20] 1976, An equation for continuous chaos, Phys. Lett. A sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Chaotic systems can be classified into continuous chaotic systems and discrete chaotic maps based on the way they evolve over time.

“Chaotic systems can be classified into two types based on the way they evolve over time: continuous chaotic systems and discrete chaotic maps [13].”

• cites [13] Mira, C. (1987). Chaotic Dynamics: From the One-Dimensional Endomorphism to the Two-Dimensional Diffeomorphism, World Scientific. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The discrete chaotic map is characterized by nonlinearity, sensitive dependence on initial conditions and parameters, and period multiplication, among other properties.

“The discrete chaotic map is characterized by nonlinearity, sensitive dependence on initial conditions and parameters, and period multiplication, among other properties [14].”

• cites [14] Avrutin, V., Gardini, L., Sushko, I., and Tramontana, F. (2019). Continuous and Discontinuous Piecewise-Smooth One-Dimensional Maps: Invariant Sets and Bifurcation Structures, World Scientific. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Strange attractors typically have a fractal structure, which means that they exhibit a consistent morphology at different scales.

“Strange attractors typically have a fractal structure, which means that they exhibit a consistent morphology at different scales.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The overall stability and the local instability make the chaotic system eventually form a self-similar hierarchy, i.e., a strange attractor.

“The overall stability and the local instability make the chaotic system eventually form a self-similar hierarchy, i.e., a strange attractor.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Overall stability and local instability are the most fundamental features of chaotic systems.

“Overall stability and local instability are the most fundamental features of chaotic systems.”

Probably not a substantial claim: may not pass S4 (based).

Chaotic systems are extremely sensitive to their initial conditions, which means that small changes in the initial state can lead to vastly different results.

“Chaotic systems are extremely sensitive to their initial conditions, which means that small changes in the initial state can lead to vastly different results.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Lorenz equation is a nonlinear chaotic system that exhibits complex dynamic behavior.

“The Lorenz equation is a nonlinear chaotic system that exhibits complex dynamic behavior.”

• cites [3] May, 1976, Simple mathematical models with very complicated dynamics, Nature sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The Logistic map exhibits complex dynamical behavior when the parameter p is in the interval (3.57, 4].

“The Logistic map exhibits complex dynamical behavior when the parameter p is in the interval (3.57, 4].”

• cites [15] Taha, 2019, Allee’s effect bifurcation in generalized logistic maps, Int. J. Bifurc. Chaos sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

When LE < 0, adjacent points tend to be stable, which means stable fixed points or periodic motion.

“When LE < 0, adjacent points tend to be stable, which means stable fixed points or periodic motion.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Sensitivity to initial conditions is the most distinctive feature of chaotic systems.

“This is the most distinctive feature of chaotic systems.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Arnold Cat map is a chaotic system that exhibits complex dynamical behavior, including periodic, quasi-periodic, and chaotic regimes.

“The Arnold Cat map is a chaotic system that exhibits complex dynamical behavior, including periodic, quasi-periodic, and chaotic regimes.”

• cites [18] Chen, 2004, A symmetric image encryption scheme based on 3D chaotic cat maps, Chaos Solitons Fractals sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

E. N. Lorenz proposed the Lorenz equation in 1963, which was the first example of a chaotic solution derived from a deterministic equation in a dissipative system.

“E. N. Lorenz [1] proposed the Lorenz equation in 1963, which was the first example of a chaotic solution derived from a deterministic equation in a dissipative system.”

• cites [1] Lorenz, 1963, Deterministic nonperiodic flow, J. Atmos. Sci. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

When LE > 0, the orbital iterations with two different inputs diverge exponentially.

“When LE > 0, the orbital iterations with two different inputs diverge exponentially.”

Classified as probably not a substantial claim.

Utilizing chaos theory in image encryption provides a new approach.

“However, utilizing chaos theory in image encryption provides a new approach.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Zhou and Bao's coupled chaotic map scheme generates a brand-new encrypted image each time it is used with the same set of security keys for an original image.

“Their scheme has some useful properties; in particular, it will generate a brand-new encrypted image each time it is used with the same set of security keys for an original image.”

• cites [59] Zhou, 2014, A new 1D chaotic system for image encryption, Signal Process. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

For time series, the larger the value of ApEn, the higher the orbital complexity generated by chaos.

“For time series, the larger the value of ApEn, the higher the orbital complexity generated by chaos.”

• cites [23] Pincus, 1991, Approximate entropy as a measure of system complexity, Proc. Natl. Acad. Sci. USA sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The main structure of a spatial-domain-based chaotic image-encryption algorithm is based on a permutation-diffusion architecture, which consists of two phases of iteration.

“The main structure of a spatial-domain-based chaotic image-encryption algorithm is based on a permutation-diffusion architecture, which consists of two phases of iteration.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Chaos-based image-encryption technology can be categorized into different types based on various classification methods.

“Chaos-based image-encryption technology can be categorized into different types based on various classification methods.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Using chaotic systems as a PRNG to generate pseudo-random sequences has certain advantages.

“It can be seen that using chaotic systems as a PRNG to generate pseudo-random sequences has certain advantages.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Symmetric spatial-domain image-encryption algorithms can be divided into two types based on the way the original image is processed: block cipher and stream cipher.

“Symmetric spatial-domain image-encryption algorithms can be divided into two types based on the way the original image is processed: block cipher and stream cipher.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

In the diffusion phase, the pixel values are sequentially modified, so that even a small change in the pixel will influence almost all the pixels in the entire image.

“In the diffusion phase, the pixel values are sequentially modified, so that even a small change in the pixel will influence almost all the pixels in the entire image.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In 1996, Jiri Fridrich introduced a five-step process for building block ciphers: designing the basic map, generalizing the map, discretizing, extension to three dimensions, and composing with a diffusion mechanism.

“After that, in 1996, Jiri Fridrich [25,26] introduced a five-step process for building block ciphers: designing the basic map, generalizing the map, discretizing, extension to three dimensions, and composing with a diffusion mechanism.”

• cites [25] Scharinger, J., and Pichler, F. (1996, January 30). Efficient image encryption based on chaotic maps. Proceedings of the 20th workshop of the Austrian Association for Pattern Recognition (OAGM/AAPR) on Pattern Recognition 1996, Munich, Germany.Not checked — no full text of the source
• cites [26] Fridrich, 1998, Symmetric ciphers based on two-dimensional chaotic maps, Int. J. Bifurc. Chaos sourceNot checked — no full text of the source

May combine two claims.

Coupling chaotic systems provides high complexity of the output cipher image and effective byte confusion and diffusion.

“Thus, coupling chaotic systems are also often constructed by researchers for image encryption because of their special advantages: high complexity of the output cipher image and effective byte confusion and diffusion, in addition to a conventional chaotic map.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

One approach is to classify chaos-based image encryption according to how the original image is processed, which can be divided into chaotic image encryption based on a block cipher and chaotic image encryption based on a stream cipher.

“One approach is to classify it according to how the original image is processed, which can be divided into chaotic image encryption based on a block cipher and chaotic image encryption based on a stream cipher.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Many researchers have focused on improving classical chaotic systems to enhance their chaotic dynamic characteristics through a process called chaotification.

“To address these issues, many researchers have focused on improving classical chaotic systems to enhance their chaotic dynamic characteristics through a process called chaotification.”

• AssumptionRests on an assumption: Classical chaotic systems have inherent limitations, such as periodicity, small key space, easy destruction of phase space, and low LE.

Probably not a substantial claim: may not pass S3 (load-bearing).

F. Pichler and J. Scharinger first proposed an encryption scheme based on a two-dimensional Baker map.

“F. Pichler and J. Scharinger [25] first proposed an encryption scheme based on a two-dimensional Baker map.”

• cites [25] Scharinger, J., and Pichler, F. (1996, January 30). Efficient image encryption based on chaotic maps. Proceedings of the 20th workshop of the Austrian Association for Pattern Recognition (OAGM/AAPR) on Pattern Recognition 1996, Munich, Germany.Not checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

x-dimensional systems have x Lyapunov exponents.

“In addition, x-dimensional systems have x Lyapunov exponents.”

May combine two claims.

Yu and Xu's 5D memristive exponential hyperchaotic system algorithm was thoroughly tested for security and the results indicated it is sufficiently robust.

“The algorithm was thoroughly tested for security, and the results indicated that it is sufficiently robust.”

• cites [66] Yu, 2023, Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic system, Integration sourceNot checked — no full text of the source

May combine two claims.

Zhu's improved hyperchaos-based method requires only two rounds of diffusion to modify pixel values and break the correlation between adjacent pixels.

“In addition, it only takes two rounds of diffusion operation to modify values of the pixel and break the correlation between adjacent pixels of the image.”

• cites [63] Zhu, 2012, A novel image encryption scheme based on improved hyperchaotic sequences, Opt. Commun. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The idea of chaotic image encryption based on a block cipher is to use a chaotic map to generate secret keys or chaotic sequences to substitute and diffuse the pixels or bits of the image to achieve a higher level of security.

“The idea of chaotic image encryption based on a block cipher is to use a chaotic map to generate secret keys or chaotic sequences to substitute and diffuse the pixels or bits of the image to achieve a higher level of security.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

There are five modes of block cipher: ECB, CBC, CFB, OFB, and CTR.

“There are five modes of block cipher: ECB, CBC, CFB, OFB, and CTR.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The larger the LE value, the more obvious the chaos characteristics.

“In addition, the larger the LE value, the more obvious the chaos characteristics.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

For the one-dimensional discrete chaotic map, an ideal system should have a trajectory that exhibits no recognizable structure or periodic cycles, although trajectories of continuous chaotic systems often have some identifiable shape.

“For the one-dimensional discrete chaotic map, an ideal system should have a trajectory that exhibits no recognizable structure or periodic cycles, although trajectories of continuous chaotic systems often have some identifiable shape.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

LE can tell if the motion system is chaotic because the chaotic system has at least one positive LE, which is different from other stochastic systems.

“LE can tell if the motion system is chaotic because the chaotic system has at least one positive LE, which is different from other stochastic systems.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

The trajectory diagram can directly show the ergodic property of a chaotic system and whether there is a cycle.

“The trajectory diagram can directly show the ergodic property of a chaotic system and whether there is a cycle.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The bifurcation diagram reflects the relationship between chaotic characteristics and control parameters.

“The bifurcation [22] diagram reflects the relationship between chaotic characteristics and control parameters.”

• cites [22] Chow, S.-N., and Hale, J.K. (2012). Methods of Bifurcation Theory, Springer Science & Business Media.Not checked yet

  Not checked in the free run.

May combine two claims.

Extending the two-dimensional Baker map to three dimensions yields better chaotic characteristics in LE and retains high security while enabling fast image encryption.

“Yaobin Mao and Guangrong Chen [38], based on the achievement of F. Pichler and J. Scharingers [43], further extended a two-dimensional Baker map to three dimensions with better chaotic characteristics in LE for fast image encryption while retaining its high security.”

• cites [38] Baptista, 1998, Cryptography with chaos, Phys. Lett. A sourceNot checked — no full text of the source
• cites [43] Mao, 2004, A novel fast image encryption scheme based on 3D chaotic baker maps, Int. J. Bifurc. Chaos sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Chaos-based image encryption can be categorized based on the characteristics of the key, which can be divided into symmetric key chaotic image encryption and asymmetric key chaotic image encryption.

“Additionally, it can be categorized based on the characteristics of the key, which can be divided into symmetric key chaotic image encryption and asymmetric key chaotic image encryption.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The goal of chaotification is to make up for these limitations and improve the performance of chaotic systems in applications such as encryption algorithms.

“The goal of chaotification is to make up for these limitations and improve the performance of chaotic systems in applications such as encryption algorithms.”

• AssumptionRests on an assumption: Classical chaotic systems have inherent limitations, such as periodicity, small key space, easy destruction of phase space, and low LE.

May combine two claims.

Huang's parameterized two-dimensional cross-chaotic Chebyshev system has a large key space and is sensitive enough to initial conditions.

“Then, the new function, which has a large key space and is sensitive enough to initial conditions, was employed to generate a pseudo-random chaotic sequence for confusion and diffusion.”

• cites [46] Huang, 2012, Image encryption algorithm using chaotic Chebyshev generator, Nonlinear Dyn. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The autocorrelation of an ideal chaotic sequence should decay rapidly with the interval of states.

“The autocorrelation of an ideal chaotic sequence should decay rapidly with the interval of states.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The strange attractors of almost all chaotic systems have fractional dimensions.

“The strange attractors of almost all chaotic systems have fractional dimensions.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Replacing traditional periodic position permutation with a total circular function reduces the correlation between adjacent pixels in the permutation stage.

“They utilized a total circular function to take the place of the traditional periodic position permutation to reduce the correlation between adjacent pixels in the permutation stage.”

• cites [47] Ye, 2012, An efficient chaotic image encryption algorithm based on a generalized Arnold map, Nonlinear Dyn. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Combining chaotic systems with stream ciphers relies heavily on integrating chaotic maps and keystream generators.

“Therefore, the combination of chaotic systems and stream ciphers relies heavily on the integration of chaotic maps and keystream generators.”

• AssumptionRests on an assumption: Stream ciphers are widely used in cryptographic fields because of their fast operation speed and high security performance.
• AssumptionRests on an assumption: The performance of the keystream generator directly determines the security performance of the stream-cipher algorithm.

Probably not a substantial claim: may not pass S4 (based).

The robustness of spatial-domain image encryption may not be satisfactory.

“However, the robustness of the spatial-domain encryption may not be satisfactory.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The GCS system of [108] can implement data authentication.

“Additionally, data authentication can also be implemented.”

• cites [108] Wu, 2019, Generalized chaos synchronization circuit simulation and asymmetric image encryption, IEEE Access sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The non-adjacent coupled map lattice (NACML) has a wider range of parameters and fewer periodic windows in the bifurcation diagram than 1D chaotic systems.

“In Zhang Ying-Qian and Wang Xing-Yuan's algorithm [95], the non-adjacent coupled map lattice (NACML),which has a wider range of parameters and fewer periodic windows in the bifurcation diagram than 1D chaotic systems, is selected in the diffusion process.”

• cites [95] Zhang, 2015, A new image encryption algorithm based on non-adjacent coupled map lattices, Appl. Soft Comput. sourceNot checked — no full text of the source

Classified as probably not a substantial claim.

Coupling low-dimensional chaotic maps may provide a new way for stream-cipher-based image encryption.

“Therefore, the coupling of low-dimensional chaotic maps may show a new way for stream-cipher-based image encryption.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The CRSA algorithm of [109] has the advantages of both RSA and chaotic systems.

“This algorithm has the advantages of both RSA and chaotic systems.”

• cites [109] Zengin, 2017, The design and implementation of hybrid RSA algorithm using a novel chaos based RNG, Chaos Solitons Fractals sourceNot checked — no full text of the source

May combine two claims.

Combining chaotic and traditional cryptographic techniques creates a more robust encryption algorithm that is resistant to attacks and can ensure the confidentiality and integrity of the encrypted image.

“This combination can take advantage of the strengths of both chaotic and traditional cryptographic techniques, creating a more robust encryption algorithm that is resistant to attacks and can ensure the confidentiality and integrity of the encrypted image.”

May combine two claims.

DWT-based encryption algorithms can achieve a higher level of security and provide better protection against attacks by decomposing the image into different frequency sub-bands.

“By decomposing the image into different frequency sub-bands, DWT-based encryption algorithms can achieve a higher level of security and provide better protection against attacks.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The method of [123] has strong resistance to the two-step iterative amplitude-phase retrieval algorithm.

“Furthermore, their method has strong resistance to the two-step iterative amplitude-phase retrieval algorithm.”

• cites [123] Zhang, 2021, Hyperchaotic image encryption using phase-truncated fractional Fourier transform and DNA-level operation, Opt. Lasers Eng. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The security of the Chaotic Key-Based Algorithm (CKBA) needs to be improved.

“However, Shujun Li and Xuan Zheng [83] estimated its security and pointed out that this algorithm is weak for the known-plaintext attack, which implies that the security of the algorithm needs to be improved.”

• cites [83] Li, S., and Zheng, X. (2002, January 26–29). Cryptanalysis of a chaotic image encryption method. Proceedings of the 2002 IEEE International Symposium on Circuits and Systems (ISCAS), Phoenix-Scottsdale, AZ, USA. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Kanso and Ghebleh's mixing and masking rules make the relationship between the plain image and the encrypted image more diffusing and confusing.

“These rules make the relationship between the plain image and the encrypted image more diffusing and confusing.”

• cites [78] Kanso, 2012, A novel image encryption algorithm based on a 3D chaotic map, Commun. Nonlinear Sci. Numer. Simul. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Asymmetric encryption structures do not have the concern of requiring secure key transmission.

“In contrast, asymmetric encryption structures do not have this concern.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Symmetric cryptosystems require the encryption and decryption parties to use the same key.

“However, it is worth noting that the encryption and decryption parties must use the same key”

May combine two claims.

Guo-Dong Ye and Hui-Shan Wu [114] introduced a 3D ILM chaotic system with large key space and high complexity.

“Recently, Guo-Dong Ye and Hui-Shan Wu [114] introduced a 3D ILM chaotic system, which has large key space and high complexity.”

• cites [114] Ye, 2022, Asymmetric image encryption algorithm based on a new 3D-ILM chaotic map, Chin. Phys. B sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Spatial-domain image-encryption algorithms have fast computation speed and do not cause additional image distortion.

“The advantages of spatial domain algorithms are their fast computation speed and the fact that the encryption process does not cause additional image distortion.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

DWT can divide signals with both frequency and time information into different sub-bands, resulting in a higher compression ratio and better image rendering by eliminating blocky artifacts.

“DWT can divide signals with both frequency and time information into different sub-bands, which can result in a higher compression ratio and better rendering of the image by eliminating blocky artifacts.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The mathematical complexity of frequency-domain encryption makes it more difficult to illegally decode the encrypted image.

“In contrast, frequency-domain encryption algorithms offer high efficiency, and the complexity of their mathematical expressions makes it more difficult to illegally decode the encrypted image.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The symmetric key must be transmitted through a secure channel to prevent leakage; otherwise the ciphertext may be breached.

“which must be transmitted through a secure channel to prevent it from being leaked.Otherwise, the ciphertext may be breached.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Liu and Sun's coupled Logistic map stream-cipher image-encryption scheme can be a good substitute for the block cipher.

“Their streamcipher-based image-encryption scheme with this key generator illustrates that it can be a good substitute for the block cipher.”

• cites [87] Liu, 2009, An Improved Image Encryption Algorithm based on Chaotic System, J. Comput. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

While chaos-based image-encryption algorithms have been significantly improved and extended, there are still some shortcomings that need to be addressed in order to optimize their performance in certain aspects, such as resistance to attacks and processing of encrypted images.

“While chaos-based image-encryption algorithms have been significantly improved and extended, there are still some shortcomings that need to be addressed in order to optimize their performance in certain aspects, such as resistance to attacks and processing of encrypted images.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Blockchain has many desirable attributes, including decentralization, anonymity, persistence, and auditability.

“As the core mechanism of Bitcoin, blockchain has many desirable attributes, including decentralization, anonymity, persistence, and auditability.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

By introducing chaotic systems into the learning and training processes of neural networks, CNNs can enhance the randomness and unpredictability of the network, making it more resistant to attacks and providing a higher degree of security.

“By introducing chaotic systems into the learning and training processes of neural networks, CNNs can enhance the randomness and unpredictability of the network, making it more resistant to attacks and providing a higher degree of security.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

The original FHN neuron model is effective in theoretical analysis and numerical simulations but has a high implementation cost.

“The original FHN neuron model is effective in theoretical analysis and numerical simulations but it has a high implementation cost.”

Probably not a substantial claim: may not pass S3 (load-bearing).

DNA methods are an effective way to resolve the problem of storage of one-time pads because of their extraordinary information density.

“Because of their extraordinary information density, DNA methods are an effective way to resolve the problem of the storage of one-time pads.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The BBEC of [154] is employed in the first step to solve the problem of key distribution and management of symmetric key encryption.

“The BBEC is employed in the first step in order to solve the problem of key distribution and management of symmetric key encryption.”

• cites [154] Abdelfatah, 2019, Secure image transmission using chaotic-enhanced elliptic curve cryptography, IEEE Access sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Blockchain can operate in a decentralized environment, enabling transactions to be decentralized, which helps to save costs and improve efficiency.

“In particular, blockchain can operate in a decentralized environment, enabling transactions to be decentralized, which helps to save costs and improve efficiency.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Chaotic image encryption can use synchronization properties of chaotic systems to synchronize multiple satellites, thus improving stability and resistance capability of satellite communications.

“use the synchronization properties of chaotic systems to synchronize multiple satellites, thus improving the stability and resistance capability of satellite communications”

• AssumptionRests on an assumption: Satellite communications face interference from multiple sources.

Probably not a substantial claim: may not pass S4 (based).

Medical images generally contain confidential information, including private information.

“Medical images generally contain confidential information, including private information, so the security of medical images is essential to protect users from all kinds of malicious attacks, avoid information loss, and ensure integrity.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Ref. [150] proposed a blockchain-based Chaotic Deep Generative Adversarial Network Encryption (BCDGE) scheme with a cloud storage system for securing medical images.

“Ref. [150] proposed a blockchain-based Chaotic Deep Generative Adversarial Network Encryption (BCDGE) scheme with a cloud storage system for securing medical images.”

• cites [150] Neela, 2022, Blockchain based Chaotic Deep GAN Encryption scheme for securing medical images in a cloud environment, Appl. Intell. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Nooshin Bigdeli and Yousef Farid [125] presented image encryption based on a chaotic neuron layer (CNL) and a permutation neuron layer (PNL), which consists of a three-input, three-output CNN.

“Based on [124], Nooshin Bigdeli and Yousef Farid [125] presented image encryption based on a chaotic neuron layer (CNL) and a permutation neuron layer (PNL), which consists of a three-input (the value of RGB), three-output (encoded streams) CNN.”

• cites [125] Bigdeli, 2012, A novel image encryption/decryption scheme based on chaotic neural networks, Eng. Appl. Artif. Intell. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

CNNs have been applied to a variety of image-encryption tasks, including image scrambling and watermarking, and have shown promising results.

“CNNs have been applied to a variety of image-encryption tasks, including image scrambling and watermarking, and have shown promising results.”

Probably not a substantial claim: may not pass S3 (load-bearing).

K. Ratnavelu and M. Kalpana [127] introduced a fuzzy cellular neural network (FCNN).

“A construct called a fuzzy cellular neural network (FCNN) was introduced by K. Ratnavelu and M. Kalpana [127].”

• cites [127] Ratnavelu, 2017, Image encryption method based on chaotic fuzzy cellular neural networks, Signal Process. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Zhengjun Liu and Qing Guo [156] proposed double image encryption based on a chaotic map and optical technology with gyrator transform.

“Zhengjun Liu and Qing Guo [156] proposed double image encryption based on a chaotic map and optical technology with gyrator transform.”

• cites [156] Liu, 2010, Double image encryption by using iterative random binary encoding in gyrator domains, Opt. Express sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

The method of applying chaos-based image encryption to medical images provides an effective way to achieve privacy protection and safe transmission of medical images.

“The method of applying chaos-based image encryption to medical images provides an effective way to achieve privacy protection and safe transmission of medical images.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Xing-Yuan Wang and Zhi-Ming Li [126] proposed a Hopfield-CNN-based image-encryption approach.

“A Hopfield-CNN-based image-encryption approach was proposed by Xing-Yuan Wang and Zhi-Ming Li [126].”

• cites [126] Wang, 2019, A color image encryption algorithm based on Hopfield chaotic neural network, Opt. Lasers Eng. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

The overall stability of the chaotic system makes it resistant enough to deal with satellite communication interferences effectively.

“Satellite communications face interference from multiple sources, and the overall stability of the chaotic system makes it resistant enough to deal with these interferences effectively.”

• AssumptionRests on an assumption: Satellite communications face interference from multiple sources.

Probably not a substantial claim: may not pass S3 (load-bearing).

Experimental results of [132] confirm that their approach can produce electrical activity with periodic spiking, chaotic, and quasi-periodic behavior, suitable for analog circuits for neuromorphic intelligence based on FHN neurons.

“Experimental results confirm that their approach can produce electrical activity with periodic spiking, chaotic, and quasi-periodic behavior, which suggests that it is suitable for implementing analog circuits for neuromorphic intelligence based on FHN neurons.”

• cites [132] Xu, 2023, Dynamical analysis of an improved FitzHugh-Nagumo neuron model with multiplier-free implementation, Nonlinear Dyn. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

Blockchain has great potential in the construction of future Internet systems.

“Therefore, blockchain has great potential in the construction of future Internet systems [148].”

• cites [148] Zheng, 2018, Blockchain challenges and opportunities: A survey, Int. J. Web Grid Serv. sourceNot checked — no full text of the source

May combine two claims.

The scheme of applying chaos theory to medical image encryption has been tested during key space analysis, histogram analysis, correlation analysis, key sensitivity analysis, and UACI/NPCR attack resistance testing, and is secure enough to effectively solve the problems in secure medical communication.

“The above scheme of applying chaos theory to medical image encryption has been tested during key space analysis, histogram analysis, correlation analysis, key sensitivity analysis, and testing of the ability to resist attack using UACI and NPCR to prove that it is secure enough to effectively solve the problems in secure medical communication.”

• AssumptionRests on an assumption: Medical image-encryption algorithms have specific requirements, such as high security, data integrity (image quality), and encryption/decryption speed.
• AssumptionRests on an assumption: Traditional encryption schemes require high computational power and a long computation time, which may lead to considerable latency, and have drawbacks such as low key space and vulnerability to attacks.

Probably not a substantial claim: may not pass S2 (checkable).

Chaotic image encryption can be suggested for microcontroller and IoT applications.

“There are many reasons why chaotic image encryption can be suggested for microcontroller and IoT applications.”

• AssumptionRests on an assumption: Data transmitted by devices in the IoT and stored in microcontrollers may involve important information such as personal privacy information and trade secrets.

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

These chaotic image-encryption algorithms applied to satellites have a considerable advantage in encryption/decryption speed compared with traditional methods.

“Furthermore, these chaotic image-encryption algorithms applied to satellites also have a considerable advantage in encryption/decryption speed compared with the traditional methods.”

May combine two claims.

The algorithm of [149] provides authentication and tracking capabilities in addition to CPA resistance.

“This algorithm provides authentication and tracking capabilities in addition to CPA resistance.”

• cites [149] Li, 2021, Fingerprint-related chaotic image encryption scheme based on blockchain framework, Multimed. Tools Appl. sourceNot checked — no full text of the source

May combine two claims.

The resulting encoded sequence of [131] is used as an image-encryption scheme, providing greater resistance to a variety of attacks.

“The resulting encoded sequence is then used as an image-encryption scheme, providing greater resistance to a variety of attacks.”

• cites [131] Bao, 2021, Discrete memristive neuron model and its interspike interval-encoded application in image encryption, Sci. China Technol. Sci. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

The chaotic image-encryption algorithm can be implemented in a simple circuit, which is ideal for use in embedded systems such as microcontrollers.

“Second, the chaotic imageencryption algorithm can be implemented in a simple circuit, which is ideal for use in embedded systems such as microcontrollers.”

May combine two claims.

The encoded sequences of [131] exhibit higher complexity and better biological interpretability than the original burst sequences.

“The encoded sequences exhibit higher complexity and better biological interpretability than the original burst sequences.”

• cites [131] Bao, 2021, Discrete memristive neuron model and its interspike interval-encoded application in image encryption, Sci. China Technol. Sci. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The BC-PMA scheme of [151] improves the accuracy of authentication and reduces the false positive rate and calculation cost.

“This scheme not only improves the accuracy of authentication but also reduces the false positive rate and calculation cost.”

• cites [151] Singh, 2022, Chaotic and Paillier secure image data sharing based on blockchain and cloud security, Expert Syst. Appl. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Junwei Suna and Chuangchuang Li [133] proposed a novel locally active hyperbolic memristor that can exhibit bistable phenomena.

“Junwei Suna and Chuangchuang Li [133] proposed a novel locally active hyperbolic memristor that can exhibit bistable phenomena.”

• cites [133] Sun, 2023, Dynamic analysis of HR-FN-HR neural network coupled by locally active hyperbolic memristors and encryption application based on Knuth-Durstenfeld algorithm, Appl. Math. Model. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based). May combine two claims.

The encryption/decryption speed of chaotic image-processing algorithms is extremely fast, and can meet the real-time requirements for data encryption and decryption in IoT.

“In addition, the encryption/decryption speed of chaotic image-processing algorithms is extremely fast, and can thus meet the real-time requirements for data encryption and decryption in IoT.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Aloka Sinha and Kehar Singh [155] suggested a scheme for image encryption using a digital signature in 2003.

“A scheme for image encryption using a digital signature was suggested by Aloka Sinha and Kehar Singh [155] in 2003.”

• cites [155] Sinha, 2003, A technique for image encryption using digital signature, Opt. Commun. sourceNot checked — no full text of the source

May combine two claims.

The structure of [124] has great security in computing but may be vulnerable to attack because of its constant weight and bias matrices.

“This structure has great security in computing but it may be vulnerable to attack because of its constant weight and bias matrices.”

• cites [124] Lian, 2009, A block cipher based on chaotic neural networks, Neurocomputing sourceNot checked — no full text of the source

May combine two claims.

Song [195] employed the YOLOv4 target detection model to identify regions of interest and created a novel image-encryption algorithm using chaotic mapping that aims to protect local images.

“Song [195] employed the YOLOv4 target detection model to identify the regions of interest and created a novel image-encryption algorithm using chaotic mapping.”

• cites [195] Song, 2022, Protection of image ROI using chaos-based encryption and DCNN-based object detection, Neural Comput. Appl. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

The unique attributes of chaos-based encryption, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, enable cross-disciplinary collaborations and further improvements in image-encryption methods.

“The unique attributes of chaos-based encryption, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, enable cross-disciplinary collaborations and further improvements in image-encryption methods.”

May combine two claims.

After an image is encrypted by an encryption algorithm, the data is in a disordered state, which makes it difficult to accurately perform feature extraction.

“However, after the image is encrypted by an encryption algorithm, the data is in a disordered state, which makes it difficult to accurately perform feature extraction.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

Chaos-based image-encryption technology has been developing rapidly, and its security, robustness, encryption efficiency, key space, and other attributes have been improved in different schemes with various methods.

“Chaos-based image-encryption technology has been developing rapidly, and its security, robustness, encryption efficiency, key space, and other attributes have been improved in different schemes with various methods.”

Probably not a substantial claim: may not pass S4 (based).

There are still some disadvantages and challenges in chaos-based image encryption.

“However, there are still some disadvantages and challenges in chaos-based image encryption.”

• AssumptionRests on an assumption: There is no absolutely secure encryption scheme.

Probably not a substantial claim: may not pass S4 (based).

Chaos-based image encryption is still one of the most effective methods for image encryption.

“Chaos-based image encryption is still one of the most effective methods for image encryption.”

• AssumptionRests on an assumption: There is no absolutely secure encryption scheme.

Probably not a substantial claim: may not pass S2 (checkable).

Chaos-based image encryption is a promising technique for image encryption.

“Overall, chaos-based image encryption is a promising technique for image encryption”

Probably not a substantial claim: may not pass S3 (load-bearing).

The elementary CA and BCS-based chaotic image compression and encryption scheme [186] can transmit the image securely and simultaneously compress it on a public network because of its excellent performance.

“The scheme can transmit the image securely and simultaneously compress it on a public network because of its excellent performance.”

• cites [186] Chai, 2020, An efficient chaos-based image compression and encryption scheme using block compressive sensing and elementary cellular automata, Neural Comput. Appl. sourceNot checked — no full text of the source

May combine two claims.

Shan [197] used the PSPNet model to obtain portrait information and introduced a new chaotic image-encryption algorithm using an upgraded perturbation-diffusion architecture; experimental results indicated good security performance.

“The experimental results indicated that this algorithm demonstrated good security performance.”

• cites [197] Shan, Y., He, M., Yu, Z., and Wu, H. (2018, January 19–21). Pixel level Image Encryption Based on Semantic Segmentation. Proceedings of the 2018 International Conference on Control, Artificial Intelligence, Robotics & Optimization (ICCAIRO), Prague, Czech Republic. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

Chaos-based image encryption plays a crucial role in practical applications.

“Moreover, chaos-based image encryption plays a crucial role in practical applications.”

May combine two claims.

Wang [196] utilized target detection and semantic segmentation to obtain portrait information and developed a chaotic image-encryption algorithm that works well for images with non-uniform content sizes.

“They also developed a chaotic image-encryption algorithm that works well for images with non-uniform content sizes.”

• cites [196] Wang, 2022, A novel content-selected image encryption algorithm based on the LS chaotic model, J. King Saud Univ.-Comput. Inf. Sci. sourceNot checked — no full text of the source

May combine two claims.

The general image-compression scheme has good compression performance, but it cannot guarantee data confidentiality.

“The general scheme has good compression performance, but it cannot guarantee the data confidentiality [184].”

• cites [184] Yuen, 2011, A chaos-based joint image compression and encryption scheme using DCT and SHA-1, Appl. Soft Comput. sourceNot checked — no full text of the source

May combine two claims.

Image retrieval schemes [193,194] are all calculated for plaintext features, and their protection of image information is limited.

“Although some excellent image retrieval schemes have been proposed in [193,194], they are all calculated for plaintext features, and their protection of image information is limited.”

• cites [193] Yue-Hei Ng, J., Yang, F., and Davis, L.S. (2015, January 7–12). Exploiting local features from deep networks for image retrieval. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Boston, MA, USA.Not checked yet

  Not checked in the free run.

• cites [194] Gordo, A., Almazán, J., Revaud, J., and Larlus, D. (2016, January 11–14). Deep image retrieval: Learning global representations for image search. Proceedings of the Computer Vision–ECCV 2016: 14th European Conference, Amsterdam, The Netherlands. sourceNot checked — no full text of the source