Mitigating Drawbacks of Logistic Map for Image Encryption Algorithms

Abstract

This paper identifies and analyses some drawbacks of the logistic map which is still one of the most used chaotic maps in image encryption algorithms. As some of the disadvantages are caused by inappropriate implementations of the logistic map, this paper proposes a set of rules which should lead to enhancement of the desired chaotic behavior. Probably the most important rule introduces alternating value of parameter utilized by the logistic map. With careful choice of values and an adapted quantization technique, some of the issues should be fixed and theoretically also the values of numerical parameters should be improved. These assumptions are verified by applying the proposed set of rules on an algorithm from our prior work. Effects of the proposed rules on the used algorithm are investigated and all necessary modifications are thoroughly discussed. The paper also compares obtained values of commonly used numerical parameters and computational complexity with some other image encryption algorithms based on more complex chaotic systems.

An Image Encryption Algorithm Using Logistic Map with Plaintext-Related Parameter Values

“…A plaintext-related technique using the Mojette transform was presented in a paper from 2019 [40]. The most significant drawbacks of LM and their solutions were discussed in a publication from 2020 [41]. Our experience in the field of plaintext-related image encryption was used in a paper presented in 2021 [42] that describes a way to introduce relations between plain image pixel intensities and an encryption algorithm during the quantization of pseudo-random sequences.…”

“…• the usage of a novel plaintext-related parameter modification scheme for LM; • the whole encryption/decryption scheme is symmetric-these operations are able to extract the required values from either plain or encrypted images; • it takes into account the knowledge about LM-previously reported drawbacks such as fixed points or periodic cycles [39,41] are suppressed by careful choice of parameter value intervals and alternation of parameter values during the generation of pseudorandom sequences. This could be viewed as a novelty since it is not common even for new proposals.…”

“…There are still some areas with suppressed chaotic behavior, such as that around r ∼ 3.85; however, the area close to r = 4 displays the most unpredictable behavior. This could be illustrated also by a plot of estimated Lyapunov exponents (LEs) λ that quantify divergences between two trajectories with a small initial difference [3,41,44]. LEs for the LM could be estimated by (2) [41]:…”

“…This could be illustrated also by a plot of estimated Lyapunov exponents (LEs) λ that quantify divergences between two trajectories with a small initial difference [3,41,44]. LEs for the LM could be estimated by (2) [41]:…”

Evaluation Technology of Classroom Students’ Learning State Based on Deep Learning

“…At present, the research on fatigue state detection mainly focuses on the field of fatigue driving, while the research on fatigue state in the field of education tends to be theoretical research, and there are few detection technologies that can be realized. As the detection technology of fatigue state in education field is similar to that of fatigue driving, the research and implementation of key technologies can refer to fatigue driving detection [ 13 , 14 ]. At present, the research on fatigue driving detection at home and abroad adopts subjective detection and objective detection.…”