S-box:six-dimensional compound hyperchaotic map and artificial bee colony algorithm

Being as unique nonlinear components of block ciphers,substitution boxes（S-boxes） directly affect the security of the cryptographic systems.It is important and difficult to design cryptographically strong S-boxes that simultaneously meet with multiple cryptographic criteria such as bijection,non-linearity,strict avalanche criterion（SAC）,bits independence criterion（BIC）,differential probability（DP） and linear probability（LP）.To deal with this problem,a chaotic S-box based on the artificial bee colony algorithm（CSABC） is designed.It uses the S-boxes generated by the six-dimensional compound hyperchaotic map as the initial individuals and employs ABC to improve their performance.In addition,it considers the nonlinearity and differential uniformity as the fitness functions.A series of experiments have been conducted to compare multiple cryptographic criteria of this algorithm with other algorithms.Simulation results show that the new algorithm has cryptographically strong S-box while meeting multiple cryptographic criteria.

A novel hyperchaotic map with sine chaotification and discrete memristor

Discrete memristor has become a hotspot since it was proposed recently.However,the design of chaotic maps based on discrete memristor is in its early research stage.In this paper,a memristive seed chaotic map is proposed by combining a quadratic discrete memristor with the sine function.Furthermore,by applying the chaotification method,we obtain a high-dimensional chaotic map.Numerical analysis shows that it can generate hyperchaos.With the increase of cascade times,the generated map has more positive Lyapunov exponents and larger hyperchaotic range.The National Institute of Standards and Technology(NIST)test results show that the chaotic pseudo-random sequence generated by cascading two seed maps has good unpredictability,and it indicates the potential in practical application.

A color image encryption algorithm based on hyperchaotic map and DNA mutation

We devise a color image encryption scheme via combining hyperchaotic map,cross-plane operation and gene theory.First,the hyperchaotic map used in the encryption scheme is analyzed and studied.On the basis of the dynamics of hyperchaotic map,a color image encryption scheme is designed.At the end of the encryption process,a DNA mutation operation is used to increase the encoding images’randomness and to improve the encryption algorithm’s security.Finally,simulation experiments,performance analysis,and attack tests are performed to prove the effectiveness and security of the designed algorithm.This work provides the possibility of applying chaos theory and gene theory in image encryption.

Cryptanalysis of 2D-SCMCI Hyperchaotic Map Based Image Encryption Algorithm

Chaos-based cryptosystems are considered a secure mode of communication due to their reliability.Chaotic maps are associated with the other domains to construct robust encryption algorithms.There exist numerous encryption schemes in the literature based on chaotic maps.This work aims to propose an attack on a recently proposed hyper-chaotic map-based cryptosystem.The core notion of the original algorithm was based on permutation and diffusion.A bitlevel permutation approach was used to do the permutation row-and column-wise.The diffusion was executed in the forward and backward directions.The statistical strength of the cryptosystem has been demonstrated by extensive testing conducted by the author of the cryptosystem.This cryptanalysis article investigates the robustness of this cryptosystem against a chosen-plaintext attack.The secret keys of the cryptosystem were retrieved by the proposed attack with 258 chosen-plain images.The results in this manuscript suggest that,in addition to standard statistical evaluations,thorough cryptanalysis of each newly suggested cryptosystem is necessary before it can be used in practical application.Moreover,the data retrieved is also passed through some statistical analysis to compare the quality of the original and retrieved data.The results of the performance analysis indicate the exact recovery of the original data.To make the cryptosystem useful for applications requiring secure data exchange,a few further improvement recommendations are also suggested.

Remote sensing image encryption algorithm utilizing 2D Logistic memristive hyperchaotic map and SHA-512

The two-dimensional Logistic memristive hyperchaotic map(2D-LMHM)and the secure hash SHA-512 are the foundations of the unique remote sensing image encryption algorithm(RS-IEA)suggested in this research.The proposed map is formed from the improved Logistic map and the memristor,which has wide phase space and hyperchaotic range and is exceptionally excellent to be utilized in specific applications.The proposed image algorithm uses the permutation-assignment-diffusion structure.Permutation generates two position matrices in a progressive manner to achieve an efficient random exchange of pixel positions,assignment is carried through on the image pixels of the permutated image to entirely remove the original image information,strengthening the relationship between permutation and diffusion,and loop diffusion in two different directions can use subtle changes of pixels to affect the whole plane.The random key and plain-image SHA-512 hash values are used to produce an additional key,which is then utilized to figure out the permutation parameters and the initial value of a chaotic map.The experimental results with the average NPCR=99.6094%(NPCR:number of pixels change rate),average UACI=33.4638%(UACI:unified average changing intensity),100%pass rate of the targets in the test set,the average correlation coefficient is 0.00075,and the local information entropy is 7.9025,which shows that the algorithm is able to defend against a variety of illegal attacks and provide more trustworthy protection than some of the existing state-of-the-art algorithms.

CONTROL OF A HYPERCHAOTIC DISCRETE SYSTEM

The Control of a hyperchaotic discrete system is investigated, A time-varying feedback control law is established on the base of local linearization. The Liapunov direct method is applied to estimate the neighborhood in which the control law can be effectively used. Numerical examples are presented to demonstrate the applications of the control law to solve the problem of stabilizing unstable periodic orbits and the problem of tracking an arbitrarily given periodic orbit.