A Novel Five-Dimensional Three-Leaf Chaotic Attractor and Its Application in Image Encryption

Abstract

This paper presents a novel five-dimensional three-leaf chaotic attractor and its application in image encryption. First, a new five-dimensional three-leaf chaotic system is proposed. Some basic dynamics of the chaotic system were analyzed theoretically and numerically, such as the equilibrium point, dissipative, bifurcation diagram, plane phase diagram, and three-dimensional phase diagram. Simultaneously, an analog circuit was designed to implement the chaotic attractor. The circuit simulation experiment results were consistent with the numerical simulation experiment results. Second, a convolution kernel was used to process the five chaotic sequences, respectively, and the plaintext image matrix was divided according to the row and column proportions. Lastly, each of the divided plaintext images was scrambled with five chaotic sequences that were convolved to obtain the final encrypted image. The theoretical analysis and simulation results demonstrated that the key space of the algorithm was larger than 10150 that had strong key sensitivity. It effectively resisted the attacks of statistical analysis and gray value analysis, and had a good encryption effect on the encryption of digital images.

Medical image encryption algorithm based on a new five-dimensional three-leaf chaotic system and genetic operation

“…In 2020, Wang et al [ 17 ] introduced two controllers w and v based on the three-dimensional chaotic system proposed by Sprott [ 40 ], feedback w to the original controller y , and feedback y , z to the new controller w , feedback v to w , feedback x , y to the new controller v . The interaction of the five controllers makes the parameter control of the system more complicated, and can generate three-leaf chaotic attractors in multiple directions.…”

“…In addition, Wang et al [ 17 ] carried out a series of dynamic analyses such as balance points and bifurcation diagrams while proposing the chaotic system. The experimental results proved that the chaotic system has strong stability.…”

“…For example, the P value of each item is slightly higher than the P value of 15 tests in [ 41 ], which means it has better randomness. In addition, Wang et al [ 17 ] also tested the time series diagrams in each direction of x , y , z , w , and v , and they all showed a chaotic state, which also shows that the chaotic sequence generated by this system is more random. The security of the image encryption algorithm is more guaranteed.…”

“…However, the use of chaotic systems for image encryption is still the mainstream direction of researchers. Therefore, this paper still uses a high-dimensional chaotic system that can increase the key space, and introduces a new five-dimensional three-leaf chaotic system that can generate three-leaf chaotic attractors in multiple directions [ 17 ], which significantly improves the randomness of chaotic sequences and effectively resists violent attacks.…”

Generation multi-scroll chaotic attractors using composite sine function and its application in image encryption

“…Essentially, chaotic systems present a high sensitivity to a minute variations of their initial conditions or a tiny perturbations, such that even a very slight disturbance can lead to that the motion track deviates completely from the system's original trajectory after a certain period of evolution. so chaotic system is widely employed in digital watermarking [1][2][3], pseudo noise code generation [4][5][6], image encryption [7][8][9], weak signal detection [10][11][12] and so on.…”