A new steganographic algorithm based on coupled chaotic maps and a new chaotic S-box

A Novel Virtual Optical Image Encryption Scheme Created by Combining Chaotic S-Box with Double Random Phase Encoding

“…We compare our obtained S-box with many S-boxes generated in [ 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. Initialization parameters are configured as the following: = 0.36, = 0.25, = 0.78, 𝑘 1 = 32.5, 𝑘 2 = 34.3, 𝑘 3 = 28.1, 𝜇 = 3.999, = 1000, and = 757.…”

“…The following observations can be obtained from Table 2: (1) the S-boxes designed in refs. [34,36,38,40,[44][45][46][47][48][51][52][53]55] outperform the obtained S-box; (2) however, the average value of the obtained S-box is closer to the ideal value, 0.5, than those designed in refs. [33,35,37,[39][40][41]43,49,50,54].…”

“…The following conclusion can be obtained from this table: (1) the average BIC-nonlinearity value of the obtained S-box is lower than those designed in refs. [33,34,36,37,39,41,[44][45][46][47][48][49][50][51][52][53][54][55]; (2) the average BIC-nonlinearity value of the obtained S-box is greater than those constructed in refs. [35,38,40,43]; (3) the average BIC-SAC value of the obtained S-box is better than those proposed in refs.…”

“…However, the constructed S-box has weak differential performance and is vulnerable to algebraic attacks [ 31 , 32 ]. To tackle this issue, the researcher constructed many chaotic S-boxes [ 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. In 2001, Jakimoski et al first constructed an S-box based on discrete chaotic systems [ 33 ].…”

“…In 2001, Jakimoski et al first constructed an S-box based on discrete chaotic systems [ 33 ]. Since then, various chaotic S-box construction methods were proposed based on discrete-time chaotic systems [ 34 , 35 , 36 , 43 , 45 , 50 , 53 , 54 , 55 ], continuous-time chaotic systems [ 37 , 38 , 39 , 40 , 41 , 42 , 44 ], hyper chaotic systems [ 46 , 47 ], and joint optimization and chaotic systems [ 48 , 49 , 51 , 52 ]. The computational complexity of optimally generating S-boxes is highest, followed by high-dimensional continuous-time chaotic systems, and low-dimensional discrete chaotic systems is the lowest.…”