2D mixed pseudo-random coupling PS map lattice and its application in S-box generation

Abstract

In this paper, firstly, we investigate a new 1D PWLCM-Sin (PS) map which derived from PWLCM and Sin map by modulo operation. Due to the stronger parameter space, bigger Lyapunov exponents and better ergodicity than simple 1D map, the PS map is more suitable for local map of spatiotemporal dynamics. Secondly, with the novel 2D pseudorandom mixed coupling method we present a spatiotemporal chaos which used PS map as local map f(x). This spatiotemporal chaos named 2D Mixed pseudo-random Coupling PS Map Lattice (2DMCPML). The experimental results of bifurcation diagrams, Kolmogorov-Sinai entropy density and spatiotemporal chaotic diagrams showed that 2DMCPML has advantages of larger parameter space, more complex chaotic behavior and more ergodic output sequence than CML. Therefore, 2DMCPML is more suitable in cryptography than CML. Subsequently, we proposed a chaos-based random S-box design algorithm employed the spatial chaotic character of 2DMCPML to generate a large number of S-boxes. The cryptographic performance indicated that generated S-boxes can resist cryptanalysis attack well. Finally, four criteria bounds are set. The numbers of S-boxes satisfying these bounds generated by 2DMCPML and several 1D chaotic maps is calculated, respectively. The result showed that spatiotemporal chaos can generate more S-boxes with high cryptographic quality than low-dimensional chaos. This new discovery is significant to the development of some cryptographic researches such as dynamic S-box algorithm.

Efficient Dynamic S-Box Generation Using Linear Trigonometric Transformation for Security Applications

“…Comparison analysis indicates that our S-box has better ability to resist differential cryptanalysis than S-boxes available in [8,45,48,49,54,60] and it is comparable with others. The LAP score of 0.125 is also slightly better than many Sboxes such as [8,23,45,48,50,[52][53][54][55][56]60,64,65]. But, S-boxes presented in [35,47,58,59,61,62] show better LAP than our S-boxes.…”

“…Table 6 indicates that the proposed Sbox's SAC score is pretty close to 0.5 and better than many recent S-box methods listed in the Table . Moreover, the pair-wise disjoint Boolean functions comprising the S-box should have as high nonlinearity as possible. We can see that the BIC-nonlinearity score of our S-box is 104.2 which is higher than many S-boxes suggested in [8,23,24,45,46,[48][49][50][51][63][64][65] indicating the decent performance of proposed S-box. Hence, the proposed method has the ability to satisfy the SAC and BIC criterions well.…”

“…Therefore, the proposed method involves the nonlinearity improvisation plan as the technique for evolving preliminary S-box for over all nonlinearity feature of the S-box. Table 3 makes it evident that the proposed S-box has considerably higher nonlinearity performance over many recently investigated S-boxes in [8,24,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][63][64][65]. The excellent nonlinearity performance over many existing studies demonstrates that the proposed method is fairly effective in making the high nonlinear transformation of plaintext to ciphertext as compared to other methods.…”

“…The proposed S-boxes doesn't have any fixed points. But, a number of S-box found to have 1 or more fixed points as in [8,23,45,47,48,51,[56][57][58][59][60][61][62][63][64][65].…”

Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

“…The main features of the chaotic systems, such as the sensitive dependence on initial conditions and control parameters, ergodicity, size of the parameter space, and mixing property, can be related to the confusion and diffusion conditions that must be applied to information to be protected by using cryptographic systems [22]. Therefore, many cryptographic systems and modules have been proposed based on chaotic systems [22][23][24][25][26][27][28][29][30][31][32][33]. In particular, chaotic maps have been successfully applied in the implementation of PRNGs [14,15,31,[34][35][36][37][38][39][40][41][42].…”