Chaotic S‐Box: Intertwining Logistic Map and Bacterial Foraging Optimization

Abstract

As the unique nonlinear component of block ciphers, Substitution box (S-box) directly affects the safety of a cryptographic system. It is important and difficult to design strong S-box that simultaneously meets multiple cryptographic criteria such as bijection, nonlinearity, strict avalanche criterion (SAC), bit independence criterion (BIC), differential probability (DP), and linear probability (LP). Though many chaotic S-boxes have been proposed, the cryptographic performance of most of them needs to be further improved. A new chaotic S-box based on the intertwining logistic map and bacterial foraging optimization is designed in this paper. It firstly iterates the intertwining logistic map to construct many S-boxes and then applies a bacterial foraging optimization algorithm to find the optimal S-box. Moreover, bacterial foraging optimization algorithm considers the nonlinearity and differential uniformity as the fitness functions in the optimization process. We experiment that the proposed S-box can effectively resist multiple types of cryptanalysis attacks.

Sine‐Cosine Optimization‐Based Bijective Substitution‐Boxes Construction Using Enhanced Dynamics of Chaotic Map

“…(c) The bits independent criterion for nonlinearity and SAC comes out as 104.07 and 0.5020 for proposed S-box. Our BIC-NL results are fairly higher than S-boxes investigated in [10,12,15,16,19,26,[28][29][30][31]34] and BIC-SAC satisfies the avalanche criterion with negligible margin like other Sboxes. Hence, satisfaction of bits independence criterion is consistent and better than most of the 8×8 S-boxes.…”

“…In [14], the Artificial Bee Colony (ABC) algorithm and hyperchaotic map are sought to yield effective 8×8 S-box, wherein a 6D hyperchaos was applied for initial population of S-boxes. The same author engaged Bacteria Foraging Optimization (BFO) with intertwining logistic map with similar approach for S-box optimization in [15]. In [16], the well-known traveling salesman problem is attempted for generating a strong S-box.…”

“…(a) The proposed S-box is proficient to supply highest nonlinearity compared to all S-boxes investigated in Table 17. The statistics of minimum (108) is equal to S-boxes in [10,11,19], maximum (110) is similar to S-boxes in [11][12][13][14][15][16][17]19], and these statistics are better than rest of the S-boxes of Table 17. It shows that proposed method can construct highly nonlinear S-boxes than most of the recent S-boxes.…”

“…As an option, a number of alternative methods are being investigated in recent past to yield S-boxes using various optimization techniques [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and chaotic systems [26][27][28][29][30][31][32]. Theoretically, a strong S-box possesses the features like balancedness, high nonlinearity, small differential uniformity and linear probability, strict avalanche effect close to 0.5, output bits independence, low autocorrelation, etc.…”

Sequential Hybrid Particle Swarm Optimization and Gravitational Search Algorithm with Dependent Random Coefficients

“…Hence, various kinds of metaheuristic algorithms that are inspired by natural phenomena have launched into a center stage in recent decades for solving complex optimization problems. Genetic algorithm (GA) [1], particle swarm optimization (PSO) [2], artificial immune system (AIS) [3], differential evolution (DE) [4], ant colony optimization (ACO) [5], glowworm swarm optimization (GSO) [6], artificial bee colony (ABC) [7], gravitational search algorithm (GSA) [8], grey wolf optimization (GWO) [9], cat swarm optimization (CSO) [10], harmony search algorithm (HS) [11], and bacterial foraging optimization algorithm (BFOA) [12] have been developed in recent years by researchers and have shown superior performance for solving a wide range of optimization problems, such as function optimization [4][5][6][7][8][9][11][12][13][14][15], fuzzy inference system [16,17], image processing [18,19], economic dispatch [20,21], and neural networks training [22,23].…”