Human Behaviour Based Optimization Supported With Self-Organizing Maps for Solving the S-Box Design Problem

Abstract

The cryptanalytic resistance of modern block and stream encryption systems mainly depends on the substitution box (S-box). In this context, the problem is thus to create an S-box with higher value of nonlinearity because this property can provide some degree of protection against linear and differential cryptanalysis attacks. In this paper, we design a scheme built on a human behavior-based optimization algorithm, supported with Self-Organizing Maps to prevent premature convergence and improve the nonlinearity property in order to obtain strong 8 × 8 substitution boxes. The experiments are compared with S-boxes obtained using other metaheuristic algorithms such as Ant Colony Optimization, Genetic Algorithm and an approach based on chaotic functions and show that the obtained S-boxes have good cryptographic properties. The obtained S-box is investigated against standard tests such as bijectivity, nonlinearity, strict avalanche criterion, bit independence criterion, linear probability and differential probability, proving that the proposed scheme is proficient to discover a strong nonlinear component of encryption systems.

Grey Wolf Optimizer and Discrete Chaotic Map for Substitution Boxes Design and Optimization

“…In a different study, Alhadawi et al [46] combined a chaotic map and the Cuckoo search method for S-box creation. Recently, Soto et al [47] proposed a way of evading premature convergence and improving the non-linearity property during S-box creation; the proposed method is based on human behaviour inspired frameworks and supported by self-organizing maps. Nafiseh and Sodeif [48] utilized ergodic chaotic maps to enhance the PSO algorithm's ability to create cryptographically robust S-boxes.…”

Enhancing the Robustness of Block Ciphers through a Graphical S-Box Evolution Scheme for Secure Multimedia Applications

“…In an identical way, we find all remaining cycles of the permutations 𝑥 and 𝑦 and given as: 𝑥 = (𝜉 1 , 𝜉 126 )(𝜉 2 , 𝜉 125 )(𝜉 3 , 𝜉 124 )(𝜉 4 , 𝜉 123 )(𝜉 5 , 𝜉 122 )(𝜉 6 , 𝜉 121 )(𝜉 7 , 𝜉 120 )(𝜉 8 , 𝜉 119 )(𝜉 9 , 𝜉 118 ) (𝜉 , 𝜉 117 )(𝜉 11 , 𝜉 116 )(𝜉 12 , 𝜉 115 )(𝜉 13 , 𝜉 114 )(𝜉 14 , 𝜉 113 )(𝜉 15 , 𝜉 112 )(𝜉 16 , 𝜉 111 )(𝜉 17 , 𝜉 110 )(𝜉 18 , 𝜉 109 ) (𝜉 , 𝜉 108 )(𝜉 20 , 𝜉 107 )(𝜉 21 , 𝜉 106 )(𝜉 22 , 𝜉 105 )(𝜉 23 , 𝜉 104 )(𝜉 24 , 𝜉 103 )(𝜉 25 , 𝜉 102 )(𝜉 26 , 𝜉 101 )(𝜉 27 , 𝜉 100 ) (𝜉 28 , 𝜉 99 )(𝜉 29 , 𝜉 98 )(𝜉 30 , 𝜉 97 )(𝜉 31 , 𝜉 96 )(𝜉 32 , 𝜉 95 )(𝜉 33 , 𝜉 94 )( 𝜉 34 , 𝜉 93 )( 𝜉 35 𝜉 92 )(𝜉 36 , 𝜉 91 )(𝜉 37 , 𝜉 90 ) (𝜉 38 , 𝜉 89 )(𝜉 39 , 𝜉 88 )(𝜉 40 , 𝜉 87 )(𝜉 41 , 𝜉 86 )(𝜉 42 , 𝜉 85 )(𝜉 43 , 𝜉 84 )(𝜉 44 64 ). 𝑦 = (0 , ∞, 1)(𝜉 1 , 𝜉 96 , 𝜉 30 ) (𝜉 2 , 𝜉 65 , 𝜉 60 )(𝜉 3 , 𝜉 120 , 𝜉 4 )(𝜉 5 , 𝜉 45 , 𝜉 77 )(𝜉 6 , 𝜉 113 , 𝜉 8 )(𝜉 7 , 𝜉 124 , 𝜉 123 ) (𝜉 , 𝜉 83 , 𝜉 35 )(𝜉 10 , 𝜉 90 , 𝜉 27 )(𝜉 11 , 𝜉 93 , 𝜉 <...…”

Multi-Objective Evolution of Strong S-Boxes Using Non-Dominated Sorting Genetic Algorithm-II and Chaos for Secure Telemedicine

“…In order to assess the proposed Pareto-optimized S-boxes, the security performance has been compared with other competing and existing S-boxes studies which are based meta-heuristics. Literature reveals that a number of metaheuristics have been investigated to obtain the optimized 8×8 S-boxes which includes the incorporation of Tiki-Taka algorithm (TTO) [48], Bacteria foraging optimization (BFO) [49], Fireworks Algorithm [50], Jaya optimization [51], Cuckoo search (CS) [52], Human behaviour based optimization (HBBO) [53], Genetic algorithms (GA) [20], Sine-cosine optimization (SCO) [54], Firefly algorithm [24], Teaching-learning based optimization (TLBO) [25], I-Chings optimization (ICO) [26], Ant colony optimization (ACO) [22], Artificial bee colony optimization (ABC) [23], and Particle swarm optimization (PSO) [55]. The Paretooptimal S-boxes from the first front from proposed method are compared.…”