Designing substitution boxes based on chaotic map and globalized firefly algorithm

Cipher strength mainly depends on the robust structure and a well-designed interaction of the components in its framework. A significant component of a cipher system, which has a significant influence on the strength of the cipher system, is the substitution box or S-box. An S-box is a vital and most essential component of the cipher system due to its direct involvement in providing the system with resistance against certain known and potential cryptanalytic attacks. Hence, research in this area has increased since the late 1980s, but there are still several issues in the design and analysis of the S-boxes for cryptography purposes. Therefore, it is not surprising that the design of suitable S-boxes attracts a lot of attention in the cryptography community. Nonlinearity, bijectivity, strict avalanche criteria, bit independence criteria, differential probability, and linear probability are the major required cryptographic characteristics associated with a strong S-box. Different cryptographic systems requiring certain levels of these security properties. Being that S- boxes can exhibit a certain combination of cryptographic properties at differing rates, the design of a cryptographically strong S-box often requires the establishment of a trade-off between these properties when optimizing the property values. To date, many S-boxes designs have been proposed in the literature, researchers have advocated the adoption of metaheuristic based S-boxes design. Although helpful, no single metaheuristic claim dominance over their other countermeasure. For this reason, the research for a new metaheuristic based S-boxes generation is still a useful endeavour. This thesis aim to provide a new design for 8 × 8 S-boxes based on firefly algorithm (FA) optimization. The FA is a newly developed metaheuristic algorithm inspired by fireflies and their flash lighting process. In this context, the proposed algorithm utilizes a new design for retrieving strong S- boxes based on standard firefly algorithm (SFA). Three variations of FA have been proposed with an aim of improving the generated S-boxes based on the SFA. The first variation of FA is called chaotic firefly algorithm (CFA), which was initialized using discrete chaotic map to enhance the algorithm to start the search from good positions. The second variation is called globalized firefly algorithm (GFA), which employs random movement based on the best firefly using chaotic maps. If a firefly is brighter than its other counterparts, it will not conduct any search. The third variation is called globalized firefly algorithm with chaos (CGFA), which was designed as a combination of CFA initialization and GFA. The obtained result was compared with a previous S-boxes based on optimization algorithms. Overall, the experimental outcome and analysis of the generated S-boxes based on nonlinearity, bit independence criteria, strict avalanche criteria, and differential probability indicate that the proposed method has satisfied most of the required criteria for a robust S-box without compromising any of the required measure of a secure S-box

A Review and Comparative Study of Firefly Algorithm and its Modified Versions

Firefly algorithm is one of the well-known swarm-based algorithms which gained popularity within a short time and has different applications. It is easy to understand and implement. The existing studies show that it is prone to premature convergence and suggest the relaxation of having constant parameters. To boost the performance of the algorithm, different modifications are done by several researchers. In this chapter, we will review these modifications done on the standard firefly algorithm based on parameter modification, modified search strategy and change the solution space to make the search easy using different probability distributions. The modifications are done for continuous as well as non-continuous problems. Different studies including hybridization of firefly algorithm with other algorithms, extended firefly algorithm for multiobjective as well as multilevel optimization problems, for dynamic problems, constraint handling and convergence study will also be briefly reviewed. A simulation-based comparison will also be provided to analyse the performance of the standard as well as the modified versions of the algorithm