This study adopted a metaheuristic approach based on the firefly algorithm (FA) optimization to generate an appropriate configuration for an 8 × 8 Substitution boxes (S-boxes). The FA can construct a strong S-box that satisfies the stipulated criteria by rapidly searching for the optimal or near-optimal feature subsets that minimize a given fitness function. The FA is a newly developed computation technique inspired by fireflies and their flash lighting process. However, FA may suffer from premature convergence when solving optimization problems. This study proposes a new FA modification, namely, globalized firefly algorithm (GFA), which employs random movement based on the best firefly using chaotic maps. The best firefly does not conduct any search in the standard firefly algorithm (SFA). The proposed algorithm utilizes a new design for retrieving strong S-boxes based on SFA and GFA.

Bijectivity, strict avalanche criteria, nonlinearity, input/output XOR distribution, bit independence criteria, and linear probability were also analyzed. The result was compared with a few previous S-box generation methods. Overall, the experimental outcome revealed that the design of the proposed S-boxes has satisfactory cryptographic characteristics.

这项研究采用了基于萤火虫算法（FA）优化的元启发式方法来为8×8替换盒（S-box）生成适当的配置。FA可以通过快速搜索最小化给定适应度函数的最佳或近似最佳特征子集来构建满足规定标准的强大S盒。FA是受萤火虫及其闪光过程启发而开发的一种新的计算技术。但是，FA在解决优化问题时可能会过早收敛。这项研究提出了一种新的FA修改，即全局萤火虫算法（GFA），该算法采用基于混沌图谱的最佳萤火虫来进行随机运动。最佳萤火虫不会在标准萤火虫算法（SFA）中进行任何搜索。

还分析了双射性，严格的雪崩准则，非线性，输入/输出XOR分布，位独立准则和线性概率。将结果与以前的一些S-box生成方法进行了比较。总体而言，实验结果表明，提出的S盒的设计具有令人满意的密码学特征。