Designing a Novel Efficient Substitution-Box by Using a Flower Pollination Algorithm and Chaos System

Abstract

Substitution box (S-box) is a crucial component of symmetric cryptosystems and is mostly used in modern cryptographic ciphers to provide strong data sanctuary. The cryptographic strength of an S-box used in a cipher is directly proportional to the data security provided by the cipher. Thus, this study used a novel approach by combining the hybrid chaos (integrated three functions of chaos maps) to generate pseudo-random number generators and metaheuristic techniques based on the flower pollination algorithm (FPA) to develop an acceptable configuration (8 × 8) S-box. Chaotic maps enhance the initial population of FPA to be an appropriate starting point for the FPA. The objective function of the FPA was the nonlinearity score of the S-box. The FPA is used to balance exploration and exploitation operations. The suggested S-box was compared with several references and passed all the security requirements of S-box, including bijection, strict avalanche criteria (SAC), output bits independence criteria (BIC), nonlinearity, histogram, entropy, correlation coefficients, unified average changing intensity (UACI) and number of pixel change rates (NPCR), in addition to the algebraic cryptanalysis test. The proposed approach had an asymptotic computational complexity of O(n2). The nonlinearity property was 107.25. It is considered an effective and acceptable result. Whereas SAC and BIC were 0.498 and 104.7857, respectively. Simultaneously, all results of UACI and NPCR were close to the predicted normal levels 33.2255 and 99.5693, respectively. While the encryption histogram is more uniform than the simple histogram. Finally, the entropy and correlation coefficients scores result of various images were close to eight and zero, respectively. Therefore, the proposed S-box is proven to be strong and resistant to cryptography attacks.