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.

Using Three-Dimensional Logistic Equations and Glowworm Swarm Optimization Algorithm to Generate S-Box

“…When compared to other ways, the GSO approach is deemed to be an adequate method with acceptable outcomes for obtaining high nonlinearity. Although there are some references that have a higher nonlinearity of Sbox than the proposed algorithm but the proposed approach achieved higher results in other S-box 103.35 0.5068 [16] 104.7857 0.498 [14] 104.21 0.5014 [12] 104 0.5002 [8] 104.07 0.5001 [13] 104.57 0.4995 [7] 103 0.4996 [9] 102.64 0.5065 [5] 103.57 0.4994 [11] 105.07 0.4938 [6] 102.64 0.5017 measurements. Therefore, it is possible to use the obtained S-box with the applications that are compatible with the results we got.…”

“…These techniques can produce S-boxes with useful characteristics. In [16] the authors used a Flower Pollination Algorithm and Chaos System method to designing an efficient S-Box. This method was provided a good confusion for the generated S-Box.…”

“…The National Security Agency has released some suggestions for assessing the cryptographic properties of S-boxes in order to prevent suspicion in DES S-boxes [20]. The following are the performance evaluation standards that are widely acknowledged and regarded as essential for creating cryptographically robust Sboxes [16]:…”

“…1 shown the results values of the Logistic equation (V) where P = 3.6, and X=0.7842 after applying Eq. ( 5) to convert the results to integer values between [0,255] [16].…”

Creation of S-Box based One-Dimensional Chaotic Logistic Map: Colour Image Encryption Approach

“…The proposed S-Box satisfied the standard Sbox criteria. Also, the researchers in [26][27][28] used chaotic systems in order to design robust S-Boxes.…”