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

Lawah, Ali Ibrahim; İbrahim, Abdullahi Abdu; Salih, Sinan Q.; Alhadawi, Hussam S.; JosephNg, P. S.

doi:10.1109/access.2023.3266290

Cited by 16 publications

(6 citation statements)

References 67 publications

(90 reference statements)

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“…Therefore, employing chaotic maps rather than the randomization parameter I could improve the accuracy of the ZOA [50]. Since the randomization setting ignores more significant changes in population movement, the chaotic structure's generation is unexpected [51]. The primary structure of the standard ZOA remains unchanged, however the equations went through some changes.…”

Section: The Proposed Chaotic Zebra Optimization Long Short-term Memo...mentioning

confidence: 99%

Hybrid Chaotic Zebra Optimization Algorithm and Long Short-Term Memory for Cyber Threats Detection

Amin,

El-Taweel,

Ali

et al. 2024

IEEE Access

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Cyber Threat Detection (CTD) is subject to complicated and rapidly accelerating developments. Poor accuracy, high learning complexity, limited scalability, and a high false positive rate are problems that CTD encounters. Deep Learning defense mechanisms aim to build effective models for threat detection and protection allowing them to adapt to the complex and ever-accelerating changes in the field of CTD. Furthermore, swarm intelligence algorithms have been developed to tackle the optimization challenges. In this paper, a Chaotic Zebra Optimization Long-Short Term Memory (CZOLSTM) algorithm is proposed. The proposed algorithm is a hybrid between Chaotic Zebra Optimization Algorithm (CZOA) for feature selection and LSTM for cyber threat classification in the CSE-CIC-IDS2018 dataset. Invoking the chaotic map in CZOLSTM can improve the diversity of the search and avoid trapping in a local minimum. In evaluating the effectiveness of the newly proposed CZOLSTM, binary and multi-class classifications are considered. The acquired outcomes demonstrate the efficiency of implemented improvements across many other algorithms. When comparing the performance of the proposed CZOLSTM for cyber threat detection, it outperforms six innovative deep learning algorithms for binary classification and five of them for multiclass classification. Other evaluation criteria such as accuracy, recall, F1 score, and precision have been also used for comparison. The results showed that the best accuracy was achieved using the proposed algorithm for binary is 99.83%, with F1-score of 99.82%, precision of 99.83%, and recall of 99.82%. The proposed CZOLSTM algorithm also achieved the best performance for multi-class classification among other compared algorithms.

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Section: The Proposed Chaotic Zebra Optimization Long Short-term Memo...mentioning

confidence: 99%

Hybrid Chaotic Zebra Optimization Algorithm and Long Short-Term Memory for Cyber Threats Detection

Amin,

El-Taweel,

Ali

et al. 2024

IEEE Access

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“…Many of them are based on advanced AI techniques, evolutionary algorithms, chaos, heuristic search, etc. [25][26][27][28].…”

Section: Related Workmentioning

confidence: 99%

“…In the last few years, many papers in the field of S-boxes generation have been published, e.g., [24][25][26][27]55]. In these papers, the authors estimate the average value of nonlinearity over all coordinate Boolean functions (1).…”

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confidence: 99%

Optimizing Hill Climbing Algorithm for S-Boxes Generation

et al. 2023

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Nonlinear substitutions or S-boxes are important cryptographic primitives of modern symmetric ciphers. They are designed to complicate the plaintext-ciphertext dependency. According to modern ideas, the S-box should be bijective, have high nonlinearity and algebraic immunity, low delta uniformity, and linear redundancy. These criteria directly affect the cryptographic strength of ciphers, providing resistance to statistical, linear, algebraic, differential, and other cryptanalysis techniques. Many researchers have used various heuristic search algorithms to generate random S-boxes with high nonlinearity; however, the complexity of this task is still high. For example, the best-known algorithm to generate a random 8-bit bijective S-box with nonlinearity 104 requires high computational effort—more than 65,000 intermediate estimates or search iterations. In this article, we explore a hill-climbing algorithm and optimize the heuristic search parameters. We show that the complexity of generating S-boxes can be significantly reduced. To search for a random bijective S-box with nonlinearity 104, only about 50,000 intermediate search iterations are required. In addition, we generate cryptographically strong S-Boxes for which additional criteria are provided. We present estimates of the complexity of the search and estimates of the probabilities of generating substitutions with various cryptographic indicators. The extracted results demonstrate a significant improvement in our approach compared to the state of the art in terms of providing linear non-redundancy, nonlinearity, algebraic immunity, and delta uniformity.

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“…It has been established that the design of S-boxes capable of withstanding cryptanalysis is a challenging task. In fact, it has been classified as an NP-hard problem [11], [12]. This classification underscores the inherent complexity involved in creating S-boxes with impeccable cryptographic properties.…”

Section: Introductionmentioning

confidence: 99%

“…The random search method, for instance, is a straightforward approach, but often yields S-boxes with inferior cryptographic properties. On the other hand, the algebraic strategy, while capable of producing S-boxes with desirable cryptographic attributes, is not well-suited for the large-scale S-box generation [9,11].…”

Section: Introductionmentioning

confidence: 99%

BH-Sbox: A Substitution Box Generating Algorithm Based on Chaotic Black Hole Algorithm

2023

IJIES

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This paper introduces a novel approach for generating strong substitution boxes (S-Boxes) using the black hole algorithm (BHA) integrated with Arnold chaotic map (ACM) and Henon chaotic map (HCM). The ACM is employed for enhanced initialization of the BHA, while the HCM is utilized for generating new stars during the searching process. The proposed algorithm, named BH-SBOX, aims to enhance the nonlinearity and cryptographic properties of the generated S-Boxes. Experimental evaluations further demonstrate that the BH-SBOX algorithm produces S-Boxes with excellent nonlinearity, strict avalanche criteria, bit independence criteria, differential uniformity, and the maximum expected linear probability. The proposed method demonstrated a high nonlinearity property, achieving a value of 108.25, which is considered successful and effective. This exceptional nonlinearity can be attributed to the utilization of the Henon map, which enables good exploration of the solution space during the search process. The chaotic and unpredictable nature of the Henon map contributes significantly to the algorithm's ability to discover S-Boxes with enhanced nonlinearity and robust cryptographic characteristics. The average bit independence criteria (BIC) and strict avalanche criteria (SAC) were found to be 102.85 and 0.50392, respectively. These results indicate that the proposed method successfully generated S-boxes with strong cryptographic properties, ensuring robustness and resistance against various attacks.

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

Cited by 16 publications

References 67 publications

Hybrid Chaotic Zebra Optimization Algorithm and Long Short-Term Memory for Cyber Threats Detection

Hybrid Chaotic Zebra Optimization Algorithm and Long Short-Term Memory for Cyber Threats Detection

Optimizing Hill Climbing Algorithm for S-Boxes Generation

BH-Sbox: A Substitution Box Generating Algorithm Based on Chaotic Black Hole Algorithm

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