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- MakaleAçık Erişim2025Scopus SJRQ1New comparative approach to multi-level thresholding: chaotically initialized adaptive meta-heuristic optimization methods
Serbet, Fatmanur; Kaya, Turgay
One method aimed at enhancing the performance of meta-heuristic optimization techniques is the incorporation of chaotic systems. Instead of irregular distributions in the search space, chaotic distributions are employed in the initial population of optimization algorithms to improve the efficiency of the search process. This approach enables search agents distributed in a chaotic manner to effectively explore the search space. The initial populations of both the well-established PSO algorithm and the enhanced WSO algorithm, which incorporates advanced search techniques, are distributed in the search space according to the characteristics of Logistic, Chebyshev, Circle, Sine, and Piecewise chaotic maps in this study. The original PSO and WSO algorithms, as well as the resulting chaotically initialized PSO and chaotically initialized WSO algorithms, were tested using 23 benchmark functions. Subsequently, the Otsu method was integrated into the tested optimization algorithms to obtain multi-level thresholding values. These algorithms were applied to five different test images with a manually determined number of thresholds. The results obtained were presented in the study and evaluated using statistical tests.
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İncele - MakaleAçık Erişim2025Scopus SJRQ1A novel post-processing approach for improving minimum nonlinearity in S-boxes: A case study based on 2D hyper chaotic Schaffer transformation map
Aydın, Yılmaz; Garipcan, Ali Murat; Özkaynak, Fatih
Substitution boxes (s-boxes), providing nonlinearity in block cipher algorithms, constitute a fundamental security layer against linear and differential cryptanalysis attacks. In this study, an innovative s-box generation method is proposed by integrating a 2D hyper-chaotic Schaffer map (SM) with biomolecular DNA-based encoding techniques. Furthermore, to enhance the security of s-box structures, a novel post-processing algorithm is developed, aiming to simultaneously optimize both the average (NLavg) and minimum (NLmin) nonlinearity levels by targeting linear components. Unlike traditional meta-heuristic methods, the proposed algorithm avoids random exploration across large search spaces, instead identifying dominant linear components through Walsh spectrum analysis and applying targeted permutation operations to suppress their effects. This strategy not only increases the NLavg value but also balances the contribution of each Boolean function to security, thereby establishing a homogeneous and consistent security structure across all input–output combinations. Comparative experimental analyses with existing methods demonstrate that the proposed approach outperforms prior techniques in terms of both cryptographic security metrics and computational efficiency. In this respect, the study presents an advanced s-box design framework, characterized by high nonlinearity and a balanced spectral distribution, suitable for integration into modern block cipher systems.
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İncele - MakaleYalnız künye2024Scopus SJRQ2A new S-box generator algorithm based on chaos and cellular automata
Artuğer, Fırat
S-boxes are very important structures for encryption algorithms. For S-boxes to be strong, they should not be as linear as possible. Obtaining an S-box with high nonlinearity is a difficult problem. For this reason, it has attracted the attention of researchers for many years. In this study, cellular automata logic was used to overcome this problem. A chaotic tent map was used for the initial population. Then, in this weak S-box, the elements were replaced with their neighbors, and the nonlinearity value was checked. When this value increased, the S-box was transferred to the next generation. With the proposed algorithm, an S-box structure with a nonlinearity value of 110.5 was obtained. This value surpasses most studies in the literature. In addition, it has been proven because of the analysis that the proposed S-box also provides other performance criteria.
AtıfScopus6WoS8OpenAlex7İncele - MakaleYalnız künye2024Scopus SJRQ2A Method for Designing Substitution Boxes Based on Chaos with High Nonlinearity
Artuğer, Fırat
Cryptography aims to design algorithms for the protection of important data transmitted over unsecured networks. These algorithms encrypt the data and render it incomprehensible even if it is captured by enemies. Today’s data encryption standard is the AES algorithm. The most important and nonlinear unit in the AES algorithm is the s-box structure. The S-box provides the mixing process in the algorithm, that is, the confusion. An s-box structure with a high nonlinearity value greatly increases the security against various attacks. Therefore, s-box is of vital importance in an encryption algorithm. When we look at the literature, chaos-based s-box structures are frequently used. However, the nonlinearity value of s-boxes produced with chaos is low. In this article, a new, fast, and very simple method is proposed to increase the nonlinearity value of chaos-based s-box structures. In the proposed method, the nonlinearity value is calculated by changing the places of the elements respectively. When the nonlinearity value increases, the s-box is updated, and the next element is passed. In this way, many iterations are not looked at in vain. This saves a lot of time. As a result of the analysis, it has been proven that the s-box structure obtained by the proposed method is cryptographically strong and has a high nonlinearity value. It is thought that the proposed method will provide many advantages for future cryptography applications.
AtıfScopus9WoS7OpenAlex8İncele - MakaleAçık Erişim2024Scopus SJRQ2Strong s-box construction approach based on Josephus problem
Artuğer, Fırat
There are two basic requirements for symmetric encryption algorithms. The first of these is diffusion. The second and most important is confusion. In these algorithms, this requirement is usually met by s-box structures. Therefore, s-box structures must be strong. So, a cryptographically good s-box will make the encryption algorithm difficult to crack. However, obtaining a strong s-box is a rather difficult problem. In this study, Josephus circle logic is used to solve this problem. Initially, with a random s-box structure, the elements are replaced according to their Josephus positions, and the s-box is made stronger. In the proposed algorithm, according to the Josephus logic, the elements that kill each other are replaced and this process continues until one element remains. The last 30 surviving elements are replaced with all elements. In this way, three different s-boxes were obtained. In two of them, the nonlinearity value was 110.5, and in one of them, the nonlinearity value was 110.75. Fixed points in the proposed s-box structures were identified and eliminated. In addition, it has been proven because of the analysis that the obtained s-box structures also meet other cryptographic requirements. In addition to leaving behind most studies in the literature, the proposed method will also provide strong s-box structures for encryption algorithms to be built in the future.
AtıfScopus15OpenAlex12İncele - MakaleAçık Erişim2023Scopus SJRQ2Chaotic quantization based JPEG for effective compression of whole slide images
Artuğer, Fırat; Özkaynak, Fatih
In today’s digital world, effectively transferring data from one point to another is an important problem. For this reason, the development of various new compression algorithms and making existing solutions more effective are examined in detail by researchers. In this study, a new method is proposed to improve the performance of JPEG algorithm. The proposed method includes an approach based on chaotic systems. Chaotic systems contain a strong entropy source. This powerful source of entropy has strong practical applications in obtaining statistically robust random values. In this study, a method is proposed to obtain quantization tables effectively by taking advantage of this potential of chaotic systems. The obtained results showed that the compression performance can be increased at the same quality factors. The proposed approach has been tested on the whole slide image (WSI) dataset. Looking at the analysis results, an average of 2.43% higher accuracy was achieved compared to the JPEG algorithm. It is thought that these results can provide an advantage especially in transferring high-dimensional images such as the DICOM standard, where the JPEG algorithm is used in practical applications.
AtıfScopus5WoS4OpenAlex7İncele - MakaleAçık Erişim2021Scopus SJRQ1A Method to Determine the Most Suitable Initial Conditions of Chaotic Map in Statistical Randomness Applications
Acikkapi, Mehmet Sahin; Ozkaynak, Fatih
The processes and systems in the real world actually contain order and symmetry. Understanding these order and symmetrical behavior has been a common effort of scientists. Chaos theory has been an interesting topic to understand these order and symmetrical behavior. One of the most important reasons for this interest is the rich dynamics of chaotic systems. A remarkable application of these systems is statistical randomness. Especially in random number generator designs based on discrete time chaotic systems, an important design parameter affecting the success of the generator (statistical randomness properties) is the initial conditions of chaotic maps. Obtaining different initial conditions that will meet the statistical requirements is important in terms of generating different random number sequences. In order to determine the initial conditions, an algorithm that updates the initial conditions depending on the number of successful statistical tests is proposed. Although the proposed design approach is similar to a back propagation neural network, it has a unique design approach. The NIST SP 800-22 test suite has been used to analyze the statistical properties of the proposed generator. It is known that the NIST SP 800-22 test suite is a hypothesis test. Therefore, in order to show the success of the proposed method in the best way, various additional analysis studies have been carried out proving that the generator outputs have a uniform distribution. Using the proposed method, six different initial conditions have been determined that provide statistical random properties for the discrete-time chaotic systems known as logistic map and tent map. 1,000,000 bits have been generated using the obtained initial conditions. These bit values are then converted to decimal values between 0-15. It is observed that the obtained numbers have a uniform distribution. These outputs are thought to be applicable in many areas such as games, simulation, modeling, determination of optimization parameters and cryptology. It is shown in a practical application for cryptographic substitution-box designs to examine the success of the outputs.
AtıfScopus34WoS23OpenAlex29İncele - MakaleAçık Erişim2021Scopus SJRQ1An effective method to improve nonlinearity value of substitution boxes based on random selection
Artuğer, Fırat; Özkaynak, Fatih
In today's digital society, new design alternatives are needed for substitution box structures, which has critical importance in developing secure information systems that are resistant to algebraic and application attacks, as new attacks negatively affect designs based on mathematical transformations. Although random selection-based substitution box structures are a good alternative against algebraic and application attacks, the low value of nonlinearity criterion is an important problem. Solution suggestions using optimization algorithms have been proposed to address this problem. “Information Sciences 523 (2020) 152–166” is the study that reached the highest nonlinearity value based on optimization algorithms to date. However, the high computational costs of optimization algorithms are another challenge that must be overcome. In this study, it has been shown that the nonlinearity values of random (chaotic) selection substitution box structures can be improved as much as mathematically based designs by using a method that is too simple to compare with optimization algorithms. It has been shown that the nonlinearity value can be improved up to 110 for random selection-based substitution box designs. Although this nonlinearity value is the highest achievable value in the literature based on the random selection principle, the fact that it requires only 2×255×255 processes in the worst case has been evaluated as an important success of the proposed method compared to other design approaches. Other advantages of the proposed method are that the improved substitution box structures are resistant to side-channel attacks, simple structure, easy hardware implementation, and successful results in practical applications such as image encryption. It is believed that all these results will be a motivation for new post-processing techniques to be designed in the future for random selection-based substitution box designs.
AtıfScopus42WoS30OpenAlex42İncele - MakaleAçık Erişim2020Scopus SJRQ2A novel method for performance improvement of chaos-based substitution boxes
Artuğer, Firat; Özkaynak, Fatih
Symmetry plays an important role in nonlinear system theory. In particular, it offers several methods by which to understand and model the chaotic behavior of mathematical, physical and biological systems. This study examines chaotic behavior in the field of information security. A novel method is proposed to improve the performance of chaos-based substitution box structures. Substitution box structures have a special role in block cipher algorithms, since they are the only nonlinear components in substitution permutation network architectures. However, the substitution box structures used in modern block encryption algorithms contain various vulnerabilities to side-channel attacks. Recent studies have shown that chaos-based designs can offer a variety of opportunities to prevent side-channel attacks. However, the problem of chaos-based designs is that substitution box performance criteria are worse than designs based on mathematical transformation. In this study, a postprocessing algorithm is proposed to improve the performance of chaos-based designs. The analysis results show that the proposed method can improve the performance criteria. The importance of these results is that chaos-based designs may offer opportunities for other practical applications in addition to the prevention of side-channel attacks.
AtıfScopus55WoS44OpenAlex56İncele - MakaleAçık Erişim2019Scopus SJRQ1Side-Channel Analysis of Chaos-Based Substitution Box Structures
Acikkapi, Mehmet Sahin; Ozkaynak, Fatih; Ozer, Ahmet Bedri
There is a theoretically strong relationship between chaos and cryptology. In practice, one of the most successful applications of this relationship is chaos-based s-box structures. However, the performance metrics of chaos-based s-box designs are worse compared to those for s-box structure based on algebraic techniques used in modern encryption algorithms, such as the AES algorithm. What is the reason for using chaos-based s-box structures, even though they have worse cryptographic characteristics? Researchers claim that they may be an alternative defense against implementation attacks, especially side-channel analyses. However, no studies have supported or refuted this claim so far. In this paper, side-channel analyses have been performed for two different chaos-based s-box structures. These two s-box structures have been selected for having with the best and worst performance measurements for s-box structures previously proposed in the literature. The results were compared with the AES s-box structure. Analysis of the results showed that chaos-based s-box structures are more resistant against side-channel attacks. Therefore, chaos-based designs may be an alternative defense against implementation attacks, as alleged. However, both algebraic and chaos-based s-box designs have been observed to be insecure if the attacker has more than 30 plaintexts in the side channel analyses. These results show that implementation analysis studies are required in the chaos-based cryptology literature.
AtıfScopus48WoS42OpenAlex51İncele - MakaleYalnız künye2011Scopus SJRQ1Uniform Big Bang-Chaotic Big Crunch optimization
Alatas, Bilal
This study proposes methods to improve the convergence of the novel optimization method, Big Bang-Big Crunch (BB-BC). Uniform population method has been used to generate uniformly distributed random points in the Big Bang phase. Chaos has been utilized to rapidly shrink those points to a single representative point via a center of mass in the Big Crunch phase. The proposed algorithm has been named as Uniform Big Bang-Chaotic Big Crunch (UBB-CBC). The performance of the UBB-CBC optimization algorithm demonstrates superiority over the BB-BC optimization for the benchmark functions. (C) 2010 Elsevier B.V. All rights reserved.
AtıfWoS48OpenAlex62İncele - MakaleAçık Erişim2010Scopus SJRQ2A method for designing strong S-Boxes based on chaotic Lorenz system
Özkaynak, Fatih; Özer, Ahmet Bedri
It is important to design cryptographically strong S-Boxes in order to design secure systems. In this study, a strong, chaos-based S-Box design is proposed. Continuous-time Lorenz system is chosen as the chaotic system. Proposed methodology is analyzed and tested for the following criteria: Bijective property, nonlinearity, strict avalanche criterion, output bits independence criterion and equiprobable input/output XOR distribution. The results of the analysis show that the proposed cryptosystem is a highly reliable system suitable for secure communication. (C) 2010 Elsevier B.V. All rights reserved.
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