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To cite this article: Dragan Lambić (2018) S-box design method based on improved onedimensional discrete chaotic map, Journal of Information and Telecommunication, 2:2, 181-191, DOI: 10.1080/24751839.2018 A new method for obtaining random bijective S-boxes based on improved one-dimensional discrete chaotic map is presented. The proposed method uses a new special case of discrete chaotic map based on the composition of permutations, in order to overcome the problem with potentially short length of the orbits. The proposed special case is based on the composition of permutations and sine function and has a larger minimum length of the orbits compared to the previous special case of the discrete-space chaotic map. The results of performance test show that the example of S-box generated by the proposed method has good cryptographic properties. The proposed method can achieve large key space, which makes it suitable for generation of larger S-boxes, and the process of generation of S-boxes is not affected by approximations of any kind. Also, proposed method has potential to operate at greater speed and with smaller memory requirements than previous S-box generation method based on discrete space chaotic map, which can be particularly useful for lightweight devices such as wireless sensor networks. ARTICLE HISTORY

In this paper, a new approach for the formation of four-member collaborative learning groups is presented. Group formation is presented by the mathematical optimization problem. Based on the proposed approach and the variable neighbourhood search (VNS) algorithm, the application that solves the presented problem and provides the appropriate division into groups is created. The proposed approach considers the scores of a pretest, interpersonal relationships, and prosocial behaviour/openness skill of students. In order to validate our approach, an experiment was designed with 108first-year university students of Belgrade Business School-Higher Educational Institution for Applied Studies. Experimental and control groups were divided into fourmember groups. The experimental group was divided by using the proposed method and the control group by student selection and random selection. Multilevel analysis is used to determine whether there is a significant difference in learning outcomes between the two groups. The experimental results showed that students from the experimental group achieved significantly higher success than the students from the control group. In addition, computational results obtained with the proposed VNS algorithms are compared and verified with the results obtained by random (Monte Carlo) method.