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.

AtıfScopus34·WoS23·OpenAlex29

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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.

AtıfScopus48·WoS42·OpenAlex51

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