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Article Citation - WoS: 2A SECOND PRE-IMAGE ATTACK AND A COLLISION ATTACK TO CRYPTOGRAPHIC HASH FUNCTION LUX(Ankara Univ, Fac Sci, 2017) Sulak, Fatih; Kocak, Onur; Saygi, Elif; Ogunc, Merve; Bozdemir, BeyzaCryptography is a science that provides the security of information in communication. One of the most important sub-branches of cryptography is the hash functions. Hash functions are known as the digital fingerprints. Following the recent attacks on the widely used hash functions MD5 and SHA-1 and the increase in computational power, the need for a new hash function standard has arisen. For this purpose, US National Institute of Standards and Technology (NIST) had announced a competition to select a standard hash function algorithm which would eventually become the Third Secure Hash Algorithm, SHA-3. Initially 64 algorithms were submitted to NIST and 51 of them were announced as the First Round Candidates. After an analysis period, 14 of these algorithms were announced as the Second Round Candidates, and 5 algorithms were announced as Finalists. The winner of the competition, Keccak, was announced in 2012. LUX is one of the 64 algorithms submitted to the SHA-3 competition by Nikolic et al. It is designed as a byte oriented stream cipher based hash function. For LUX-256, Schmidt-Nielsen gave a distinguisher and later Wu et al. presented collision attacks, both of which for reduced rounds of LUX. As a result of these attacks, LUX is eliminated in the first round. In this work, we first give a procedure for the second preimage attack. Then we extend this to the collision and second preimage attacks for the reduced rounds of LUX hash family. Moreover, we implement the attacks and give the specific examples by taking the padding into consideration.Article Citation - WoS: 2ON THE LIMIT OF DISCRETE q-HERMITE I POLYNOMIALS(Ankara Univ, Fac Sci, 2019) Alwhishi, Sakina; Adıgüzel, Rezan Sevinik; Turan, MehmetThe main purpose of this paper is to introduce the limit relationsbetween the discrete q-Hermite I and Hermite polynomials such that the orthogonality property and the three-terms recurrence relations remain valid.The discrete q-Hermite I polynomials are the q-analogues of the Hermite polynomials which form an important class of the classical orthogonal polynomials.The q-di§erence equation of hypergeometric type, Rodrigues formula and generating function are also considered in the limiting case.Article Citation - WoS: 2Modifications of Knuth Randomness Tests for Integer and Binary Sequences(Ankara Univ, Fac Sci, 2018) Kocak, Onur; Sulak, Fatih; Doganaksoy, Ali; Uguz, MuhiddinGenerating random numbers and random sequences that are indistinguishable from truly random sequences is an important task for cryptography. To measure the randomness, statistical randomness tests are applied to the generated numbers and sequences. Knuth test suite is the one of the first statistical randomness suites. This suite, however, is mostly for real number sequences and the parameters of the tests are not given explicitly. In this work, we review the tests in Knuth Test Suite. We give test parameters in order for the tests to be applicable to integer and binary sequences and make suggestions on the choice of these parameters. We clarify how the probabilities used in the tests are calculated according to the parameters and provide formulas to calculate the probabilities. Also, some tests, like Permutation Test and Max-of-t-test, are modified so that the test can be used to test integer sequences. Finally, we apply the suite on some widely used cryptographic random number sources and present the results.Article Citation - WoS: 1Existence of Solutions for Impulsive Boundary Value Problems on Infinite Intervals(Ankara Univ, Fac Sci, 2023) Akgöl, Sibel DoğruThe paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example.Article An Application of Stochastic Maximum Principle for a Constrained System With Memory(Ankara Univ, Fac Sci, 2025) Savku, EmelIn this research article, we study a stochastic control problem in a theoretical frame to solve a constrained task under memory impact. The nature of memory is modeled by Stochastic Differential Delay Equations and our state process evolves according to a jump-diffusion process with time-delay. We work on two specific types of constraints, which are described in the stochastic control problem as running gain components. We develop two theorems for corresponding deterministic and stochastic Lagrange multipliers. Furthermore, these theorems are applicable to a wide range of continuous-time stochastic optimal control problems in a diversified scientific area such as Operations Research, Biology, Computer Science, Engineering and Finance. Here, in this work, we apply our results to a financial application to investigate the optimal consumption process of a company via its wealth process with historical performance. We utilize the stochastic maximum principle, which is one of the main methods of continuous-time Stochastic Optimal Control theory. Moreover, we compute a real-valued Lagrange multiplier and clarify the relation between this value and the specified constraint.Article Citation - WoS: 2Predicting Credit Card Customer Churn Using Support Vector Machine Based on Bayesian Optimization(Ankara Univ, Fac Sci, 2021) Ünlü, Kamil DemirberkIn this study, we have employed a hybrid machine learning algorithm to predict customer credit card churn. The proposed model is Support Vector Machine (SVM) with Bayesian Optimization (BO). BO is used to optimize the hyper-parameters of the SVM. Four different kernels are utilized. The hyper-parameters of the utilized kernels are calculated by the BO. The prediction power of the proposed models are compared by four different evaluation metrics. Used metrics are accuracy, precision, recall and F1-score. According to each metrics linear kernel has the highest performance. It has accuracy of %91. The worst performance achieved by sigmoid kernel which has accuracy of %84.
