Boolean functions play an important role in the design and analysis of symmetric-key cryptosystems, as well as having applications in other fields such as coding theory. Boolean functions acting on large number of inputs introduces the problem of computing the cryptographic properties. Traditional methods of computing these properties involve transformations which require computation and memory resources exponential in the number of input variables. When the number of inputs is large, Boolean functions are usually defined by the algebraic normal form (ANF) representation. In this thesis, methods for computing the weight and nonlinearity of Boolean functions from the ANF representation are investigated. The relation between the ANF coecients and the weight of a Boolean function was introduced by Carlet and Guillot. This expression allows the weight to be computed in $mathcal{O}(2^p)$ operations for a Boolean function containing p monomials in its ANF. In this work, a more ecient algorithm for computing the weight is proposed, which eliminates the unnecessary calculations in the weight expression. By generalizing the weight expression, a formulation of the distances to the set of linear functions is obtained. Using this formulation, the problem of computing the nonlinearity of a Boolean function from its ANF is reduced to an associated binary integer programming problem. This approach allows the computation of nonlinearity for Boolean functions with high number of input variables and consisting of small number of monomials in a reasonable time.

Boolean functions play an important role in the design and analysis of symmetric-key cryptosystems, as well as having applications in other fields such as coding theory. Boolean functions acting on large number of inputs introduces the problem of computing the cryptographic properties. Traditional methods of computing these properties involve transformations which require computation and memory resources exponential in the number of input variables. When the number of inputs is large, Boolean functions are usually defined by the algebraic normal form (ANF) representation. In this thesis, methods for computing the weight and nonlinearity of Boolean functions from the ANF representation are investigated. The relation between the ANF coefficients and the weight of a Boolean function was introduced by Carlet and Guillot. This expression allows the weight to be computed in $mathcal{O}(2^p)$ operations for a Boolean function containing $p$ monomials in its ANF. In this work, a more efficient algorithm for computing the weight is proposed, which eliminates the unnecessary calculations in the weight expression. By generalizing the weight expression, a formulation of the distances to the set of linear functions is obtained. Using this formulation, the problem of computing the nonlinearity of a Boolean function from its ANF is reduced to an associated binary integer programming problem. This approach allows the computation of nonlinearity for Boolean functions with high number of input variables and consisting of small number of monomials in a reasonable time.

In this thesis, various numerical methods are developed to solve nonsmooth and in particular, nonconvex optimization problems. More speci

A well known birthday paradox is one the most important problems in cryptographic applications. Incremental hash functions or digital signatures in public key cryptography and low-weight parity check equations of LFSRs in stream ciphers are examples of such applications which benet from birthday problem theories to run their attacks. Wagner introduced and formulated the k-dimensional birthday problem and proposed an algorithm to solve the problem in O(k.m^ 1/log k ). The generalized birthday solutions used in some applications to break Knapsack based systems or collision nding in hash functions. The optimized birthday algorithms can solve Knapsack problems of dimension n which is believed to be NP-hard. Its equivalent problem is Subset Sum Problem nds the solution over Z/mZ. The main property for the classication of the problem is density. When density is small enough the problem reduces to shortest lattice vector problem and has a solution in polynomial time. Assigning a variable to each element of the lists, decoding them into a matrix and considering each row of the matrix as an equation lead us to have a multivariate polynomial system of equations and all solution of this type can be a solution for the k- list problem such as F4, F5, another strategy called eXtended Linearization (XL) and sl. We discuss the new approaches and methods proposed to reduce the complexity of the algorithms. For particular cases in over-determined systems, more equations than variables, regarding to have a single solutions Wolf and Thomea work to make a gradual decrease in the complexity of F5. Moreover, his group try to solve the problem by monomials of special degrees and linear equations for small lists. We observe and compare all suggested methods in this

Population dynamics is the dominant branch of mathematical biology. The first model for population dynamics was developed by Thomas Malthus. A more complicated model was developed by Pierre Fran&ccedil / ois Verhulst and it is called the logistic equation. Our aim in this thesis is to extend the models using piecewise constant arguments and to find the conditions when the models have fixed points, periodic solutions and chaos with investigation of stability of periodic solutions.

The purpose of the study was to investigate the effects of real data based and calculator supported statistics activities on 7th grade students&amp / #8217 / statistics performance and attitudes towards statistics when the statistics performance of the students prior to the instruction and the previous mathematics grades were controlled. A quasi-experimental design was used to investigate the research problem. The research was conducted by 84 seventh grade students. There were three groups in the study. Two of them were experimental groups and one of them was control group. The first group received instruction by the traditional method (TM), the second group received instruction by real data based and calculator supported statistical activities (RDBCSSA), and the third group was instructed by real data based statistical activities (RDBSA), the number of the subjects was 28, 27 and 29 respectively. Data were collected through three different measuring instruments: 1.Statistical Performance Test 1 (SPT1) / 2.Statistical Performance Test 2 (SPT2) / 3.Statistics Attitude Scale (SAS). The SPT1 was used as a pre-test. The SPT2 was administered as a post-test. SPT1 and SPT2 were used to determine the statistics performance of the students before and after the instruction. SAS was used to determine the attitudes of the students toward statistics. The data of this study were analyzed by analysis of variance (ANOVA) and analysis of covariance (ANCOVA). The results revealed that there was no significant mean difference among the groups with respect to statistics performance. Also there was no significant mean difference among the groups with respect to attitudes towards statistics. The mean scores of the Statistics Attitude Scale items were calculated and the results revealed that the students had positive attitudes to the statements in Statistics Attitude Subscale 1 (Confidence in Learning Statistics) and they were neutral to the statements of the Statistics Attitude Subscale 2. Also the students wrote their opinions about the teaching methods and their impressions were analyzed by making a frequency table. Most of the TM students mentioned that the examples should be more attractive such that the activity sheets could contain real data based examples. However some of the students mentioned that traditional method was good and the subject was understood very well. Most of the RDBSA students mentioned that the teaching method was enjoyable. Most of the RDBCSSA students expressed that the calculators made the lessons enjoyable and the study easy.

While the amount of textual data available to us is constantly increasing, managing the texts by human effort is clearly inadequate for the volume and complexity of the information involved. Consequently, requirement for automated extraction of useful knowledge from huge amounts of textual data to assist human analysis is apparent. Text mining (TM) is mostly an automated technique that aims to discover knowledge from textual data. In this thesis, the notion of text mining, its techniques, applications are presented. In particular, the study provides the definition and overview of concepts in text categorization. This would include document representation models, weighting schemes, feature selection methods, feature extraction, performance measure and machine learning techniques. The thesis details the functionality of text mining as a quality improvement tool. It carries out an extensive survey of text mining applications within service sector and manufacturing industry. It presents two broad experimental studies tackling the potential use of text mining for the hotel industry (the comment card analysis), and in automobile manufacturer (miles per gallon analysis). Keywords: Text Mining, Text Categorization, Quality Improvement, Service Sector, Manufacturing Industry.

This thesis examines verifiability and receipt freeness in cryptographic voting protocols in detail and points out the contradiction between these requirements. Firstly, an extensive electronic voting requirement set is clearly defined, and then the voting dilemma is described. This is followed by a suggestion of an applicable solution to overcome the voting dilemma by introducing Predefined Fake Vote (PreFote) scheme. Based on a comprehensive literature review, a classification of the existing privacy preserving approaches and a taxonomy of the existing cryptographic voting protocols extending the previous studies are provided. Thereby, a complete and secure cryptographic voting protocol satisfying all electronic voting security requirements at the same time seems non-existent. Hence, an alternative privacy preserving approach is highly needed. Pseudo-Voter Identity (PVID) scheme, proposed in the present study, is a practical and low cost one. The PVID scheme is based on RSA blind signature, and it allows recasting without sacrificing uniqueness. Furthermore, this study proposes a dynamic ballot mechanism including an extension with PreFotes. This study, wherein the PVID scheme and extended dynamic ballots with PreFotes are employed, proposes a practical, complete and secure cryptographic voting protocol over a network for large scale elections, which fulfils all of the electronic voting security requirements: privacy, eligibility, uniqueness, fairness, uncoercibility, receipt-freeness, individual verifiability and accuracy. Lastly, a method to analyse voting systems based on security requirements is suggested, and a detailed analysis of the proposed protocol, which uses this method, concludes this study.

Synchronous stream ciphers constitute an important class of symmetric ciphers. After the call of the eSTREAM project in 2004, 34 stream ciphers with different design approaches were proposed. In this thesis, we aim to provide a general framework to analyze stream ciphers statistically. Firstly, we consider stream ciphers as pseudo random number generators and study the quality of their output. We propose three randomness tests based on one dimensional random walks. Moreover, we theoretically and experimentally analyze the relations of various randomness tests. We focus on the ideas of algebraic, time memory tradeoff (TMTO) and correlation attacks and propose a number of chosen IV distinguishers. We experimentally observe statistical weaknesses in some of the stream ciphers that are believed to be secure.

Developing remote sensing instrumentation allows obtaining information about an area rapidly and with low costs. This fact offers a challenge to remote sensing algorithms aimed at extracting information about an area from the available re&not / mote sensing data. A very typical and important problem being interpretation of satellite images. A very efficient approach to remote sensing is employing discrim&not / inant functions to distinguish different landscape classes from satellite images. Various methods on this direction are already studied. However, the efficiency of the studied methods are still not very high. In this thesis, we will improve efficiency of remote sensing algorithms. Besides we will investigate improving boundary detection methods on satellite images.