Correlation of sequences and quadratic forms

Genişel, Cansu
Sequences are widely used in code division multiple access communication systems. In a shared communication channel distinct sequences are assigned to distinct users. Low correlation sequences should be used in order to separate each user. In this thesis, quadratic forms and their properties are introduced. Sequence families constructed by quadratic forms and their correlations are studied. We give a construction of a binary sequence family when n = 3k and k is an odd integer. This sequence family has six- valued correlation distribution and its maximum correlation magnitude is given. Our sequence family is a subfamily of Generalized Modified Gold sequence family. At the end, we compare the correlation properties of our sequence family with some other known sequence families.


Sequence families with good correlation distribution
Tekin, Eda; Özbudak, Ferruh; Department of Cryptography (2016)
In this thesis we focus on two main properties of sequences which have wide range of applications in code division multiple access: autocorrelation and cross-correlation. First, necessary properties of sequences, some known perfect autocorrelation sequences and some known sequence families with their cross-correlation properties are given. Then, a perfect autocorrelation sequence [18] is generalized with respect to a number theoretic constraint of n for a given prime power q. This generalization enables the...
Modular exponentiation methods in cryptography
Yünüak, Hasan Bartu; Cenk, Murat; Department of Cryptography (2017)
Modular exponentiation has an important role in many cryptographic algorithms. These exponentiation methods differ in the bases used and their representations, the repeating aspect, and for which algorithms they are used for: fixed or variable base. Our research aims to compare the efficiencies and implementation timings for some selected algorithms. Also, we look at the options for using a dedicated cubing algorithm, and compare them with the current algorithms.
Joint linear complexity of multisequences consisting of linear recurring sequences
Fu, Fang-Wei; Niederreiter, Harald; Özbudak, Ferruh (Springer Science and Business Media LLC, 2009-04-01)
The linear complexity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, the joint linear complexity of multisequences has been investigated. In this paper, we study the joint linear complexity of multisequences consisting of linear recurring sequences. The expectation and variance of the joint linear complexity of random multisequences consisting of linear recurring sequences are determined. These results extend the ...
On the efficient implementation of RSA
Güner, Hatice Kübra; Cenk, Murat; Department of Cryptography (2015)
Modular exponentiation is an essential operation for many asymmetric key cryptosystems such as RSA in which encryption and decryption are based on modular exponentiation. Therefore, efficiency of the system is effected with running time of the modular exponentiation algorithm. At the same time, key sizes also influence the efficiency of the algorithm. Over the years key sizes had to be increased to provide security. To make RSA practical, one of usable choices is acceleration of the modular exponentiation a...
Evaluation of Security Information and Event Management Systems for Custom Security Visualization Generation
Sonmez, Ferda Ozdemir; Günel Kılıç, Banu (2018-12-04)
Security Information and Event Management Systems (SIEM) are generally very complex systems encapsulating a large number of functions with different behaviors. Visualization is a common way of data presentation in these systems along with other data presentation ways such as reporting, alerting, text messaging. However, generation of the visualization has different steps. If the data is in a custom format, rather than a predefined format which either obeys a standard or a known file structure, the generatio...
Citation Formats
C. Genişel, “Correlation of sequences and quadratic forms,” M.S. - Master of Science, Middle East Technical University, 2017.