Sonlu cisimler üzerindeki x^k-cx-d polinomlarının iki uygulaması üzerine ve daha fazlası



Character sums of quadratic forms over finite fields and the number of rational points for some classes of artin-schreier type curves
Coşgun, Ayhan; Doğanaksoy, Ali; Department of Mathematics (2017)
Exponential sums of quadratic forms over finite fields have many applications to various areas such as coding theory and cryptography. As an example to these applications, there is an organic connection between exponential sums of quadratic forms and the number of rational points of algebraic curves defined over finite fields. This connection is central in the application of algebraic geometry to coding theory and cryptography. In this thesis, different facts and techniques of theory of finite fields are co...
Drinfeld modular curves with many rational points over finite fields
Cam, Vural; Özbudak, Ferruh; Department of Mathematics (2011)
In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a b...
Large sparse matrix-vector multiplication over finite fields
Mangır, Ceyda; Cenk, Murat; Manguoğlu, Murat; Department of Cryptography (2019)
Cryptographic computations such as factoring integers and computing discrete logarithms require solving a large sparse system of linear equations over finite fields. When dealing with such systems iterative solvers such as Wiedemann or Lanczos algorithms are used. The computational cost of both methods is often dominated by successive matrix-vector products. In this thesis, we introduce a new algorithm for computing a large sparse matrix-vector multiplication over finite fields. The proposed algorithm is im...
Results on complexity of multiplication over finite fields
Cenk, Murat; Özbudak, Ferruh; Department of Cryptography (2009)
Let n and l be positive integers and f (x) be an irreducible polynomial over Fq such that ldeg( f (x)) < 2n - 1, where q is 2 or 3. We obtain an effective upper bound for the multiplication complexity of n-term polynomials modulo f (x)^l. This upper bound allows a better selection of the moduli when Chinese Remainder Theorem is used for polynomial multiplication over Fq. We give improved formulae to multiply polynomials of small degree over Fq. In particular we improve the best known multiplication complexi...
On the trace based public key cryptosystems over finite fields
Ashraf, Muhammad; Akyıldız, Ersan; Kırlar, Barış Bülent; Department of Cryptography (2013)
In this thesis, the trace based Public Key Cryptosystems (PKC) are explored from theoretical and implementation point of view. We will introduce cryptographic protocols for the ones they are not discussed yet. We introduce improved trace based exponentiation algorithm for fifth degree recursive relation. The Discrete Log Problem (DLP), that is computing $x$, given $y=\alpha^x$ and $<\alpha>=G\subset \F_q^*$, based Public Key Cryptosystems (PKC) are being studied since late 1970's. Such development of PKC wa...
Citation Formats
C. İrimağzı, Sonlu cisimler üzerindeki x^k-cx-d polinomlarının iki uygulaması üzerine ve daha fazlası. 2023.