Results on algebraic curves over finite fields with applications incoding theory and cryptography

Date

2016-06-04

Author

Özbudak, Ferruh

Metadata

Show full item record

Item Usage Stats

48
views

0
downloads

URI

https://hdl.handle.net/11511/81310

Collections

Unverified, Conference / Seminar

Suggestions

OpenMETU
Core

Results on characterizations of plateaued functions in arbitrary characteristic Mesnager, Sihem; Özbudak, Ferruh; Sınak, Ahmet (2016-01-01) Bent and plateaued functions play a significant role in cryptography since they can have various desirable cryptographic properties. In this work, we first provide the characterizations of plateaued functions in terms of the moments of their Walsh transforms. Next, we generalize the characterizations of Boolean bent and plateaued functions in terms of their second-order derivatives to arbitrary characteristic. Moreover, we present a new characterization of plateaued functions in terms of fourth power moment...
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...
Results on characterization of Plateaued Functions in Arbitrary Characteristics Mesnager, Sihem; Özbudak, Ferruh; Sınak, Ahmet (2015-09-04)
Results on lcz sequences and quadratic forms Saygı, Elif; Özbudak, Ferruh; Department of Cryptography (2009) In this thesis we study low correlation zone (LCZ) sequence sets and a class of quadratic forms. In the first part we obtain two new classes of optimal LCZ sequence sets. In our first construction using a suitable orthogonal transformation we extend some results of [21]. We give new classes of LCZ sequence sets defined over Z4 in our second construction. We show that our LCZ sequence sets are optimal with respect to the Tang, Fan and Matsufiji bound [37]. In the second part we consider some special lineariz...
Studies on non-weakly regular bent functions and related structures Pelen, Rumi Melih; Özbudak, Ferruh; Department of Mathematics (2020) Interest in bent functions over finite fields arises both from mathematical theory and practical applications. There has been lots of literature addressing various properties of bent functions. They have a number of applications consisting of coding theory, cryptography, and sequence designs. They’re divided into four subclasses: regular bent functions that are contained within the class of weakly regular bent functions that are contained within the class of dual-bent functions. Additionally, there are non-...

Citation Formats

F. Özbudak, “Results on algebraic curves over finite fields with applications incoding theory and cryptography,” 2016, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/81310.