Storage free basis conversion over composite finite fields of odd characteristics

Date

2013-09-19

Author

Sial, M Riaz
Akyıldız, Ersan

Metadata

Show full item record

Item Usage Stats

179
views

0
downloads

We study the Finite Fields of type Fq, q = p2pn from the efficient implementation point of view. We found that we can represent these fields with irreducible polynomials in the form f(x) = xp − x − a. By using this representation we have found a way of constructing normal basis for the field, together with transmission matrix between normal basis and algebraic basis (Polynomial Basis) of Fq and vice versa. The key point is that this matrix and its inverse can be computed very efficiently without any memory requirement.

Subject Keywords

Finite fields, Composite field, Basis conversion, Polynomial basis, Normal basis, Vandermonde matrix, Reciprocal polynomial

URI

https://hdl.handle.net/11511/88172

Conference Name

International Information Security and Cryptology Conference, ( 20 - 21 Eylül 2013)

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Free storage basis conversion over extension field Harold, Ndangang Yampa; Akyıldız, Ersan; Department of Cryptography (2014) The representation of elements over finite fields play a great impact on the performance of finite field arithmetic. So if efficient representation of finite field elements exists and conversion between these representations is known, then it becomes easy to perform computation in a more efficient way. In this thesis, we shall provide a free storage basis conversion in the extension field F_(q^p) of F_q between Normal basis and Polynomial basis and vice versa. The particularity of this thesis is that, our t...
Stability analysis of recurrent neural networks with piecewise constant argument of generalized type Akhmet, Marat; Yılmaz, Elanur (2010-09-01) In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.
Approximation based curvilinear local search for optimization problems Yaman, Fatih; YILMAZ, ASIM EGEMEN; Leblebicioğlu, Mehmet Kemal (2016-01-01) Purpose - The purpose of this paper is to propose a local approximation-based search method to optimize any function. For this purpose, an approximation method is combined with an estimation filter, and a new local search mechanism is constituted.
Impulsive Hopfield-type neural network system with piecewise constant argument Akhmet, Marat; Yılmaz, Elanur (2010-08-01) In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
Classification of function fields with class number three BİLHAN, Mehpare; Buyruk, Dilek; Özbudak, Ferruh (2015-11-01) We give the full list of all algebraic function fields over a finite field with class number three up to isomorphism. Our list consists of explicit equations of algebraic function fields which are mutually non-isomorphic over the full constant field.

Citation Formats

M. R. Sial and E. Akyıldız, “Storage free basis conversion over composite finite fields of odd characteristics,” presented at the International Information Security and Cryptology Conference, ( 20 - 21 Eylül 2013), Ankara, Türkiye, 2013, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88172.