Polynomial Multiplication over Finite Fields Using Field Extensions and Interpolation

2009 ◽  
Author(s):  
Murat Cenk ◽  
Cetin Kaya Koc ◽  
Ferruh Ozbudak
Keyword(s):  
Finite Fields ◽  
Polynomial Multiplication ◽  
Field Extensions

scholarly journals Faster Polynomial Multiplication over Finite Fields

2017 ◽  
Vol 63 (6) ◽  
pp. 1-23 ◽  
Author(s):  
David Harvey ◽  
Joris Van Der Hoeven ◽  
Grégoire Lecerf
Keyword(s):  
Finite Fields ◽  
Polynomial Multiplication

scholarly journals On the multiplicative order of elements in Wiedemann's towers of finite fields

2015 ◽  
Vol 7 (2) ◽  
pp. 220-225
Author(s):  
R. Popovych
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Field Extensions ◽  
Fermat Numbers ◽  
Multiplicative Order ◽  
Order Of Elements

We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative order $O(x_{i} )$.

scholarly journals A New Secret Sharing Scheme Based on Polynomials over Finite Fields

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1200
Author(s):  
Selda Çalkavur ◽  
Patrick Solé ◽  
Alexis Bonnecaze
Keyword(s):  
Finite Fields ◽  
Secret Sharing ◽  
Secret Sharing Scheme ◽  
Polynomial Multiplication ◽  
Sharing Scheme ◽  
Polynomials Over Finite Fields

In this paper, we examine a secret sharing scheme based on polynomials over finite fields. In the presented scheme, the shares can be used for the reconstruction of the secret using polynomial multiplication. This scheme is both ideal and perfect.

scholarly journals GENERATORS OF FINITE FIELDS WITH PRESCRIBED TRACES

2021 ◽  
pp. 1-12
Author(s):  
LUCAS REIS ◽  
SÁVIO RIBAS
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Special Class ◽  
Existence Results ◽  
Primitive Elements ◽  
Field Extensions ◽  
Intermediate Field

Abstract This paper explores the existence and distribution of primitive elements in finite field extensions with prescribed traces in several intermediate field extensions. Our main result provides an inequality-like condition to ensure the existence of such elements. We then derive concrete existence results for a special class of intermediate extensions.

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