Polynomial Multiplication over Finite Fields Using Field Extensions and Interpolation

Author(s):  
Murat Cenk ◽  
Cetin Kaya Koc ◽  
Ferruh Ozbudak
2017 ◽  
Vol 63 (6) ◽  
pp. 1-23 ◽  
Author(s):  
David Harvey ◽  
Joris Van Der Hoeven ◽  
Grégoire Lecerf

2015 ◽  
Vol 7 (2) ◽  
pp. 220-225
Author(s):  
R. Popovych

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 $O(x_{i} )$.


Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1200
Author(s):  
Selda Çalkavur ◽  
Patrick Solé ◽  
Alexis Bonnecaze

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.


Author(s):  
LUCAS REIS ◽  
SÁVIO RIBAS

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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