Polynomial multiplication over finite fields: from quadratic to straight-line complexity

2006 ◽  
Vol 15 (3) ◽  
pp. 252-262 ◽  
Author(s):  
Nader H. Bshouty ◽  
Michael Kaminski
Keyword(s):  
Finite Fields ◽  
Polynomial Multiplication ◽  
Straight Line

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 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.

On the power of straight- line computations in finite fields

1982 ◽  
Vol 28 (6) ◽  
pp. 875-880 ◽  
Author(s):  
A. Lempel ◽  
G. Seroussi ◽  
J. Ziv
Keyword(s):  
Finite Fields ◽  
Straight Line

scholarly journals Multiplicative complexity of polynomial multiplication over finite fields

1989 ◽  
Vol 36 (1) ◽  
pp. 150-170 ◽  
Author(s):  
Michael Kaminski ◽  
Nader H. Bshouty
Keyword(s):  
Finite Fields ◽  
Polynomial Multiplication ◽  
Multiplicative Complexity

Polynomial multiplication over binary finite fields: new upper bounds

2019 ◽  
Vol 10 (3) ◽  
pp. 197-210 ◽  
Author(s):  
Alessandro De Piccoli ◽  
Andrea Visconti ◽  
Ottavio Giulio Rizzo
Keyword(s):  
Finite Fields ◽  
Upper Bounds ◽  
Polynomial Multiplication
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