Linearization of bivariate polynomial matrices expressed in non monomial basis

2014 ◽  
Vol 26 (2) ◽  
pp. 503-517
Author(s):  
Aikaterini S. Karetsou ◽  
Nicholas P. Karampetakis
Keyword(s):  
Polynomial Matrices ◽  
Bivariate Polynomial ◽  
Monomial Basis

scholarly journals Some Further Results on the Reduction of Two-Dimensional Systems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Dongmei Li ◽  
Yingying Gui ◽  
Jinwang Liu ◽  
Man Wu
Keyword(s):  
Two Dimensional ◽  
Polynomial Matrices ◽  
Bivariate Polynomial ◽  
Equivalence Problems

The reduction of two-dimensional systems plays an important role in the theory of systems, which is closely associated with the equivalence of the bivariate polynomial matrices. In this paper, the equivalence problems on several classes of bivariate polynomial matrices are investigated. Some new results on the equivalence of these matrices are obtained. These results are useful for reducing two-dimensional systems.

Interpolation algorithm of Leverrier–Faddev type for polynomial matrices

2006 ◽  
Vol 42 (3-4) ◽  
pp. 345-361 ◽  
Author(s):  
Marko D. Petković ◽  
Predrag S. Stanimirović
Keyword(s):  
Interpolation Algorithm ◽  
Polynomial Matrices

scholarly journals Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?

2020 ◽  
Vol 14 (1) ◽  
pp. 293-306
Author(s):  
Claire Delaplace ◽  
Alexander May
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Discrete Logarithm ◽  
Field Size ◽  
Square Root ◽  
Multivariate Polynomial ◽  
Bivariate Polynomial ◽  
Testing Problem ◽  
Polynomial Zero ◽  
Representation Technique

AbstractWe give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields a p1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to an o(p)-algorithm for ECDLP, since all involved lists are of size as small as $\begin{array}{} p^{\frac 3 4}, \end{array}$ only their computation is yet too costly.

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