scholarly journals On the Newton-like method for the inclusion of a polynomial zero

2007 ◽  
Vol 1 (1) ◽  
pp. 217-227
Author(s):  
Petkovic Ljiljana ◽  
Petkovic Miodrag
Keyword(s):  
Polynomial Zero

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.

Efficient Reduction of Polynomial Zero-One Optimization to the Quadratic Case

2008 ◽  
Vol 18 (4) ◽  
pp. 1398-1413 ◽  
Author(s):  
Christoph Buchheim ◽  
Giovanni Rinaldi
Keyword(s):  
Efficient Reduction ◽  
Polynomial Zero ◽  
Quadratic Case

SCARFS, an efficient polynomial zero-finder system

1993 ◽  
Vol 24 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Tien Chi Chen
Keyword(s):  
Polynomial Zero

scholarly journals A computational test for the existence of polynomial zero

1989 ◽  
Vol 17 (7) ◽  
pp. 1109-1114 ◽  
Author(s):  
M.S. Petković ◽  
L.D. Petković
Keyword(s):  
Polynomial Zero
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