SCARFS, an efficient polynomial zero-finder system

Author(s):  
Tien Chi Chen
Keyword(s):  
2020 ◽  
Vol 14 (1) ◽  
pp. 293-306
Author(s):  
Claire Delaplace ◽  
Alexander May

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.


2008 ◽  
Vol 18 (4) ◽  
pp. 1398-1413 ◽  
Author(s):  
Christoph Buchheim ◽  
Giovanni Rinaldi

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

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

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

Sign in / Sign up

Export Citation Format

Share Document