Exact bivariate polynomial factorization over ℚ by approximation of roots

2014 ◽  
Vol 28 (1) ◽  
pp. 243-260 ◽  
Author(s):  
Yong Feng ◽  
Wenyuan Wu ◽  
Jingzhong Zhang ◽  
Jingwei Chen
Keyword(s):  
Polynomial Factorization ◽  
Bivariate Polynomial

scholarly journals An application of bivariate polynomial factorization on decoding of Reed-Solomon based codes

2018 ◽  
Vol 12 (1) ◽  
pp. 166-177
Author(s):  
Ivan Pavkov ◽  
Nebojsa Ralevic ◽  
Ljubo Nedovic
Keyword(s):  
Efficient Algorithm ◽  
Sufficient Condition ◽  
Polynomial Factorization ◽  
Necessary And Sufficient Condition ◽  
Bivariate Polynomials ◽  
Bivariate Polynomial ◽  
Integer Coefficients ◽  
Necessary And Sufficient ◽  
The Given

A necessary and sufficient condition for the existence of a non-trivial factorization of an arbitrary bivariate polynomial with integer coefficients was presented in [2]. In this paper we develop an efficient algorithm for factoring bivariate polynomials with integer coefficients. Also, we shall give a proof of the optimality of the algorithm. For a given codeword, formed by mixing up two codewords, the algorithm recovers those codewords directly by factoring corresponding bivariate polynomial. Our algorithm determines uniquely the given polynomials which are used in forming the mixture of two codewords.

Sparse bivariate polynomial factorization

2014 ◽  
Vol 57 (10) ◽  
pp. 2123-2142 ◽  
Author(s):  
WenYuan Wu ◽  
JingWei Chen ◽  
Yong Feng
Keyword(s):  
Polynomial Factorization ◽  
Bivariate Polynomial

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.

Comments on "Polynomial factorization using the Routh criterion"

1972 ◽  
Vol 60 (4) ◽  
pp. 471-471
Author(s):  
A.M. Davis ◽  
E. Mastascusa ◽  
W. Rave ◽  
B. Turner
Keyword(s):  
Polynomial Factorization
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