By Topic

Solving systems of polynomial congruences modulo a large prime

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Ming-Deh Huang ; Dept. of Comput. Sci., Univ. of Southern California, Los Angeles, CA, USA ; Yiu-Chung Wong

We consider the following polynomial congruences problem: given a prime p, and a set of polynomials f1,...,fmFp[x1,...,xn] of total degree at most d, solve the system f1=...=fm=0 for solution(s) in Fpn. We give a randomized algorithm for the decision version of this problem. When the system has Fp-rational solutions our algorithm finds one of them as well as an approximation of the total number of such solutions. For a fixed number of variables, the algorithm runs in random polynomial time with parallel complexity poly-logarithmic in d, m and p, using a polynomial number of processors. As an essential step of the algorithm, we also formulate an algebraic homotopy method for extracting components of all dimensions of an algebraic set. The method is efficiently parallelizable

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996