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2010

Parallel sparse polynomial interpolation over finite fields

8 years 6 months ago
Parallel sparse polynomial interpolation over finite fields
We present a probabilistic algorithm to interpolate a sparse multivariate polynomial over a finite field, represented with a black box. Our algorithm modifies the algorithm of BenOr and Tiwari from 1988 for interpolating polynomials over rings with characteristic zero to characteristic p by doing additional probes. To interpolate a polynomial in n variables with t non-zero terms, Zippel's (1990) algorithm interpolates one variable at a time using O(ndt) probes to the black box where d bounds the degree of the polynomial. Our new algorithm does O(nt) probes. It interpolates each variable independently using O(t) probes which allows us to parallelize the main loop giving an advantage over Zippel's algorithm. We have implemented both Zippel's algorithm and the new algorithm in C and we have done a parallel implementation of our algorithm using Cilk [2]. In the paper we provide benchmarks comparing the number of probes our algorithm does with both Zippel's algorithm an...
Seyed Mohammad Mahdi Javadi, Michael B. Monagan
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2010
Where CAP
Authors Seyed Mohammad Mahdi Javadi, Michael B. Monagan
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