On Approximating the Entropy of Polynomial Mappings

We investigate the complexity of the following computational problem: Polynomial Entropy Approximation (PEA): Given a low-degree polynomial mapping p : Fn Fm , where F is a finite field, approximate the the output entropy H(p(Un)), where Un is the uniform distribution on Fn and H may be any of several entropy measures. We show:

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Zeev Dvir, Dan Gutfreund, Guy N. Rothblum, Salil P. Vadhan
• Keywords: Algorithm, ECCC 2010, Entropy, Polynomials