 
Summary: Computationally Private Randomizing Polynomials
and Their Applications
(EXTENDED ABSTRACT)
Benny Applebaum Yuval Ishai Eyal Kushilevitz
Computer Science Department, Technion
{abenny,yuvali,eyalk}@cs.technion.ac.il
Abstract
Randomizing polynomials allow to represent a function
f(x) by a lowdegree randomized mapping ^f(x, r) whose
output distribution on an input x is a randomized encoding
of f(x). It is known that any function f in L/poly (and in
particular in NC1
) can be efficiently represented by degree
3 randomizing polynomials. Such a degree3 representation
gives rise to an NC0
4 representation, in which every bit of
the output depends on only 4 bits of the input.
In this paper, we study the relaxed notion of computa
tionally private randomizing polynomials, where the output
distribution of ^f(x, r) should only be computationally in
