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Computationally Private Randomizing Polynomials and Their Applications #

Summary: Computationally Private Randomizing Polynomials
and Their Applications #
Benny Applebaum Yuval Ishai Eyal Kushilevitz
Computer Science Department, Technion
March 5, 2006
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 uniform­#L/poly (and in particular in NC 1 ) can be efficiently represented by degree­3
randomizing polynomials. Such a degree­3 representation gives rise to an NC 0
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 computationally private randomizing polynomials,
where the output distribution of “
f(x, r) should only be computationally indistinguishable from a ran­
domized encoding of f(x). We construct degree­3 randomizing polynomials of this type for every
polynomial­time computable function, assuming the existence of a cryptographic pseudorandom gen­


Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science


Collections: Computer Technologies and Information Sciences