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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 low-degree 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 NC1
) can be efficiently represented by degree-3
randomizing polynomials. Such a degree-3 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 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 degree-3 randomizing polynomials of this type for every
polynomial-time computable function, assuming the existence of a cryptographic pseudorandom gen-
erator (PRG) in uniform-L/poly. (The latter assumption is implied by most standard intractability
assumptions used in cryptography.) This result is obtained by combining a variant of Yao's garbled


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


Collections: Computer Technologies and Information Sciences