Polarization and Oblivious Polarization Sample Clauses

Polarization and Oblivious Polarization. ǁ − ǁ ≤ ǁ − ǁ ≥ { } Circuit polarization was introduced by Xxxxx and Xxxxxx in [17] in the context of statistical zero knowledge. It can be described as follows: assume that two circuits are given, which on uniform random input yield output distributions C0 and C1 over 0, 1 A, respectively. We look for an efficient method to polarize the circuits: if C0 C1 α, for some parameter α, the method should output circuits which are near disjoint, if C0 C1 β, for some parameter β, then the method should output circuits which produce very close distributions. In general, such a method uses a description of the circuits given. Here, we focus on methods which use the given circuits in a black-box manner, obliviously and with random input only.

Polarization and Oblivious Polarization. In general, a method to polarize two circuits can use the description of the circuits given. Here, we focus on methods with several restrictions. First, they use the given circuits with uniform and independent random input in a black-box manner only. Second, they output all the samples obtained, but do not do any other computation with them. ∈ { } The following process can be used to describe such a method com- pletely: on input b 0, 1 (this denotes which distribution should be produced) and k (a “security” parameter), algorithm A outputs a list of query bits (Q0, Q1, . . . , Qn—1) and some side information Rb. The output