Hiding instances in multioracle queries
Abadi, Feigenbaum, and Kilian have considered instance-hiding schemes . Let f be a function for which no randomized polynomial-time algorithm is known; randomized polynomial-time machine A wants to query an oracle B for f to obtain f(x), without telling B exactly what x is. It is shown in  that, if f is an NP-hard function, A cannot query a single oracle B while hiding all but the size of the instance, assuming that the polynomial hierarchy does not collapse. This negative result holds for all oracles B, including those that are non-r.e.
In this paper, we generalize the definition of instance-hiding schemes to allow A to query several oracles B1,..., Bm that are not allowed to communicate. We show that every function f does have a multioracle instance-hiding scheme, thus settling a question of Rivest.
KeywordsBoolean Function Kolmogorov Complexity Arithmetic Circuit Polynomial Hierarchy Random Tape
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