On the Hidden Shifted Power Problem

Details On the Hidden Shifted Power Problem On the Hidden Shifted Power Problem

2011-10-04

arxiv.org/abs/1110.0812v2

Computer Science

Computational Complexity

Moubariz Garaev (who has now become a co-author) has introduced some new ideas that have led to stronger results. Several impr

Scientific paper

We consider the problem of recovering a hidden element $s$ of a finite field $\F_q$ of $q$ elements from queries to an oracle that for a given $x\in \F_q$ returns $(x+s)^e$ for a given divisor $e\mid q-1$. We use some techniques from additive combinatorics and analytic number theory that lead to more efficient algorithms than the naive interpolation algorithm, for example, they use substantially fewer queries to the oracle.

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