  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.
