On the Hidden Shifted Power Problem

Jean Bourgain; Moubariz Z. Garaev; Sergei V. Konyagin; Igor E. Shparlinski

On the Hidden Shifted Power Problem

Computational Complexity 2012-01-04 v2 Number Theory

Authors: Jean Bourgain , Moubariz Z. Garaev , Sergei V. Konyagin , Igor E. Shparlinski

Abstract

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.

Cite

@article{arxiv.1110.0812,
  title  = {On the Hidden Shifted Power Problem},
  author = {Jean Bourgain and Moubariz Z. Garaev and Sergei V. Konyagin and Igor E. Shparlinski},
  journal= {arXiv preprint arXiv:1110.0812},
  year   = {2012}
}

Comments

Moubariz Garaev (who has now become a co-author) has introduced some new ideas that have led to stronger results. Several imprecision of the previous version have been corrected too

On the Hidden Shifted Power Problem

Abstract

Cite

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