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## Sub-Linear Root Detection, and New Hardness Results, for Sparse Polynomials Over Finite Fields

When t is not fixed we show that, for p prime, detecting roots in $\F_p$  for f is NP-hard with respect to BPP-reductions. Finally, we prove that if the complexity of root detection is sub-linear (in a refined sense),  relative to the straight-line program encoding, then  $NEXP \not\subseteq P/poly$.

His research interests are in the areas of theoretical computer science, cryptography and computational number theory.