Noisy polynomial interpolation modulo prime powers

Abstract

We consider the noisy polynomial interpolation problem of recovering an unknown s-sparse polynomial f(X) over the ring Zpk of residues modulo pk, where p is a small prime and k is a large integer parameter, from approximate values of the residues of f(t)∈Zpk. Similar results are known for residues modulo a large prime p, however the case of prime power modulus pk, with small p and large k, is new and requires different techniques. We give a deterministic polynomial time algorithm, which for almost given more than a half bits of f(t) for sufficiently many randomly chosen points t∈Zpk∗, recovers f(X).