Noisy polynomial interpolation modulo prime powers
Marek Karpinski, Igor Shparlinski

TL;DR
This paper introduces a deterministic polynomial-time algorithm for noisy polynomial interpolation over rings modulo prime powers, extending known results from prime moduli to prime power moduli with small primes and large exponents.
Contribution
It provides the first known deterministic algorithm for recovering sparse polynomials over rings modulo prime powers from approximate evaluations.
Findings
Algorithm recovers polynomials with more than half the bits of evaluations.
Works for small primes p and large exponents k.
Applicable to almost all randomly chosen points.
Abstract
We consider the {\it noisy polynomial interpolation problem\/} of recovering an unknown -sparse polynomial over the ring of residues modulo , where is a small prime and is a large integer parameter, from approximate values of the residues of . Similar results are known for residues modulo a large prime , however the case of prime power modulus , with small and large , is new and requires different techniques. We give a deterministic polynomial time algorithm, which for almost given more than a half bits of for sufficiently many randomly chosen points , recovers .
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