Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields

Gábor Ivanyos,Marek Karpinski,Miklos Santha,Nitin Saxena,Igor E. Shparlinski

Algorithmica（2017）

引用 5|浏览68

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摘要

We consider the problem of recovering (that is, interpolating) and identity testing of a “hidden” monic polynomial f , given an oracle access to f(x)^e for x∈𝔽_q , where 𝔽_q is finite field of q elements (extension fields access is not permitted). The naive interpolation algorithm needs O(e f) queries and thus requires e f

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关键词

Hidden polynomial power,Black-box interpolation,Nullstellensatz,Rational function,Deterministic algorithm,Randomised algorithm,Quantum algorithm

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