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Skew polynomials are a class of non-commutative polynomials that have severalapplications in computer science, coding theory and cryptography. Inparticular, skew polynomials can be used to construct and decode evaluationcodes in several metrics, like e.g. the Hamming, rank, sum-rank and skewmetric. In this paper we propose a fast divide-and-conquer variant of theK\"otter-Nielsen-H{\o}holdt (KNH) interpolation over free modules over skewpolynomial rings. The proposed KNH interpolation can be used to solve theinterpolation step of interpolation-based decoding of (interleaved) Gabidulin,linearized Reed-Solomon and skew Reed-Solomon codes efficiently, which havevarious applications in coding theory and code-based quantum-resistantcryptography.

Fast K\"otter-Nielsen-H\o holdt Interpolation over Skew Polynomial Rings