论文标题
快速Kötter-nielsen-Høholdt插值偏斜多项式环
Fast Kötter-Nielsen-Høholdt Interpolation over Skew Polynomial Rings
论文作者
论文摘要
偏差多项式是一类非交通性多项式，在计算机科学，编码理论和密码学中具有多个应用。特别是，偏斜多项式可用于构建和解码几个指标的评估代码，例如锤子，等级，总和和偏斜度量。在本文中，我们提出了Kötter-Nielsen-Høhoushold（KNH）插值的快速分裂和诱饵变体，上面旋转偏斜多项式环上的自由模块。所提出的KNH插值可用于求解基于插值的（嵌入式）Gabidulin，线性化的Reed-Solomon和Skew Reed-Solomon代码的插值分解步骤，它们在编码理论和基于代码的基于代码的量子固定密码中具有各种应用。
Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography. In particular, skew polynomials can be used to construct and decode evaluation codes in several metrics, like e.g. the Hamming, rank, sum-rank and skew metric. In this paper we propose a fast divide-and-conquer variant of the Kötter-Nielsen-Høholdt (KNH) interpolation over free modules over skew polynomial rings. The proposed KNH interpolation can be used to solve the interpolation step of interpolation-based decoding of (interleaved) Gabidulin, linearized Reed-Solomon and skew Reed-Solomon codes efficiently, which have various applications in coding theory and code-based quantum-resistant cryptography.
