Skew多项式是由 Ore 扩张给出的， Ore 扩张是一种定义非交换多项式环的方法，最早由 Ore 提出。他的工作总结推广了希尔伯特和 Schlessinger 的工作。由于skew多项式的非交换性和线性性，我们可以用它来构造代数代码，也可以用它来构造密码。我们将研究两种特殊情形的稀疏skew多项式乘法，主要的工具是利用稀疏多项式的插值算法。我们的算法复杂度是完全多项式于其输入和输出规模的. Skew多项式的一些特殊情形被证明与n阶矩阵的乘法是等价的，当研究稀疏skew多项式的乘法时，可以有助于我们稀疏矩阵的研究。由于矩阵应用的普遍性和重要性，一点点的改进都有深远的意义。研究稀疏skew多项式的乘积，可以使我们将快速算法有效的推广到多变元情形，这只需很简单的一般的Kronecker替换的技巧。

Skew polynomials are given by the Ore extension, which is a way to define non commutative polynomial rings and was First proposed by Ore. His work generalizes the work of Hilbert and Schlessinger. Because of the non commutativity and linearity of skew polynomials, we can use it to construct algebraic codes, or we can use it to construct cryptography. We will study multiplication of two special cases of sparse skew polynomial, the main tool is to use sparse polynomial interpolation algorithm. The complexity of our algorithm is completely polynomial in its input and output size. Some special cases of skew polynomials are proved to be equivalent to the multiplication of n-order matrices. Studying the multiplication of sparse skew polynomials can help the research of sparse matrix. Because of the universality and importance of matrix application, a little improvement has far-reaching significance. By studying the multiplication of sparse skew polynomials, we can effectively extend the fast algorithm to the multivariate case, which only needs a general Kronecker substitution technique.