We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases, indicating that the aforementioned lower bound is quasi-optimal. In fact, our lower bound is quasi-optimal in the sense of bilinear complexity. In addition, we discuss the average bilinear complexity of simultaneous multiplication of skew polynomials and the complexity of skew polynomial multiplication in the case of towers of extensions.

翻译：我们建立了两个斜多项式相乘复杂性的下界。该下界与Caruso和Borgne在2017年猜想的上界一致（至多相差一个对数因子）。针对三种特殊情况，我们给出了算法，表明上述下界是拟最优的。事实上，从双线性复杂性的角度来看，我们的下界是拟最优的。此外，我们还讨论了斜多项式同时乘法的平均双线性复杂性，以及扩展塔情形下斜多项式乘法的复杂性。