algorithm - 为什么 Shamir Secret Sharing 使用拉格朗日多项式？

Question

我读到牛顿多项式具有更好的计算复杂性，但 Shamir 改用拉格朗日多项式。有谁知道不使用牛顿多项式是否有特殊原因？

谢谢

Answer 1

我只能猜测:

Other than that, Lagrange is easier to calculate than the difference methods, and is (probably rightly) regarded by many as the best choice when one already knows what polynomial degree will be needed. And when all the interpolation will be done at one x value, with only the data points' y values varying from one problem to another, Lagrange's formula becomes so much more convenient that it begins to be the only choice to consider.

http://en.wikipedia.org/wiki/Newton_polynomial#Strengths_and_weaknesses_of_various_formulae