This article presents a new method for calculating square roots in GF(p) byexponentiating in GF(p^3) or equivalently modulo irreducible cubic polynomials.This algorithm is in some ways similar to the Cipolla-Lehmer algorithm which isbased on exponentiating in GF(p^2). Another less well known square rootalgorithm based on quadratic sums is also given. In addition to this, severalconjectures about the output of this GF(p^3) square root algorithm arementioned.
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机译：本文介绍了一种通过对GF（p ^ 3）或等效模不可约三次多项式求幂的方法来计算GF（p）的平方根的新方法。该算法在某种程度上类似于基于GF（p）求幂的Cipolla-Lehmer算法。 p ^ 2）。还给出了另一个基于平方和的鲜为人知的平方根算法。除此之外，还提到了关于该GF（p ^ 3）平方根算法的输出的几个猜想。
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