关于有限域上无二次非剩余的平方根
On Taking Square Roots without Quadratic Nonresidues over Finite Fields
摘要：
我们提出了一个新的想法来计算平方根有限域，没有被赋予任何二次非剩余，没有假设任何未经证明的假设。算法是确定性的，证明是初等的。在某些情况下，平方根算法在具有$q$元素的有限域上以$\tilde{O}(\log^2 q)$位运算运行。作为应用，我们构造了一个确定性素性证明算法，该算法在$\tilde{O}(\log^3 N)$中运行，对某些整数$N$。
英文摘要：
We present a novel idea to compute square roots over finite fields, without being given any quadratic nonresidue, and without assuming any unproven hypothesis. The algorithm is deterministic and the proof is elementary. In some cases, the square root algorithm runs in $\tilde{O}(\log^2 q)$ bit operations over finite fields with $q$ elements. As an application, we construct a deterministic primality proving algorithm, which runs in $\tilde{O}(\log^3 N)$ for some integers $N$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
