## On taking square roots and constructing quadratic nonresidues over finite fields (2007)

by
Tsz-Wo Sze

Citations: | 1 - 1 self |

### BibTeX

@MISC{Sze07ontaking,

author = {Tsz-Wo Sze},

title = {On taking square roots and constructing quadratic nonresidues over finite fields },

year = {2007}

}

### OpenURL

### Abstract

We present a novel idea to compute square roots over some families of finite fields. Our algorithms are deterministic polynomial time and can be proved by elementary means (without assuming any unproven hypothesis). In some particular finite fields Fq, there are algorithms for taking square roots with Õ(log2 q) bit operations. As an application of our square root algorithms, we show a deterministic primality testing algorithm for some form of numbers. For some positive integer N, this primality testing algorithm runs in Õ(log3 N).