An Algorithm to Find Square Root of Quadratic Residues over Finite Fields using Primitive Elements

Quadratic residue is an important concept in number theory because it has both theoretical and practical application in mathematics and other areas such as computer science and communication. We also have a same concept of quadratic residue in general finite fields. Finding a square root of a quadratic residue in finite fields is an essential problem in computational algebra. In this paper we present an algorithm of computing square root of quadratic residue in finite fields using a primitive element.