A generalized qth root algorithm

Algorithms which find roots (i.e., given s> q find u such that IL* = s) over the rationales are well known and fairly straight forward. But how do you find roots over finite fields? Just as in the rational case, a qchroot on an element s in a finite field F is an element u E F such that 2~9 z s. Cryptographic algorithms often require finding qthroots over GF(p), as in Rabin’s public encryption scheme (see [2]). Even so, no simple generalized technique exists for finding qthroots if q divides the order of the multiplicative group of the field. The purpose of this paper is to describe a generalized technique for computing qthroots over GF(p). reduces to the simplified square root technique that most cryptographers use. 2 Problem Description.