A method includes receiving a first element of a Galois Field of order q.sup.m, where q is a prime number and m is a positive integer. The first element is raised to a predetermined power so as to form a second element z, wherein the predetermined power is a function of q.sup.m and an integer p, where p is a prime number which divides q.sup.m−1. The second element z is raised to a p.sup.th power to form a third element. If the third element equals the first element, the second element multiplied by a p.sup.th root of unity raised to a respective power selected from a set of integers between 0 and p−1 is output as at least one root of the first element.

A data processing apparatus is provided, for performing a digit-recurrence square root operation on an input value. Receiver circuitry receives a remainder value of a previous iteration of the digit-recurrence square root operation. Comparison circuitry compares most significant bits of the remainder value of the previous iteration with a number of selection constants, in order to output a next digit of a result of the digit-recurrence square root operation. The comparison circuitry compares at most 3 fractional bits of the remainder value of the previous iteration with the plurality of selection constants.

A data processing apparatus is provided, for performing a digit-recurrence square root operation on an input value. Receiver circuitry receives a remainder value of a previous iteration of the digit-recurrence square root operation. Comparison circuitry compares most significant bits of the remainder value of the previous iteration with a number of selection constants, in order to output a next digit of a result of the digit-recurrence square root operation. The comparison circuitry compares at most 3 fractional bits of the remainder value of the previous iteration with the plurality of selection constants.