Improved Computation of Square Roots in Specific Finite Fields
Dong‐Guk Han, Dooho Choi, Howon Kim · IEEE Transactions on Computers · 2008
In this paper, we study exponentiation in the specific finite fields F, with very special exponents such as those that occur in algorithms for computing square roots. Here, q is a prime power, q = pk, where k > 1, and k is odd. Our algorithmic approach improves the corresponding exponentiation resulted from the better rewritten exponent. To the best of our knowledge, it is the first major improvement to the Tonelli-Shanks algorithm, for example, the number of multiplications can be reduced to at least 60 percent on the average when p= 1 (mod 16). Several numerical examples are given that show the speedup of the proposed methods.