Square root computation in finite fields - Adiguzel-Goktas, Ebru; Ozdemir, Enver (Springer Science and Business Media LLC, 2024)
AbstractIn this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular curves offers a broad perspective to compare and further improve the existing methods in addition to offering a new avenue for square root computation algorithms in finite fields.
Keywords: Singular curves; Computational methods for problems pertaining to field theory; Mathematics - Number Theory; Q99; Symbolic computation and algebraic computation; square roots; singular curves; elliptic curves; FOS: Mathematics; Elliptic curves; Square roots; Number Theory (math.NT); Primary 11Y99; Number-theoretic algorithms; complexity