Adiguzel-Goktas, EbruOzdemir, Enver2025-09-252025-09-2520240925-10221573-7586https://doi.org/10.1007/s10623-024-01374-1https://hdl.handle.net/20.500.12573/4679In 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.eninfo:eu-repo/semantics/openAccessSquare RootsSingular CurvesElliptic Curves68Q99Primary 11Y99Article10.1007/s10623-024-01374-12-s2.0-85187433176