Abstract
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.
Publisher
Springer Science and Business Media LLC
Reference14 articles.
1. Bach E.: Explicit bounds for primality testing and related problems. Math. Comput. 55(191), 355–380 (1990).
2. Cipolla M.: Un metodo per la risoluzione della congruenza di secondo grado. Napoli Rend. 9, 154–163 (1903).
3. Cohen H.: A Course in Computational Algebraic Number Theory. Springer, New York (2000).
4. Cohen H., Frey G.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. Chapman & Hall/CRC, Boca Raton (2005).
5. Müller S.: On strong lucas pseudoprimes. Comb. Gen. Algebra 10, 237–249 (1998).