On the Computation of Square Roots in Finite Fields
- Siguna Müller
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In this paper, two improvements for computing square roots in finite fields are presented. Firstly, we give a simple extension of a method by O. Atkin, which requires two exponentiations in FM q , when q≡9 mod 16. Our second method gives a major improvement to the Cipolla–Lehmer algorithm, which is both easier to implement and also much faster. While our method is independent of the power of 2 in q−1, its expected running time is equivalent to 1.33 as many multiplications as exponentiation via square and multiply. Several numerical examples are given that show the speed-up of the proposed methods, compared to the routines employed by Mathematica, Maple, respectively Magma.
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- On the Computation of Square Roots in Finite Fields
Designs, Codes and Cryptography
Volume 31, Issue 3 , pp 301-312
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- Kluwer Academic Publishers
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- finite fields
- square roots
- efficient computation
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- Siguna Müller (1)
- Author Affiliations
- 1. Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W, Calgary, AB, T2N 1N4, Canada