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Presented is a square root algorithm in 𝔽 q which generalises Atkins's square root algorithm [see reference 6] for q ≡ 5 (mod 8) and Müller's algorithm [see reference 7] for q ≡ 9 (mod 16). The presented algorithm precomputes a primitive 2 s -th root of unity ξ where s is the largest positive integer satisfying 2 s |q−1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for square root computation and is favourably compared with the algorithms of Atkin, Müuller and Kong et al.
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5. Nishihara, N., Harasawa, R., Sueyoshi, Y., Kudo, A.: ‘A remark on the computation of cube roots in finite fields’, .
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7. Müller, S.: ‘On the computation of square roots in finite fields’, Des. Codes Cryptogr., 2004, 31, pp. 301–312 (doi: 10.1023/B:DESI.0000015890.44831.e2).
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8. Kong, F., Cai, Z., Yu, J., Li, D.: ‘Improved generalized Atkin algorithm for computing square roots in finite fields’, Inf. Process. Lett., 2006, 98, 1, pp. 1–5 (doi: 10.1016/j.ipl.2005.11.015).
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D.G. Han ,
D. Choi ,
H. Kim
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Improved computation of square roots in specific finite fields.
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2 ,
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196
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N. Nishihara ,
R. Harasawa ,
Y. Sueyoshi ,
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F. Kong ,
Z. Cai ,
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Improved generalized Atkin algorithm for computing square roots in finite fields.
Inf. Process. Lett.
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1 ,
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5
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S. Lindhurst
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S. Müller
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D.H. Lehmer
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A.O.L. Atkin
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