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Open AccessArticle

Normal Bases on Galois Ring Extensions

by 1,* and 2
1
Department of Mathematical Sciences, Xi’an University of Technology, Xi’an 710048, China
2
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(12), 702; https://doi.org/10.3390/sym10120702
Received: 27 September 2018 / Revised: 8 November 2018 / Accepted: 27 November 2018 / Published: 3 December 2018
Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension. View Full-Text
Keywords: Galois ring; optimal normal basis; multiplicative complexity; finite field Galois ring; optimal normal basis; multiplicative complexity; finite field
MDPI and ACS Style

Zhang, A.; Feng, K. Normal Bases on Galois Ring Extensions. Symmetry 2018, 10, 702. https://doi.org/10.3390/sym10120702

AMA Style

Zhang A, Feng K. Normal Bases on Galois Ring Extensions. Symmetry. 2018; 10(12):702. https://doi.org/10.3390/sym10120702

Chicago/Turabian Style

Zhang, Aixian; Feng, Keqin. 2018. "Normal Bases on Galois Ring Extensions" Symmetry 10, no. 12: 702. https://doi.org/10.3390/sym10120702

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