scholarly journals Implementation of Finite Field Arithmetic Operations for Polynomial and Normal Basis Representations

Author(s):  
Mirza Maulana ◽  
Wenny Franciska Senjaya ◽  
Budi Rahardjo ◽  
Intan Muchtadi-Alamsyah ◽  
Marisa W. Paryasto
Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng

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.


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