Optimal Normal Bases

1993 ◽  
pp. 93-114
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Normal Bases

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

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.

Normal Bases

1993 ◽  
pp. 69-92
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Normal Bases

Optimal normal bases

1992 ◽  
Vol 2 (4) ◽  
pp. 315-323 ◽  
Author(s):  
Shuhong Gao ◽  
Hendrik W. Lenstra
Keyword(s):  
Normal Bases

scholarly journals Optimal Normal Bases Over Finite Fields

2021 ◽  
Vol 67 (6) ◽  
pp. 58-61
Author(s):  
Duggirala Meher Krishna ◽  
Duggirala Ravi
Keyword(s):  
Finite Fields ◽  
Normal Bases

scholarly journals Artin-Schreier-Witt extensions and normal bases

2012 ◽  
Vol 42 (3) ◽  
pp. 325-354
Author(s):  
Noriyuki Suwa
Keyword(s):  
Normal Bases
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