Consideration of Generating Suitable Parameters for Constructing type (h, m) Gauss Period Normal Basis

2021 ◽  
Author(s):  
Keiji Yoshimoto ◽  
Yuta Kodera ◽  
Takuya Kusaka ◽  
Yasuyuki Nogami
Keyword(s):  
Normal Basis ◽  
Gauss Period

scholarly journals Cyclic Vector Multiplication Algorithm Based on a Special Class of Gauss Period Normal Basis

ETRI Journal ◽  
2007 ◽  
Vol 29 (6) ◽  
pp. 769-778 ◽  
Author(s):  
Hidehiro Kato ◽  
Yasuyuki Nogami ◽  
Tomoki Yoshida ◽  
Yoshitaka Morikawa
Keyword(s):  
Special Class ◽  
Normal Basis ◽  
Cyclic Vector ◽  
Gauss Period ◽  
Multiplication Algorithm

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.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

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