Efficient Multiplier over Finite Field Represented in Type II Optimal Normal Basis

2006 ◽  
Author(s):  
Youbo Wang ◽  
Zhiguang Tian ◽  
Xinyan Bi ◽  
Zhendong Niu
Keyword(s):  
Finite Field ◽  
Normal Basis ◽  
Type Ii

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 basis of the finite field F/sub 2/(p-1)p/sup m/ over F/sub 2/

1997 ◽  
Vol 43 (2) ◽  
pp. 737-739
Author(s):  
Muzhong Wang ◽  
I.F. Blake
Keyword(s):  
Finite Field ◽  
Normal Basis
Sign in / Sign up

Export Citation Format

Share Document