Efficient Reconfigurable Implementation of Canonical and Normal Basis Multipliers Over Galois Fields GF(2m) Generated by AOPs

2006 ◽  
Author(s):  
J. L. Imaña ◽  
J. M. Sánchez
Keyword(s):  
Normal Basis ◽  
Galois Fields

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.

Sign in / Sign up

Export Citation Format

Share Document