Fast Inversion in <formula formulatype="inline"><tex Notation="TeX">${\schmi{GF(2^m)}}$</tex></formula> with Normal Basis Using Hybrid-Double Multipliers

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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Fast Normal Basis Multiplication Using General Purpose Processors

Selected Areas in Cryptography - Lecture Notes in Computer Science ◽

10.1007/3-540-45537-x_18 ◽

2001 ◽

pp. 230-244 ◽

Cited By ~ 5

Author(s):

Arash Reyhani-Masoleh ◽

M. Anwar Hasan

Keyword(s):

General Purpose ◽

Normal Basis ◽

General Purpose Processors

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Hardware architectures for inversion in GF(2m) using polynomial and gaussian normal basis

2010 IEEE ANDESCON ◽

10.1109/andescon.2010.5633137 ◽

2010 ◽

Cited By ~ 2

Author(s):

Vladimir Trujillo-Olaya ◽

Jaime Velasco-Med

Keyword(s):

Normal Basis ◽

Gaussian Normal Basis ◽

Hardware Architectures

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

Sixth International Conference on Intelligent Systems Design and Applications ◽

10.1109/isda.2006.138 ◽

2006 ◽

Cited By ~ 1

Author(s):

Youbo Wang ◽

Zhiguang Tian ◽

Xinyan Bi ◽

Zhendong Niu

Keyword(s):

Finite Field ◽

Normal Basis ◽

Type Ii

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

Mathematica Slovaca ◽

10.2478/s12175-010-0046-2 ◽

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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