Finding Irreducible and Primitive Polynomials

1999 ◽  
pp. 45-64
Author(s):  
Igor E. Shparlinski
Keyword(s):  
Primitive Polynomials

Some primitive polynomials over finite fields

2001 ◽  
Vol 21 (3) ◽  
pp. 412-416 ◽  
Author(s):  
Seunghwan Chang ◽  
June Bok Lee
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

RS (255, 249) Codec Based on All Primitive Polynomials Over GF( $$2^8$$ )

2017 ◽  
pp. 69-81 ◽  
Author(s):  
Jagannath Samanta ◽  
Jaydeb Bhaumik ◽  
Soma Barman ◽  
Sk. G. S. Hossain ◽  
Mandira Sahu ◽  
...  
Keyword(s):  
Primitive Polynomials

scholarly journals Implementation of reconfigurable galois field multipliers over2m using primitive polynomials

2018 ◽  
Vol 7 (2.12) ◽  
pp. 386
Author(s):  
B Raj Narain ◽  
Dr T. Sasilatha
Keyword(s):  
Galois Field ◽  
Hardware Architecture ◽  
Fixed Length ◽  
Primitive Polynomials

The Galois field multiplier finds extensive use in cryptographic solutions and applications. The Galois field multiplier can be implemented as fixed bitwise or reconfigurable. For fixed length, the data is restricted to the fixed length. But in reconfigurable GF multipliers, the bit length of the multiplier is flexible and is independent of hardware architecture. This paper proposes a method to implement a reconfigurable GF multiplier for various bit values from 8 to 128 bits. This paper compares the area complexity of various bit size in Xilinx Spartan 3E family FPGA and estimates the resources required for the implementation.  

Critical role of primitive polynomials in an LFSR based testing technique

1988 ◽  
Vol 24 (15) ◽  
pp. 953 ◽  
Author(s):  
A. Ahmad ◽  
N.K. Nanda ◽  
K. Garg
Keyword(s):  
Critical Role ◽  
Testing Technique ◽  
Primitive Polynomials

scholarly journals A construction of primitive polynomials over finite fields

2017 ◽  
Vol 65 (12) ◽  
pp. 2424-2431 ◽  
Author(s):  
Sara D. Cardell ◽  
Joan-Josep Climent
Keyword(s):  
Finite Fields ◽  
Primitive Polynomials ◽  
Polynomials Over Finite Fields

scholarly journals A modification of Fitzgerald's characterization of primitive polynomials over a finite field

2008 ◽  
Vol 14 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Vichian Laohakosol ◽  
Umarin Pintoptang
Keyword(s):  
Finite Field ◽  
Primitive Polynomials
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