Open AccessGF(2 n ) bit‐parallel squarer using generalised polynomial basis for new class of irreducible pentanomials
Author(s) -
Xiong Xi,
Fan Haining
Publication year - 2014
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2014.0006
Subject(s) - xor gate , primitive polynomial , basis (linear algebra) , mathematics , class (philosophy) , polynomial , arithmetic , polynomial basis , bit (key) , discrete mathematics , combinatorics , finite field , computer science , algorithm , logic gate , mathematical analysis , geometry , computer security , artificial intelligence
Explicit formulae and complexities of bit‐parallel GF(2 n ) squarers for a new class of irreducible pentanomials x n + x n− 1 + x k + x + 1, where n is odd and 1 < k < ( n − 1)/2 are presented. The squarer is based on the generalised polynomial basis of GF(2 n ). Its gate delay matches the best results, whereas its XOR gate complexity is n + 1, which is only about two thirds of the current best results.