Fast modular reduction and squaring in GF(2m)

We present an efficient bit-parallel algorithm for squaring in GF(2m) using polynomial basis. This algorithm achieves competitive efficiency while being aimed at any choice of low-weight irreducible polynomial. For a large class of irreducible polynomials it is more efficient than the previously bes...

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Bibliographic Details
Published in:Information processing letters Vol. 132; pp. 33 - 38
Main Authors: Niehues, L. Boppre, Custódio, R., Panario, D.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2018
Subjects:
Cryptography
Finite field
Number theory
Polynomial
Squaring
Polynomial
Finite field
Cryptography
Number theory
Squaring
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:We present an efficient bit-parallel algorithm for squaring in GF(2m) using polynomial basis. This algorithm achieves competitive efficiency while being aimed at any choice of low-weight irreducible polynomial. For a large class of irreducible polynomials it is more efficient than the previously best general squarer. In contrast, other efficient squarers often require a change of basis or are suitable for only a small number of irreducible polynomials. Additionally, we present a simple algorithm for modular reduction with equivalent cost to the state of the art for general irreducible polynomials. This fast reduction is used in our squaring method. •We propose a new algorithm for squaring elements in binary finite field extensions.•The algorithm is very efficient for squaring elements defined using any low weight polynomial.•A general efficient algorithm for polynomial modular reduction of any weight is described.•The square algorithm is extended to finite field extensions of any odd characteristic.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2017.12.002