Low-Complexity Bit-Parallel Square Root Computation over GF(2^) for All Trinomials

In this contribution, we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied to any type of irreducible polynomials. We derive explicit formulas for the space and time complexities associated with the square ro...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. 57; no. 4; pp. 472 - 480
Main Authors: Rodriguez-Henriquez, F., Morales-Luna, G., Lopez, J.
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Complexity theory
Computation
Computational efficiency
Computations in finite fields
Computer arithmetic
Computing time
Delay
Elliptic curves
Equations
Finite element methods
Galois fields
Hardware
Logic gates
Mathematical analysis
Operators
Polynomials
Roots
Computations in finite fields
Computer arithmetic
Algorithms
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:In this contribution, we introduce a low-complexity bit-parallel algorithm for computing square roots over binary extension fields. Our proposed method can be applied to any type of irreducible polynomials. We derive explicit formulas for the space and time complexities associated with the square root operator when working with binary extension fields generated using irreducible trinomials. We show that, for those finite fields, it is possible to compute the square root of an arbitrary field element with equal or better hardware efficiency than the one associated with the field squaring operation. Furthermore, a practical application of the square root operator in the domain of field exponentiation computation is presented.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2007.70822