Paper 2006/133

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

Francisco Rodríguez-Henríquez, Guillermo Morales-Luna, and Julio López-Hernández

Abstract

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 for any type of irreducible polynomials. We derive explicit formulae for the space and time complexities associated to 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 to the field squaring operation. Furthermore, a practical application of the square root operator in the domain of field exponentiation computation is presented. It is shown that by using as building blocks squarers, multipliers and square root blocks, a parallel version of the classical square-and-multiply exponentiation algorithm can be obtained. A hardware implementation of that parallel version may provide a speedup of up to 50\% percent when compared with the traditional version.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
number theoryimplementation
Contact author(s)
francisco @ cs cinvestav mx
History
2006-04-03: received
Short URL
https://ia.cr/2006/133
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2006/133,
      author = {Francisco Rodríguez-Henríquez and Guillermo Morales-Luna and Julio López-Hernández},
      title = {Low Complexity Bit-Parallel Square Root Computation over {GF}($2^m$) for all Trinomials},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/133},
      year = {2006},
      url = {https://eprint.iacr.org/2006/133}
}
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