Paper 2012/685

Square root computation over even extension fields

Gora Adj and Francisco Rodríguez-Henríquez

Abstract

This paper presents a comprehensive study of the computation of square roots over finite extension fields. We propose two novel algorithms for computing square roots over even field extensions of the form $\F_{q^{2}}$, with $q=p^n,$ $p$ an odd prime and $n\geq 1$. Both algorithms have an associate computational cost roughly equivalent to one exponentiation in $\F_{q^{2}}$. The first algorithm is devoted to the case when $q\equiv 1 \bmod 4$, whereas the second one handles the case when $q\equiv 3 \bmod 4$. Numerical comparisons show that the two algorithms presented in this paper are competitive and in some cases more efficient than the square root methods previously known.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
Modular square rootfinite field arithmeticLegendre symbol
Contact author(s)
francisco @ cs cinvestav mx
History
2013-07-18: last of 5 revisions
2012-12-10: received
See all versions
Short URL
https://ia.cr/2012/685
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/685,
      author = {Gora Adj and Francisco Rodríguez-Henríquez},
      title = {Square root computation over even extension fields},
      howpublished = {Cryptology ePrint Archive, Paper 2012/685},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/685}},
      url = {https://eprint.iacr.org/2012/685}
}
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