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Title:
Square root computation over even extension fields
Authors: Gora Adj, 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.
ePrint: https://eprint.iacr.org/2012/685
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