http://dx.doi.org/10.4153/CMB-2011-126-x
8 pages
Published:2011-06-27
Igor E. Shparlinski, Department of Computing, Macquarie University, North Ryde, Sydney, NSW 2109, Australia Katherine E. Stange, Department of Mathematics, Stanford University, Stanford, CA 94305, USA
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Abstract
We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, \dots$, evaluated at a given point $P$ on an elliptic curve over a finite field of $q$ elements. Our bounds are nontrivial if the order of $P$ is at least $q^{1/2 + \varepsilon}$ for some fixed $\varepsilon > 0$. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences that was recently brought up by K. Lauter and the second author.
© Canadian Mathematical Society, 2012
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