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arXiv · 0912.5246

Character sums with division polynomials

Igor E Shparlinski·Katherine E. Stange
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Abstract

We obtain nontrivial estimates of quadratic character sums of division polynomials $\Psi_n(P)$, $n=1,2, ...$, 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 $q^{1/2 + \epsilon}$ for some fixed $\epsilon > 0$. This work is motivated by an open question about statistical indistinguishability of some cryptographically relevant sequences which has recently been brought up by K. Lauter and the second author.

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Igor E Shparlinski, Katherine E. Stange. 2009-12-29. Character sums with division polynomials. https://doi.org/10.4153/cmb-2011-126-x

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