%0 Journal Article
%T Character sums with division polynomials
%A Igor E Shparlinski
%A Katherine E. Stange
%J Mathematics
%D 2009
%I arXiv
%R 10.4153/CMB-2011-126-x
%X 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.
%U http://arxiv.org/abs/0912.5246v4