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1. CMB 2011 (vol 55 pp. 850)

Shparlinski, Igor E.; Stange, Katherine E.
Character Sums with Division Polynomials
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.

Keywords:division polynomial, character sum
Categories:11L40, 14H52

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