Geodesic
Character Sums with Division Polynomials
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 850-857

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DOI

We obtain nontrivial estimates of quadratic character sums of division polynomials ${{\text{ }\!\!\psi\!\!\text{ }}_{n}}\left( P \right)$ , $n\,=\,1,\,2,\,\ldots $ , 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.
DOI : 10.4153/CMB-2011-126-x
Mots-clés : 11L40, 14H52, division polynomial, character sum 
Shparlinski, Igor E.; Stange, Katherine E. Character Sums with Division Polynomials. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 850-857. doi: 10.4153/CMB-2011-126-x
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     title = {Character {Sums} with {Division} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {850--857},
     year = {2012},
     volume = {55},
     number = {4},
     doi = {10.4153/CMB-2011-126-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-126-x/}
}
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