Character Sums with Division Polynomials

Canadian mathematical bulletin

Igor E. Shparlinski²  Katherine E. Stange¹ 

[1] Department of Mathematics, Stanford University, Stanford, CA 94305, USA;Department of Computing, Macquarie University, North Ryde, Sydney, NSW 2109, Australia

关键词: division polynomial;    character sum;   

DOI  :  10.4153/CMB-2011-126-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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.

【 授权许可】

Unknown