Abstract
AbstractWe obtain nontrivial estimates of quadratic character sums of division polynomials Ψn(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 q1/2+∈ for some fixed ∈ > 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.
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