TY - JOUR

T1 - Character sums with division polynomials

AU - Shparlinski, Igor E.

AU - Stange, Katherine E.

PY - 2012/12

Y1 - 2012/12

N2 - We obtain nontrivial estimates of quadratic character sums of division polynomialsΨn(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+ε for some fixed ε > 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.

AB - We obtain nontrivial estimates of quadratic character sums of division polynomialsΨn(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+ε for some fixed ε > 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.

UR - http://www.scopus.com/inward/record.url?scp=84871772074&partnerID=8YFLogxK

U2 - 10.4153/CMB-2011-126-x

DO - 10.4153/CMB-2011-126-x

M3 - Article

AN - SCOPUS:84871772074

SN - 0008-4395

VL - 55

SP - 850

EP - 857

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -