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 -