TY - JOUR
T1 - Certain exponential sums and random walks on elliptic curves
AU - Lange, Tanja
AU - Shparlinski, Igor E.
PY - 2005/4
Y1 - 2005/4
N2 - For a given elliptic curve E, we obtain an upper bound on the discrepancy of sets of multiples zsG where zs runs through a sequence Z = (z1,..., zT-) such that kz1,..., kz T is a permutation of z1,..., zT, both sequences taken modulo t, for sufficiently many distinct values of k modulo t. We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.
AB - For a given elliptic curve E, we obtain an upper bound on the discrepancy of sets of multiples zsG where zs runs through a sequence Z = (z1,..., zT-) such that kz1,..., kz T is a permutation of z1,..., zT, both sequences taken modulo t, for sufficiently many distinct values of k modulo t. We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.
UR - http://www.scopus.com/inward/record.url?scp=17044431081&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:17044431081
SN - 0008-414X
VL - 57
SP - 338
EP - 350
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 2
ER -