Abstract
For a given elliptic curve E, we obtain an upper bound
on the discrepancy of sets of
multiples z_sG where z_s runs through a sequenc
Z=(z_1, \ldots ,z_T)
such that k= z_1,..., kz_T is a permutation of
z_1,...,z_T, both sequences taken modulo t, for
sufficiently many distinct modulo t values of k.
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.
Original language | English |
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Journal | Canadian Journal of Mathematics - Journal Canadien de Mathématiques |
Volume | 57 |
Issue number | 2 |
Pages (from-to) | 338-350 |
ISSN | 0008-414X |
Publication status | Published - 2005 |