^{1} Department of Mathematics, Technical University of Denmark^{2} Department of Applied Mathematics and Computer Science, Technical University of Denmark^{3} Macquarie University^{4} Macquarie University

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.

Type:

Journal article

Language:

English

Published in:

Canadian Journal of Mathematics, 2005, Vol 57, Issue 2, p. 338-350