Certain exponential sums and random walks on elliptic curves

Tanja Lange*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)338-350
Number of pages13
JournalCanadian Journal of Mathematics
Issue number2
Publication statusPublished - Apr 2005


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