Certain Exponential Sums and Random Walks on Elliptic Curves
Tanja Lange, Igor E. Shparlinski · Canadian Journal of Mathematics · 2005
Abstract 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, … , kzT 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.