Abstract view
Certain Exponential Sums and Random Walks on Elliptic Curves


Published:20050401
Printed: Apr 2005
Tanja Lange
Igor E. Shparlinski
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 sequence
$\cZ=\(z_1, \dots, z_T\)$
such that $k z_1,\dots, kz_T $ is a permutation of
$z_1, \dots, z_T$, 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.
MSC Classifications: 
11L07, 11T23, 11T71, 14H52, 94A60 show english descriptions
Estimates on exponential sums Exponential sums Algebraic coding theory; cryptography Elliptic curves [See also 11G05, 11G07, 14Kxx] Cryptography [See also 11T71, 14G50, 68P25, 81P94]
11L07  Estimates on exponential sums 11T23  Exponential sums 11T71  Algebraic coding theory; cryptography 14H52  Elliptic curves [See also 11G05, 11G07, 14Kxx] 94A60  Cryptography [See also 11T71, 14G50, 68P25, 81P94]
