For a given elliptic curve $E$, we obtain an upper boundon the discrepancy of sets ofmultiples $z_sG$ 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 $t$, forsufficiently many distinct values of $k$ modulo $t$.We apply this result to studying an analogue of the power generatorover an elliptic curve. These results are elliptic curve analoguesof those obtained for multiplicative groups of finite fields andresidue rings.
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机译：对于给定的椭圆曲线$ E $，我们获得一个上界，即多个$ z_sG $集的差异，其中$ z_s $通过序列$ cZ =（z_1，点，z_T）$使得$ k z_1，dots，kz_T $是$ z_1，点，z_T $的排列，两个序列均以$ t $取模，足够$ k $取$ t $取模的许多不同值。我们将此结果应用于研究椭圆曲线上的发电机类似物。这些结果是有限域和残环的乘法组获得的椭圆曲线类似物。
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