On the power generator and its multivariate analogue

Alina Ostafe, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We obtain a new estimate on the discrepancy of the power generator over a part of the period that improves several previous results. We also introduce a multidimensional analogue and show that the corresponding vector sequence is uniformly distributed, provided it is of a sufficiently large period. This result is based on a recent estimate of T. Cochrane and C. Pinner on binomial exponential sums. Our construction extends the class of nonlinear pseudorandom number generators for which a power saving against the trivial bound is possible in estimates of their discrepancy. It has several additional properties such as high nonlinearity and inhomogeneity which may be useful for its cryptographic applications.

Original languageEnglish
Pages (from-to)238-249
Number of pages12
JournalJournal of Complexity
Issue number2
Publication statusPublished - Apr 2012


Dive into the research topics of 'On the power generator and its multivariate analogue'. Together they form a unique fingerprint.

Cite this