Improving random number generators on micro-computers
The short and concise conclusion of this report reads mainly: The prudent (user of program packages) examines the [statistical] characteristics of embedded random number generators (RNG) before application, and that not only derived from its complete output sequence as a whole entity, but also from (n-tuples and) subsequences thereof, selected in the same way as actually in the envisaged application. - Herein with ``Embedded RNG'' is meant: RNG belonging to a package offered in the market, but distributed without any sufficient description of its implementation (which situation tends to become more and more a common habit) and without any substantial warranty concerning originator and use within the package. Conditio sine qua non: The RNG can be called and examined separately and independently from the rest of the package by the user applying statistical tests to the output via calling programs. The report itself describes an actual examination of three such RNG's - no identification given, only results - and subsequent trials of successively improving their weakness by modifying their output with the output of the same or another weak RNG (without revealing more of this latter one) along the lines of other authors. As main indicator for weakness (failure) is emphasized the outcome of tests for ``low order serial correlation'' i.e. auto-correlation of the output with shifts (``lags'') of up to 16 places. The improvements are guided by qualitative considerations on the effect of the details and parameters of the modifications and by judging the numerical results of the main test and a set of other tests recommended in the standard (and mentioned) literature. For this a special described classifying tabular scheme is employed.
auto-correlation of the output with shifts
scientific article; zbMATH DE number 4141371