Inversive generator of the second order with a variable shift for the sequence of PRN's

Abstract. The inversive congruential generator of second order modulo a prime power is investigated. This generator generalizes the inversive congruential generator of the first order studied in the works of Eichenauer, Lehn, Topuzoǧlu, Niederreiter, Shparlinski etc. Also we prove that the produced sequences of pseudo random numbers pass the \(s\)-dimensional test on the uniform distribution for \(s=1,2,3\).