A multiple recursive non-linear congruential pseudo random number generator

1987-9
Eichenauer, Johanna
Grothe, Heather L.
Lehn, Juergen
Topuzoglu, Alev
On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n≥0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n≥0, the sequence of non-negative integers with xN(n)≢0 (mod p). The non-linear generator is defined by zn≡xN(n)+1·x −1N(n) (mod p), n≥0, where x −1N(n) denotes the inverse element of xN(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length pr and all (p−1)r r-tupels (y1,...,yr) with 1≤y1,...,yr≤p are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2].

Citation Formats
J. Eichenauer, H. L. Grothe, J. Lehn, and A. Topuzoglu, “A multiple recursive non-linear congruential pseudo random number generator,” Manuscripta Mathematica, vol. 59, no. 3, pp. 331–346, 1987, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52239.