The present method generates machine-independent uniform random sequences of real numbers in the interval (0.,1.) excluding 1. It uses a set of up to 1024 independent multiplicative congruential generators working with:• modulii which are chosen prime numbers whose values have been fixed according to the positive 31-bit positive integer arithmetic available and in the form of 2.P'+1, where P's are also primes.• multipliers which are selected from one of their corresponding primitive elements as multipliers to achieve each full cycle independently. The "astronomical" maximum periodicity can be considered as infinite: O (10 6021 ) ; it can be adjusted if required by the user in the sequential version RAN01 or statistically reaching the maximum in the improved "stagger" version DAN01. An "acceptable" composite period is estimated to be O (10 189 ) for a set of only 32 of such independent generators: this fact could find a nice application in the realization of efficient hash-functions in smart cards.An implementation in structured FORTRAN 77 shows very good results in terms of statistical proprieties, velocity and periodicity.
ACM SIGSAC Review – Association for Computing Machinery
Published: Feb 1, 1989