Inversive Congruential Generator - Advantages of CIG

Advantages of CIG

The CIG are accepted for practical purposes for a number of reason.

Firstly, binary sequences produced in this way are free of undesirable statistical deviations. Inversive sequences extensively tested with variety of statistical tests remain stable under the variation of parameter.

Secondly, there exists a steady and simple way of parameter choice, based on the Chou algorithm that guarantees maximum period length.

Thirdly, compound approach has the same properties as single inversive generators but it also provides period length significantly greater than obtained by a single Inversive Congruential Generator. They seem to be designed for application with multiprocessor parallel hardware platforms.

There exists an algorithm which allows designing compound generators with predictable period length, predictable linear complexity level, with excellent statistical properties of produced bit streams.

The procedure of designing this complex structure starts with defining finite field of p elements and ends with choosing the parameters a and c for each Inversive Congruential Generator being the component of the compound generator. It means that each generator is associated to a fixed IMP polynomial. Such a condition is sufficient for maximum period of each Inversive Congruential Generator and finally for maximum period of the compound generator. The construction of IMP polynomials is the most efficient approach to find parameters for Inversive Congruential Generator with maximum period length.