Uniformly distributed sequences in computer algebra or how to construct program generators of random numbers (Q1269954)

The author surveys work, mostly by himself and M. V. Larin, on a purely algebraic approach to the problem of pseudorandom number generation. In this approach, the model is that of a finite universal algebra over which a sequence is generated by a given polynomial recursion. The main question the author addresses is when the generated sequence has the maximum possible period length. A detailed account of results for the most useful finite universal algebras is given. Statistical properties of the generated sequences are discussed only on a modest scale. For the proofs, the author refers mostly to Russian sources, some of which are not easily accessible in the West.