Fast lattice reduction for F2-linear pseudorandom number generators

An efficient lattice reduction method for F2-linear pseudorandom number generators using Mulders and Storjohann algorithm

On the F2-linear relations of Mersenne Twister pseudorandom number generators

Sequence generators obtained by linear recursions over the two-element field F2, i.e., F2-linear generators, are widely used as pseudorandom number generators. For example, the Mersenne Twister MT19937 is one of the most successful applications. An advantage of such generators is that we can assess them quickly by using theoretical criteria, such as the dimension of equidistribution with v-bit ...

Lattice Structure of Nonlinear Pseudorandom Number Generators in Parts of the Period

Recently, we showed that an extension of Marsaglia’s lattice test for segments of sequences over arbitrary fields and the linear complexity profile provide essentially equivalent quality measures for the intrinsic structure of pseudorandom number sequences. More precisely, the knowledge of the linear complexity profile yields a value S such that the largest dimension for passing the above latti...

On the linear complexity and lattice test of nonlinear pseudorandom number generators

One of the main contributions which Harald Niederreiter made to mathematics is related to pseudorandom sequences theory. In this paper we study several measures for asserting the quality of pseudorandom sequences, involving generalizations of linear complexity and lattice tests and relations between them.

Aperiodic pseudorandom number generators based on infinite words

In this paper we study how certain families of aperiodic infinite words can be used to produce aperiodic pseudorandom number generators (PRNGs) with good statistical behavior. We introduce the well distributed occurrences (WELLDOC) combinatorial property for infinite words, which guarantees absence of the lattice structure defect in related pseudorandom number generators. An infinite word u on ...