Fast lattice reduction for $\mathbf {F}_{2}$-linear pseudorandom number generators

Fast lattice reduction for F2-linear pseudorandom number generators

Sequences generated by an F2-linear recursion have wide applications, in particular, pseudorandom number generation. The dimension of equidistribution with v-bit accuracy is a most important criterion for the uniformity of the generated sequence. The fastest known method for computing these dimensions is proposed by Couture and L’Ecuyer, based on Lenstra’s lattice basis reduction and the dual l...

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

Fast and Small Nonlinear Pseudorandom Number Generators for Computer Simulation

In this paper we present Tyche, a nonlinear pseudorandom number generator designed for computer simulation. Tyche has a small 128-bit state and an expected period length of 2. Unlike most nonlinear generators, Tyche is consistently fast across architectures, due to its very simple iteration function derived from ChaCha, one of today’s fastest stream ciphers. Tyche is especially amenable for the...

Empirical Pseudorandom Number Generators

The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”grow-and-cut procedure”. We extend this concept to real numbers and call this the real congruence, which produces another class of random number...

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.