Geradores de Números Pseudo-Aleatórios baseados em Recorrências Lineares sobre GF(2^e)

In this work we introduce new PRNGs based on linear recurrences over the Galois field GF(2^e). We analyze the period properties of the linear recurrence and identify the conditions under which the proposed PRNGs achieve the maximum period of 2^e − 1. A logical circuit diagram using balanced binary tree structures is proposed and its complexity is analyzed. The statistical quality of the proposed PRNGs is evaluated using the NIST and TestU01 statistical test suites. The results show that, for specific configurations, the PRNGs pass all the applied tests.