The generation of random sequences is the basis of simulation and can be used in many different areas such as Statistics, Computer Science, Systems Management and Control, Biology, Particle Physics, Cryptography or Cyber-Security, among others. It is crucial that the numbers generated were random or at least, behave as such. The fundamental statistical properties required for such sequences are randomness and independence and, from a cryptographic perspective, unpredictability. There is a variety of methods to generate these sequences. The main ones are physical and arithmetic methods. In this work, a detailed study of the main arithmetic methods is carried out. On the other hand, the necessity of secure sequence generation will be analyzed and new lines of ongoing research focusing applications in Internet of Things and new generator designs will be described.
"A brief and understandable guide to pseudo-random number generators and specific models for security." Statist. Surv. 16 137 - 181, 2022. https://doi.org/10.1214/22-SS136