Introduction

Ever since the antiquity, random number generation has played an important role both in common everyday life activities, such as leisure games, as well as in the advancement of science. One of the oldest ways in which humans generated random numbers has been through the use of dice. It does not seem to be known when dice were invented, but they have been employed since ancient times, alongside with coin flipping, for predicting the future, decision-making, fortune-telling, gambling, dispute resolution, and leisure games. The bias in the case of coin tossing has been studied extensively^[1],

Currently used for all these and also Monte Carlo simulations, game decisions, and cryptography

which fields of cryptography?

The theory behind the generation of random numbers, as well as the ability to potentially predict the outcome of this process, has been heavily studied by mathematics, in an attempt to either ensure the randomness of the process or gain an advantage in correctly predicting its future outcomes. In particular, probability theory is one of the main mathematical fields relevant to random number generation.

cryptographically secure random number generator

Random numbers have also been employed in cryptography, exactly due to their properties. This fact, in conjunction with the ongoing digitalisation of our world, has, more recently, led to an interest in random number generation within the framework of computer science. In this context, random number generation systems are classified into two main categories: PseudoRandom Number Generators (PRNGs) and True Random Number Generators, with the former generating sequences of numbers that appear to be random, but are in fact completely predictable when the initial value (being referred to as the seed) and conditions used for the number generation process are known, and with the latter generating truly random sequences of numbers that can only be predicted (correctly) with negligible probability, even if the initial value and conditions are known.

Chaos, deterministic, yet rather "random"

Quantum effects, truly random and unpredictable

Repetition^[1]

Coin tossing leads to bits...

Random Number Generation Systems in Computer Science

Pseudorandom number generation, based on algorithms

True random number Generators