In this paper, we present approaches to generating random numbers, along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches, presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses, as well as their potential application domains, so that the reader can judge what would be the best approach for the application at hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed; then, suitable preprocessing can enhance its randomness; then, the output of preprocessing can feed different types of generators, e.g., a linear congruential generator, a cryptographically secure one and one based on the combination of one-way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined, giving the final random sequence. Moreover, we present a set of practical randomness tests that can be applied to the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e., eLotteries and cryptographic key generation.

This paper we present approaches for generating random numbers along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses as well as their potential application domains so as the reader can judge what would be the best approach for the application in hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed, then suitable preprocessing can enhance its randomness and then the output of the preprocessing can feed different types of generators, e.g. a linear congruential generator, a cryptographically secure one and one based on the combination of one way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined giving the final random sequence. Moreover, we present a set of practical randomness tests which can be applied on the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e. eLotteries and cryptographic key generation.