Compact, digital pseudo-random number generator

Introduction: Many applications require the realization of a random number generator featuring some desirable properties [1]; often such a device is at the very heart of a system. Examples of applications in the electronic field include cryptography, for which the period length serves as a minimum protection versus brute force attacks, and initialization of parameters for training of neural networks. We require that the system generates a sequence of numbers featuring good statistical properties, i.e. as uniform as possible. In the case of cryptography reproducibility is also crucial; in general, when the system requires a repeatable sequence, a pseudo random sequence is needed, that is, a sequence generated by a single number (the seed) by a chaotic process simulating randomness, as opposed to real noise generators. We would like to obtain the longest possible period before the repetition of the sequence. Moreover, when the generator algorithm is planned to be translated into hardware, the preference will be for the simplest circuit. The proposed scheme features a good statistical behavior, easy scalability to increase the length of the period, very simple realization with digital hardware, and the ability to produce also the zero value as part of the output sequence, thus implementing a random variable with values in [0, 255) as often assumed by applications, without requiring additional computations that would reduce the compactness of the circuit.