Pseudo-random number generation with β-encoders

The [Formula: see text]-encoder is an analog circuit that converts an input signal [Formula: see text] into a finite bit stream [Formula: see text]. The bits [Formula: see text] are correlated and therefore are not immediately suitable for random number generation, but they can be used to generate bits [Formula: see text] that are (nearly) uniformly distributed. In this paper, we study two such methods. In the first part the bits [Formula: see text] are defined as the digits of the base-2 representation of the original input x. Under the assumption that there is no noise in the amplifier we then study a question posed by Jitsumatsu and Matsumura on how many bits [Formula: see text] are needed to correctly determine the first n bits [Formula: see text]. In the second part, we show this method fails for random amplification factors. Nevertheless, even in this case, nearly uniformly distributed bits can still be generated from [Formula: see text] using modern cryptographic techniques.