Pseudo-random number generation with β-encoders

International Journal of Mathematics for Industry, vol. 16

Abstract

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.

Authors 3

1. Charlene Kalle Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The Netherlands

2. Evgeny A. Verbitskiy Aachen Mathematisch Instituut

   Leiden University · University of Amsterdam

   Affiliation as printed

   Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The Netherlands

   Mathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The Netherlands

3. Benthen Zeegers Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut, Leiden University, Niels Bohrweg 1, 2333CA Leiden, The Netherlands