Embedding information in physically generated random bit sequences while maintaining certified randomness

¹ Department of Physics, Bar-Ilan University - Ramat-Gan 52900, Israel
² Gonda Interdisciplinary Brain Research Center, and the Goodman Faculty of Life Sciences, Bar-Ilan University Ramat-Gan 52900, Israel
³ Department of Physics, The Jack and Pearl Resnick Institute for Advanced Technology, Bar-Ilan University Ramat-Gan, 52900 Israel
⁴ Department of Applied Mathematics, Jerusalem College of Technology (JCT) - Jerusalem, Israel

^(b) ido.kanter@biu.ac.il

Received: 28 August 2019
Accepted: 17 October 2019

Abstract

Ultrafast physical random bit generation at hundreds of Gb/s rates, with verified randomness, is a crucial ingredient in secure communication and has recently emerged using optics-based physical systems. Here we examine the inverse problem and measure the ratio of information bits that can be systematically embedded in a random bit sequence without degrading its certified randomness. These ratios exceed 0.01 in experimentally obtained long random bit sequences. Based on these findings we propose a high-capacity private-key cryptosystem with a finite key length, where the existence as well as the content of the communication is concealed in the random sequence. Our results call for a rethinking of the current quantitative definition of practical classical randomness as well as the measure of randomness generated by quantum methods, which have to include bounds using the proposed inverse information embedding method.