  Ultrafast physical random bit generation at hundreds of Gb/s rates, with
verified randomness, is a crucial ingredient in secure communication and have
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.

Signal Processing;Chaotic Dynamics;Computational Physics