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Ultrafast physical random bit generation at hundreds of Gb/s rates, withverified randomness, is a crucial ingredient in secure communication and haverecently emerged using optics based physical systems. Here we examine theinverse problem and measure the ratio of information bits that can besystematically embedded in a random bit sequence without degrading itscertified randomness. These ratios exceed 0.01 in experimentally obtained longrandom bit sequences. Based on these findings we propose a high-capacityprivate-key cryptosystem with a finite key length, where the existence as wellas the content of the communication is concealed in the random sequence. Ourresults call for a rethinking of the current quantitative definition ofpractical classical randomness as well as the measure of randomness generatedby quantum methods, which have to include bounds using the proposed inverseinformation embedding method.

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