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.Introduction. -Emerging classical and quantum secure communication methods rely on long, truly random, bit strings, which are used to scramble the information by applying mathematical functions. The mathematical definition of an ideal process for generating random bit sequences is straightforward -the next bit in the sequence is zero or one with equal probability independent of the previous bits. However, from a practical viewpoint, given a seemingly random sequence, how can one be sure that it is indeed random? It is possible that such a question is impossible to answer. Under such circumstances what does it imply about secure communications?Two decades ago the only available fast random bit generators (RBGs) were based on pseudo-random generators [1,2].The security using such random bit sequences is, however, undermined as a result of the deterministic nature of their generation. Concern about security has become even greater with the emergence of more sophisticated attacks on the growing communication networks with ever-increasing numbers of end users. The emergence of non-deterministic ultrafast physical RBGs began in 2008, based on the combined threshold and XOR gated bit outputs of two chaotic diode lasers, producing 1.7 Gb/s random bits with certified randomness [3]. The physical implementation required some constraints such as an incommensurate ratio between the lengths of the external laser cavities of the two similar lasers. A method based on a single chaotic laser whose chaotic intensity fluctuations are digitized and multi-bit extracted ( fig. 1) was introduced in 2009 and produced 12.5 Gb/s [4]. Subsequently, the single laser method was generalized and achieved generation rates of 300 Gb/s with certified randomness using higher order derivatives of the digitized signal [5]. This method has been further adopted and generalized [6,7] with rates moving toward Tb/s [8,9] using many variants including different types of lasers[10-