Fig. 1. Efficiency of extracting bits from raw unbiased random sequence. a+b represents for a group of required probability. For each probability with parameter a+b, the corresponding discrete points in this figure represents the minimum combined bit (n) it requires. When more combined bits are required, the efficiency of the algorithm will be lower.

Fig. 2. Experimental setup.

Fig. 3. (a) Bias |e[N]| versus the sample size of the generated bRN sequence; red line is its 3-standard-deviation line, 3σe=(3N−1/2)/2, where N=1,2,3,…, 16 Mbits; (b) autocorrelation coefficient R[k] as a function of the delay bit k for a 16×106 output URN stream; red line is its corresponding 3-standard-deviation line, 3σc=3N−1/2, where N=16  Mbits.

Fig. 4. (a) Autocorrelation of uRNs (p1:p0=3∶1) generated from our adjustable UQRNG. Average value within 100 bit delay is 2.96×10−4; (b) autocorrelation of URNs (p1:p0=3∶1) converted from BRNs generated by Quantis. Average value within 100 bit delay is −1.56×10−4.

Fig. 5. Min-entropy evaluation.

Table 1. Typical Result of NIST Statistical Tests