An amplified spontaneous emission (ASE) light source using an Er-doped fiber is an ideal random-number source in principle because ASE originates from vacuum fluctuations. Interferometrically measured ASE light directly reflects vacuum fluctuations in phase space; the interferometer does not need to be stabilized because the phase is completely random, and measurable random numbers are a continuous variable because vacuum fluctuations are continuous. These characteristics make the random-number source practical and ideal. Evaluated randomness was sufficiently ideal at the accuracy level of measurements and evaluations.

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The unit of random numbers is ${{10}^6}$. Uniformity and proportion are evaluated for 1000 units. ${f_{\rm r}} = {0}.{625}\;{\rm GSps}$. When a test consists of multiple terms, the worst case is shown. Typical criteria are ${P} \mbox{-} {{\rm value}_T} \ge {0}.{0001}$ and proportion $ \ge \;{980/1000}$.

Failure counts for the 188 terms are shown. U denotes the uniformity test, and P denotes the proportion test. When both tests result in a zero count, each test is a “pass.” The tests use 1000 or 2000 units of random-number sequences. Each test was performed 4 times for the 1000-unit case and twice for the 2000-unit case at each sampling rate. The 2000-unit case used the same data as the 1000-unit case. The numbers indicated in parentheses in (c) express the counts of the values larger than the pass range under the ${2}\sigma $ condition. The failure counts in the differential data are reasonable, judging from their statistical fluctuations.

Table 3.

Failure Counts and Rates in the NIST SP800-22 Test

The rows labelled “${3}\sigma $” and “${2}\sigma $” indicate the results of the two-sided test, and the row labelled “${2}\sigma $ (lower side)” indicates the results of a one-sided test.

The unit of random numbers is ${{10}^6}$. Uniformity and proportion are evaluated for 1000 units. ${f_{\rm r}} = {0}.{625}\;{\rm GSps}$. When a test consists of multiple terms, the worst case is shown. Typical criteria are ${P} \mbox{-} {{\rm value}_T} \ge {0}.{0001}$ and proportion $ \ge \;{980/1000}$.

Failure counts for the 188 terms are shown. U denotes the uniformity test, and P denotes the proportion test. When both tests result in a zero count, each test is a “pass.” The tests use 1000 or 2000 units of random-number sequences. Each test was performed 4 times for the 1000-unit case and twice for the 2000-unit case at each sampling rate. The 2000-unit case used the same data as the 1000-unit case. The numbers indicated in parentheses in (c) express the counts of the values larger than the pass range under the ${2}\sigma $ condition. The failure counts in the differential data are reasonable, judging from their statistical fluctuations.

Table 3.

Failure Counts and Rates in the NIST SP800-22 Test

The rows labelled “${3}\sigma $” and “${2}\sigma $” indicate the results of the two-sided test, and the row labelled “${2}\sigma $ (lower side)” indicates the results of a one-sided test.