The National Institute of Standarization and Technology (NIST) Statistical Test Suite (STS) for Random Number Generators. See http://csrc.nist.gov/rng/ USED INPUT PARAMETERS ===================== Although this testsuite allows a lot of parameters to be specified, the results of the test become meaningless when the parameters are not picked to be what was intended. It took quite some effort (reading the documentation of the testsuite) to figure out what the optimal values are. For example, http://csrc.nist.gov/rng/SP800-22b.pdf paragraph 2.7.7 says "The test code has been written to assume a sequence length of n = 10^6 (entered via a calling parameter) and M = 131072 (hard coded). If values other than these are desired, be sure that M > 0.01 · n and N = [n/M]." Hence, we need to use bitstream sizes of 1,000,000: It is also my experience that with larger bitstreams (I tried 5,000,000) the FFT Test starts to fail; the reason seems to be that the spreading of the p-values become less than the accuracy of the builtin threshold. $ assess 1000000 This value must be > 0.01n = 10,000. Enter Block Frequency Test block length: 50000 This value must be 9 or 10: Enter NonOverlapping Template Test Block Length: 9 This value must be 9 or 10: Enter Overlapping Template Test Block Length: 9 With n == 1000000, this must be 7 and 1280. See a table in the .pdf file. Enter Universal Test Block Length: 7 Enter Universal Test Number Of Initialization Steps: 1280 This must be m < [log2 n] - 2 = 17.9. It is my experience that problems occur already at 14 though, which was reproduced for true random bitstreams of other sources (I mailed NIST, no reply yet). Enter Approximate Entropy Test Block Length: 3 Also here, must be < [log2 n] - 2 = 17.9. Enter Serial Test Block Length: 16 For this test, n must be >= 1000000 (ok thus), and 500 <= M <= 5000 where n/M >= 200. Enter Linear Complexity Test Subsequence Length: 1000 Our input file is 512,000,000 bits, so we can specify 512 bitstreams: How many bitstreams should be generated? 512 All tests are being passed. ------------------------------------------------------------------------------ RESULTS FOR THE UNIFORMITY OF P-VALUES AND THE PROPORTION OF PASSING SEQUENCES ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 P-VALUE PROPORTION STATISTICAL TEST ------------------------------------------------------------------------------ 36 39 52 46 59 58 47 56 54 53 0.272977 0.9900 Frequency 59 52 49 45 63 58 35 43 50 46 0.177628 0.9860 Block-Frequency 40 43 52 53 51 53 48 54 59 47 0.775337 0.9860 Cusum 41 47 48 53 49 60 47 54 55 46 0.798139 0.9920 Cusum 53 46 50 46 44 51 47 50 60 53 0.916599 0.9900 Runs 60 50 47 44 48 53 42 60 50 46 0.662091 0.9820 Long-Run 54 56 45 54 47 52 45 49 44 54 0.931185 0.9860 Rank 50 67 54 55 57 54 49 42 33 39 0.042808 0.9960 FFT 44 48 52 49 47 50 46 46 54 64 0.743915 0.9880 Aperiodic-Template 54 62 39 46 42 60 51 54 45 47 0.331408 0.9840 Aperiodic-Template 50 54 52 43 39 44 57 58 49 54 0.624627 0.9860 Aperiodic-Template 56 47 35 51 58 49 49 56 40 59 0.270265 0.9860 Aperiodic-Template 36 51 44 60 49 57 47 47 53 56 0.444691 0.9940 Aperiodic-Template 54 60 48 46 54 41 53 45 53 46 0.755819 0.9900 Aperiodic-Template 46 61 56 54 50 36 55 48 51 43 0.411840 0.9940 Aperiodic-Template 42 57 58 50 56 54 46 44 52 41 0.603841 0.9900 Aperiodic-Template 44 48 55 56 52 42 56 46 52 49 0.873987 0.9900 Aperiodic-Template 40 46 51 53 46 46 49 56 68 45 0.284024 0.9920 Aperiodic-Template 43 46 47 51 59 46 57 50 58 43 0.670396 0.9820 Aperiodic-Template 46 51 53 46 42 53 47 60 47 55 0.820143 0.9900 Aperiodic-Template 47 43 61 54 52 41 54 51 53 44 0.653773 0.9900 Aperiodic-Template 38 53 43 46 46 60 56 54 52 52 0.546283 0.9940 Aperiodic-Template 60 44 54 46 51 40 49 49 55 52 0.739918 0.9880 Aperiodic-Template 56 49 49 59 47 48 53 40 54 45 0.775337 0.9920 Aperiodic-Template 51 43 49 45 53 62 49 41 58 49 0.583145 0.9860 Aperiodic-Template 47 39 57 52 56 53 51 44 47 54 0.759756 0.9880 Aperiodic-Template 54 52 54 51 43 47 58 39 54 48 0.739918 0.9860 Aperiodic-Template 58 57 49 61 49 39 48 41 47 51 0.433590 0.9920 Aperiodic-Template 57 50 52 58 47 56 44 47 49 40 0.723804 0.9880 Aperiodic-Template 47 63 48 36 47 48 53 54 44 60 0.272977 0.9940 Aperiodic-Template 52 53 44 47 44 57 60 46 46 51 0.786830 0.9940 Aperiodic-Template 46 41 50 52 59 47 43 61 56 45 0.490483 0.9920 Aperiodic-Template 50 51 51 55 61 39 44 48 55 46 0.637119 0.9920 Aperiodic-Template 47 54 42 51 46 61 47 46 52 54 0.794391 0.9900 Aperiodic-Template 38 46 51 65 53 56 57 42 46 46 0.241741 0.9960 Aperiodic-Template 40 47 48 54 43 54 46 57 51 60 0.616305 0.9860 Aperiodic-Template 43 52 55 43 53 59 45 49 58 43 0.624627 0.9900 Aperiodic-Template 47 66 43 44 61 62 41 43 47 46 0.080519 0.9940 Aperiodic-Template 50 61 51 53 51 44 46 41 55 48 0.751866 0.9840 Aperiodic-Template 65 55 57 49 54 46 49 45 36 44 0.224821 0.9880 Aperiodic-Template 47 51 43 40 62 42 60 51 61 43 0.173770 1.0000 Aperiodic-Template 65 49 52 48 59 51 39 45 42 50 0.310049 0.9920 Aperiodic-Template 54 40 52 54 58 55 51 43 46 47 0.739918 0.9840 Aperiodic-Template 61 44 40 50 47 46 45 42 65 60 0.125200 0.9860 Aperiodic-Template 48 51 49 55 50 42 51 39 52 63 0.554420 0.9940 Aperiodic-Template 56 54 39 51 62 41 49 40 51 57 0.275709 0.9860 Aperiodic-Template 57 40 53 56 48 49 50 45 50 52 0.870856 0.9920 Aperiodic-Template 47 53 54 46 37 50 56 57 50 50 0.731886 0.9860 Aperiodic-Template 51 48 49 54 46 60 50 43 60 39 0.518106 0.9980 Aperiodic-Template 43 69 53 45 45 48 52 46 42 57 0.206629 0.9960 Aperiodic-Template 71 56 48 47 34 55 47 45 57 40 0.024521 0.9820 Aperiodic-Template 51 60 48 39 45 49 50 46 60 52 0.591409 0.9800 Aperiodic-Template 49 51 58 50 41 50 53 50 43 55 0.867692 0.9900 Aperiodic-Template 60 51 56 56 41 41 47 54 47 47 0.579021 0.9920 Aperiodic-Template 46 49 48 49 49 57 54 40 55 53 0.880145 0.9940 Aperiodic-Template 56 57 43 55 38 43 51 51 61 45 0.350485 0.9880 Aperiodic-Template 51 40 44 50 38 67 50 40 67 53 0.022300 0.9860 Aperiodic-Template 58 53 46 49 38 46 48 52 61 49 0.574903 0.9860 Aperiodic-Template 46 48 54 48 58 44 50 57 58 37 0.490483 0.9940 Aperiodic-Template 48 51 51 52 54 49 38 47 46 64 0.550347 0.9920 Aperiodic-Template 53 41 40 48 48 57 45 58 51 59 0.498313 0.9920 Aperiodic-Template 41 45 50 48 52 49 54 45 50 66 0.510153 0.9900 Aperiodic-Template 39 57 58 44 61 50 43 53 39 56 0.206629 0.9900 Aperiodic-Template 34 43 43 53 45 66 49 62 49 56 0.056785 0.9980 Aperiodic-Template 54 57 42 57 44 47 53 42 53 51 0.727851 0.9900 Aperiodic-Template 59 43 44 57 46 42 47 46 54 62 0.383827 0.9880 Aperiodic-Template 44 70 47 46 35 52 52 54 51 49 0.114040 0.9920 Aperiodic-Template 51 43 34 53 49 37 55 58 66 54 0.049984 0.9860 Aperiodic-Template 49 53 44 52 46 48 51 45 56 56 0.948298 0.9900 Aperiodic-Template 48 40 56 46 58 52 41 53 44 62 0.360287 0.9900 Aperiodic-Template 55 52 49 51 51 35 42 58 55 52 0.506194 0.9860 Aperiodic-Template 56 51 45 50 42 53 54 52 48 49 0.955835 0.9920 Aperiodic-Template 55 57 42 50 50 46 46 43 62 49 0.607993 0.9880 Aperiodic-Template 48 50 54 57 49 39 58 36 50 59 0.301194 0.9900 Aperiodic-Template 49 52 46 48 42 48 56 58 56 45 0.827279 0.9860 Aperiodic-Template 56 55 53 50 45 53 48 40 47 53 0.873987 0.9920 Aperiodic-Template 53 34 46 53 50 46 49 62 50 57 0.350485 0.9900 Aperiodic-Template 40 38 40 50 57 55 63 55 50 52 0.195864 0.9920 Aperiodic-Template 46 37 52 48 56 56 52 45 52 56 0.670396 0.9920 Aperiodic-Template 54 63 47 50 42 45 50 50 47 52 0.747898 0.9940 Aperiodic-Template 55 39 43 58 47 46 50 54 48 60 0.526105 0.9920 Aperiodic-Template 53 49 46 51 52 36 61 52 54 46 0.566688 0.9900 Aperiodic-Template 44 48 52 49 47 50 46 46 54 64 0.743915 0.9880 Aperiodic-Template 45 42 47 54 46 61 55 47 46 57 0.637119 0.9860 Aperiodic-Template 57 46 52 60 53 46 35 52 43 56 0.337688 0.9880 Aperiodic-Template 45 38 46 50 54 49 53 59 50 56 0.682823 0.9880 Aperiodic-Template 50 41 43 55 44 63 42 54 53 55 0.394195 0.9900 Aperiodic-Template 49 54 63 50 52 49 56 39 44 44 0.494392 0.9960 Aperiodic-Template 50 45 44 60 48 44 46 52 41 70 0.120909 0.9940 Aperiodic-Template 42 43 55 57 41 56 42 57 52 55 0.444691 0.9940 Aperiodic-Template 54 58 57 61 35 61 43 43 54 34 0.022605 0.9880 Aperiodic-Template 56 47 47 47 53 48 57 58 47 40 0.743915 0.9900 Aperiodic-Template 43 60 44 39 55 47 58 43 62 49 0.215574 0.9900 Aperiodic-Template 54 45 52 64 50 45 59 44 48 39 0.337688 0.9820 Aperiodic-Template 54 57 43 54 63 46 55 48 40 40 0.284024 0.9900 Aperiodic-Template 40 51 47 47 61 44 52 57 55 46 0.595549 0.9940 Aperiodic-Template 57 49 50 52 44 51 49 44 58 46 0.900569 0.9920 Aperiodic-Template 51 48 39 55 43 62 53 52 50 47 0.603841 0.9880 Aperiodic-Template 59 42 49 50 46 56 54 43 52 49 0.801865 0.9920 Aperiodic-Template 46 53 47 53 39 58 42 51 54 57 0.620465 0.9940 Aperiodic-Template 46 55 60 44 43 56 58 45 52 41 0.463512 0.9860 Aperiodic-Template 49 46 56 42 63 61 39 51 42 51 0.220159 0.9940 Aperiodic-Template 52 51 47 37 50 43 41 55 57 67 0.140453 0.9900 Aperiodic-Template 49 45 32 58 49 52 51 48 60 56 0.262249 0.9940 Aperiodic-Template 56 49 42 49 54 55 53 52 45 45 0.903338 0.9900 Aperiodic-Template 42 50 51 55 42 50 59 47 52 52 0.830808 0.9960 Aperiodic-Template 48 55 50 42 51 48 42 51 51 62 0.723804 0.9920 Aperiodic-Template 56 45 61 50 51 41 62 50 42 42 0.295391 0.9940 Aperiodic-Template 57 50 59 52 43 52 41 52 39 55 0.498313 0.9960 Aperiodic-Template 63 44 49 55 54 53 41 47 50 44 0.570792 0.9940 Aperiodic-Template 40 53 58 52 55 44 44 52 51 51 0.779188 0.9860 Aperiodic-Template 34 49 59 49 60 46 48 63 42 50 0.128132 0.9980 Aperiodic-Template 44 49 69 53 55 44 45 47 38 56 0.135720 0.9860 Aperiodic-Template 58 49 42 58 52 47 43 51 44 56 0.682823 0.9880 Aperiodic-Template 50 52 44 55 53 41 51 52 64 38 0.350485 0.9800 Aperiodic-Template 43 50 51 44 45 39 41 55 72 60 0.030399 0.9920 Aperiodic-Template 48 60 51 67 53 45 41 42 40 53 0.135720 0.9840 Aperiodic-Template 51 49 66 48 50 53 48 41 44 50 0.550347 0.9900 Aperiodic-Template 49 57 63 56 44 47 49 37 53 45 0.344048 0.9960 Aperiodic-Template 70 48 55 51 48 40 45 53 50 40 0.146982 0.9900 Aperiodic-Template 56 37 47 60 49 54 49 47 47 54 0.603841 0.9960 Aperiodic-Template 56 38 51 43 39 56 50 53 49 65 0.189625 0.9840 Aperiodic-Template 53 48 56 50 47 53 57 40 54 42 0.747898 0.9880 Aperiodic-Template 57 50 33 62 45 61 44 50 53 45 0.123755 0.9840 Aperiodic-Template 46 52 54 49 52 38 56 46 63 44 0.452173 0.9940 Aperiodic-Template 41 50 44 53 56 45 56 50 48 57 0.786830 0.9940 Aperiodic-Template 39 54 58 49 53 64 46 45 46 46 0.383827 0.9900 Aperiodic-Template 57 47 43 45 57 56 62 44 44 45 0.422638 0.9880 Aperiodic-Template 47 53 55 54 50 45 49 40 57 50 0.861264 0.9960 Aperiodic-Template 52 52 46 47 47 52 53 58 54 39 0.823725 0.9780 Aperiodic-Template 58 54 44 51 54 45 53 43 49 49 0.886162 0.9860 Aperiodic-Template 42 42 49 49 55 53 42 66 46 56 0.295391 0.9940 Aperiodic-Template 52 39 52 45 42 60 54 50 58 48 0.530120 0.9840 Aperiodic-Template 43 41 61 45 45 50 52 58 55 50 0.546283 0.9960 Aperiodic-Template 60 42 50 42 48 47 43 50 58 60 0.429923 0.9900 Aperiodic-Template 53 62 45 55 39 39 48 59 49 51 0.301194 0.9960 Aperiodic-Template 53 55 44 58 51 42 45 46 48 58 0.723804 0.9860 Aperiodic-Template 56 42 43 57 51 54 51 50 41 55 0.695200 0.9860 Aperiodic-Template 52 47 54 51 44 53 54 44 52 49 0.976878 0.9860 Aperiodic-Template 47 54 48 49 50 54 54 53 55 36 0.755819 0.9880 Aperiodic-Template 42 48 60 57 56 44 58 53 47 35 0.217857 0.9960 Aperiodic-Template 56 58 50 47 48 45 42 50 57 47 0.816537 0.9920 Aperiodic-Template 53 49 50 40 52 58 46 61 43 48 0.599693 0.9860 Aperiodic-Template 45 49 45 62 52 49 50 49 52 47 0.892036 0.9920 Aperiodic-Template 45 47 47 47 48 47 53 56 50 60 0.897763 0.9900 Aperiodic-Template 43 53 53 51 51 61 44 47 48 49 0.851383 0.9940 Aperiodic-Template 49 58 53 47 46 42 48 56 50 51 0.906069 0.9900 Aperiodic-Template 45 53 63 48 40 50 47 47 57 50 0.587274 0.9940 Aperiodic-Template 46 57 54 50 44 50 45 64 46 44 0.554420 0.9940 Aperiodic-Template 43 61 43 61 54 44 44 49 45 56 0.366918 0.9920 Aperiodic-Template 44 39 37 59 37 58 58 61 57 50 0.041709 0.9900 Aperiodic-Template 51 34 45 41 44 60 61 60 53 51 0.102526 0.9800 Aperiodic-Template 52 52 55 50 51 47 47 48 48 50 0.998821 0.9820 Aperiodic-Template 54 49 55 42 52 56 41 45 48 58 0.699313 1.0000 Aperiodic-Template 56 42 52 43 55 47 51 47 64 43 0.452173 0.9900 Aperiodic-Template 53 49 47 49 53 36 60 54 53 46 0.603841 0.9900 Aperiodic-Template 54 46 56 61 41 45 54 51 37 55 0.340858 0.9820 Periodic-Template 54 60 54 45 44 51 52 48 40 52 0.727851 0.9840 Universal 50 42 41 48 46 47 63 57 53 53 0.514124 0.9920 Apen 37 34 31 35 36 26 35 30 26 28 0.814197 0.9906 Random-Excursion 30 30 35 33 33 34 22 33 33 35 0.874288 0.9937 Random-Excursion 37 24 31 29 28 39 37 35 33 25 0.514765 0.9874 Random-Excursion 26 35 20 30 31 33 39 30 36 38 0.361032 0.9874 Random-Excursion 23 27 25 33 35 32 40 36 38 29 0.388266 0.9937 Random-Excursion 36 44 26 24 23 24 33 36 38 34 0.088312 0.9874 Random-Excursion 42 25 24 39 30 36 26 34 32 30 0.296135 0.9780 Random-Excursion 48 35 27 26 28 29 34 32 31 28 0.202617 0.9811 Random-Excursion 33 29 29 27 27 28 40 40 34 31 0.613623 0.9906 Random-Excursion-V 36 23 22 28 40 33 37 40 31 28 0.182518 0.9906 Random-Excursion-V 36 25 20 34 27 32 31 41 37 35 0.236022 0.9811 Random-Excursion-V 39 20 28 27 30 29 29 36 45 35 0.099226 0.9811 Random-Excursion-V 38 21 26 38 24 42 31 31 36 31 0.141906 0.9874 Random-Excursion-V 36 27 36 24 37 33 26 34 32 33 0.713838 0.9906 Random-Excursion-V 40 31 25 28 25 32 32 36 29 40 0.452294 0.9906 Random-Excursion-V 38 37 26 27 33 22 36 23 38 38 0.170041 0.9906 Random-Excursion-V 30 37 37 30 25 26 38 29 34 32 0.700637 0.9874 Random-Excursion-V 30 30 26 24 34 24 30 39 45 36 0.139321 0.9969 Random-Excursion-V 28 37 25 19 34 25 42 32 36 40 0.065546 0.9874 Random-Excursion-V 34 33 22 33 37 30 32 25 27 45 0.192356 0.9780 Random-Excursion-V 38 37 29 29 31 22 32 38 31 31 0.613623 0.9843 Random-Excursion-V 41 33 35 28 34 30 30 21 37 29 0.434302 0.9811 Random-Excursion-V 38 32 29 38 36 30 31 24 34 26 0.653908 0.9780 Random-Excursion-V 37 29 41 29 31 35 36 26 34 20 0.277927 0.9906 Random-Excursion-V 31 31 37 25 37 39 38 27 25 28 0.428390 0.9874 Random-Excursion-V 27 42 30 25 42 35 28 24 35 30 0.189030 0.9843 Random-Excursion-V 61 42 50 52 47 47 46 43 52 60 0.583145 0.9880 Serial 44 58 55 53 62 46 49 36 48 49 0.357000 0.9880 Serial 65 47 52 73 42 32 36 57 54 42 0.000513 0.9880 Lempel-Ziv 60 49 62 39 45 37 62 57 43 46 0.059734 0.9940 Linear-Complexity - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - The minimum pass rate for each statistical test with the exception of the random excursion (variant) test is approximately = 0.976651 for a sample size = 500 binary sequences. The minimum pass rate for the random excursion (variant) test is approximately 0.973261 for a sample size = 318 binary sequences. For further guidelines construct a probability table using the MAPLE program provided in the addendum section of the documentation. - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - -