That list teaches a vocabulary in which to speak about randomness. Since my attempt draws its inspiration from addition, I fear it may not pass other tests.
Thank you for the list. Also, many PRNG’s to call. That will help immensely. You have shown patience in addressing my effort, but I’m not optimistic about larger ranges. 0-9 is < 16, and it may hold up in that limited capacity. On Tue, Nov 15, 2022 at 7:58 AM Wes Turner <wes.tur...@gmail.com> wrote: > google/paranoid_crypto has a number of Randomness Tests in Python IIR > From grep '^#' > https://github.com/google/paranoid_crypto/blob/main/docs/randomness_tests.md > : > > ```md > # Randomness tests > ## Goal of the tests > ## Non-goals > ## Usage > ## Tests > ### NIST SP 800-22 > #### Frequency (Monobits) Test > #### Frequency Test within a Block > #### Runs Test > #### Test for the Longest Run of Ones in a Block > #### Binary Matrix Rank Test > #### Discrete Fourier Transform (Spectral) Test > #### Non-Overlapping Template Matching Test > #### Overlapping Template Matching Test. > #### Maurer’s “Universal Statistical” Test > #### Linear Complexity Test > #### Serial Test. > #### Approximate Entropy Test > #### Cumulative Sums (Cusum) Test. > #### Random Excursions Test. > #### Random Excursions Variant Test > ### Additional tests > #### FindBias > #### LargeBinaryMatrixRank > #### LinearComplexityScatter > ## Interface > ### Repeating tests > ## Testing > ### Pseudorandom number generators for testing > #### urandom > #### mt19937 > #### gmp_n > #### mwc_n > #### java > #### lcgnist > #### xorshift128+ > #### xorshift* > #### xorwow > #### pcg64, philox, sfc64 > #### jsf32, jsf64 > ## Design decisions > ``` > > $ grep '^\s*class' > https://github.com/google/paranoid_crypto/blob/main/paranoid_crypto/lib/randomness_tests/rng.py > : > > ```python > class Rng: > class Urandom(Rng): > class Shake128(Rng): > class Mt19937(Rng): > class GmpRand(Rng): > class XorShift128plus(Rng): > class XorShiftStar(Rng): > class Xorwow(Rng): > class JavaRandom(Rng): > class LcgNist(Rng): > class Mwc(Rng): > class NumpyRng(Rng): > class Lehmer(Rng): > class Pcg64(NumpyRng): > class Philox(NumpyRng): > class Sfc64(NumpyRng): > class SubsetSum(Rng): > ``` > > From > https://github.com/google/paranoid_crypto/blob/16e5f47fcc11f51d3fb58b50adddd075f4373bbc/paranoid_crypto/lib/randomness_tests/random_test_suite.py#L42-L80 > : > > ```python > NIST_TESTS = [ > (nist_suite.Frequency, []), > (nist_suite.BlockFrequency, []), > (nist_suite.Runs, []), > (nist_suite.LongestRuns, []), > (nist_suite.BinaryMatrixRank, []), > (nist_suite.Spectral, []), > (nist_suite.NonOverlappingTemplateMatching, []), > (nist_suite.OverlappingTemplateMatching, []), > (nist_suite.Universal, []), > (nist_suite.LinearComplexity, [512]), > (nist_suite.LinearComplexity, [1024]), > (nist_suite.LinearComplexity, [2048]), > (nist_suite.LinearComplexity, [4096]), > (nist_suite.Serial, []), > (nist_suite.ApproximateEntropy, []), > (nist_suite.RandomWalk, []), > ] > > > EXTENDED_NIST_TESTS = [ > (extended_nist_suite.LargeBinaryMatrixRank, []), > # Computing the linear complexity has quadratic complexity. > # A consequence of this is that LinearComplexityScatter only > # uses a fraction of the input. A parameter [n, m] means > # that n m-bit sequences are tested, where the i-th sequence > # consists of the bits i, i + n, ..., i + (m-1) * m. > (extended_nist_suite.LinearComplexityScatter, [32, 100000]), > (extended_nist_suite.LinearComplexityScatter, [64, 50000]), > (extended_nist_suite.LinearComplexityScatter, [128, 40000]), > ] > > > LATTICE_TESTS = [ > (lattice_suite.FindBias, [256]), > (lattice_suite.FindBias, [384]), > (lattice_suite.FindBias, [512]), > (lattice_suite.FindBias, [1024]), > ] > > > TESTS = NIST_TESTS + EXTENDED_NIST_TESTS + LATTICE_TESTS > ``` > > > - [ ] ENH: paranoid_crypto: add a __main__ so that python -m > paranoid_crypto.randomness_tests calls eg: > - [x] > https://github.com/google/paranoid_crypto/blob/main/examples/randomness.py > - [ ] REF: examples/randomness.py -> lib/randomness_tests/main.py > - [ ] ENH: paranoid_crypto.randomness_tests: add a __main__ so that > `python -m paranoid_crypto.randomness_tests -h` works > - [ ] ENH: setup.py: console_scripts entrypoint for > examples/randomness_tests/main.py > > - [ ] DOC: > https://en.wikipedia.org/wiki/Randomness_test#Notable_software_implementations: > link to google/paranoid_crypto > > > > On Tue, Nov 15, 2022 at 7:25 AM Chris Angelico <ros...@gmail.com> wrote: > >> On Tue, 15 Nov 2022 at 22:41, Chris Angelico <ros...@gmail.com> wrote: >> > >> > (I'm assuming that you sent this personally by mistake, and am >> > redirecting back to the list. My apologies if you specifically didn't >> > want this to be public.) >> > >> > On Tue, 15 Nov 2022 at 22:34, James Johnson <jj126...@gmail.com> wrote: >> > > >> > > It’s been a couple of years ago, but as I recall the duplicates >> seemed to be of two or three responses, not randomly distributed. >> > > >> > > I looked at my code, and I DID salt the hash at every update. >> > > >> > > At this point, my curiosity is engaged to know if this s/w solution >> is as good as others. I don’t have the training to test how often 9 follows >> 5, for example, but I am competitive enough to ask how it holds up against >> MTprng. I think it’s possibly very good, for s/w, and I’m emboldened to ask >> you to modify the code (it requires you data enter the numbers back to the >> machine, allowing time to pass;) to accumulate the results for 2 or 3 >> million, and see how it holds up. I don’t think the numbers track the bell >> curve on distribution . I speculate it’s more square. I suppose this is >> desirable in a PRNG? >> > > >> > >> > I'll get you to do the first step of the modification. Turn your code >> > into a module that has a randbelow() function which will return a >> > random integer from 0 up to the provided argument. (This is equivalent >> > to the standard library's random.randrange() function when given just >> > one argument.) If you like, provide several of them, as randbelow1, >> > randbelow2, etc. >> > >> > Post that code, and then I'll post a test harness that can do some >> > analysis for you. >> >> Here's a simple test harness. There are other tests you could use, but >> this one is pretty straight-forward. >> >> https://github.com/Rosuav/shed/blob/master/howrandom.py >> >> For each test, it counts up how many times each possible sequence >> shows up, then displays the most and least common, rating them >> according to how close they came to a theoretical perfect >> distribution. A good random number generator should produce results >> that are close to 100% for all these tests, but the definition of >> "close" depends on the pool size used (larger means closer, but also >> means more CPU time) and the level of analysis done. In my testing, >> all of the coin-flip data showed values +/- 1%, and the others never >> got beyond 10%. >> >> This is the same kind of analysis that was used in the page that I >> linked to earlier, so you can play with it interactively there if >> you're curious. It also has better explanations than I would give. >> >> Again, there are plenty of other types of tests you could use, but >> this is a pretty easy one. True randomness should show no biases in >> any of these results, though there will always be some variance. >> >> ChrisA >> _______________________________________________ >> Python-ideas mailing list -- python-ideas@python.org >> To unsubscribe send an email to python-ideas-le...@python.org >> https://mail.python.org/mailman3/lists/python-ideas.python.org/ >> Message archived at >> https://mail.python.org/archives/list/python-ideas@python.org/message/5OWDW5XUE5JYAW3QKMNZYKXH3NNBPNNW/ >> Code of Conduct: http://python.org/psf/codeofconduct/ >> > _______________________________________________ > Python-ideas mailing list -- python-ideas@python.org > To unsubscribe send an email to python-ideas-le...@python.org > https://mail.python.org/mailman3/lists/python-ideas.python.org/ > Message archived at > https://mail.python.org/archives/list/python-ideas@python.org/message/T3CM5FIVVUZRDP7RQ2QRNQTPWUR4WAR7/ > Code of Conduct: http://python.org/psf/codeofconduct/ > -- Truth causes consequences; consequences bring pain; pain exorcises guilt!
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