Timeline for Question about a new pseudo-random number generator
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2020 at 0:33 | vote | accept | Vincent Granville | ||
| Oct 10, 2020 at 19:09 | history | edited | Vincent Granville | CC BY-SA 4.0 |
Added note at the bottom
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| Oct 7, 2020 at 10:38 | comment | added | Vincent Granville | Obviously, one flaw of all RNG's with $q=1$ (first-order recurrence) is that you never see twice the same word within any period cycle. In true randomness, repetition occurs without causing the cycle to repeat itself entirely. As an example, if you pick up 10 integers randomly between $0$ and $3$, some number MUST appear at least twice. | |
| Oct 7, 2020 at 5:51 | history | edited | Vincent Granville | CC BY-SA 4.0 |
edited body
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| Oct 7, 2020 at 3:54 | history | edited | Vincent Granville | CC BY-SA 4.0 |
Added new material to sections "possible improvements" and "source code"
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| Oct 7, 2020 at 0:32 | answer | added | acacia | timeline score: 1 | |
| Oct 5, 2020 at 23:35 | history | edited | Vincent Granville | CC BY-SA 4.0 |
I added #!/usr/bin/perl at the top in the source code as requested in the answer to my question. Now you know it's written in Perl.
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| Oct 5, 2020 at 20:33 | answer | added | acacia | timeline score: 2 | |
| Oct 5, 2020 at 16:03 | history | edited | Vincent Granville | CC BY-SA 4.0 |
Added reference on modern tests of ransomness
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| Oct 4, 2020 at 15:46 | comment | added | Vincent Granville | Another feature (if $N$ prime): the distribution of zero's in $B_n$ follows a Binomial distribution as expected, when computed on many many $B_n$'s. Also the correlation between the number of zero's in $B_n$ versus $B_{n+1}$ is rather close to zero ($0.06$ in one of my tests). And $X_n$ follows a uniform distribution on $[0, 1]$ when $N$ is large. | |
| Oct 4, 2020 at 15:35 | comment | added | Vincent Granville | @ Ville: Essentially yes. First, shift the bits, then reverse the bits. Then a XOR. $N$ even performs rather poorly. Best performance is obtained with some special primes. | |
| Oct 4, 2020 at 10:44 | comment | added | Padraig Ó Catháin | This looks similar in idea to the S-boxes used in AES, DES and similar cryptosystems. (The details are more complicated but they typically apply a permutation of the input bits, then apply a fixed function to small blocks, and iterate these steps for a large number of rounds.) When they were developed, there was a lot of research into necessary and sufficient conditions for security. Maybe these translate into guarantees of good pseudo-random behaviour here? At least, that's where I would start looking. | |
| Oct 4, 2020 at 8:43 | comment | added | Ville Salo | In any case if it's late near over $\mathbb{Z}_2$ probably it's not very secure. | |
| Oct 4, 2020 at 8:40 | comment | added | Ville Salo | So XOR with left shift then reverse? So I guess for even $N$ at least, grouping the $k$th and $(N-1-k)$th bit into one, it's a linear cellular automaton on $A^{\mathbb{Z}_n}$ with alphabet $A = \mathbb{Z}^2_2$? | |
| Oct 4, 2020 at 6:27 | history | edited | Vincent Granville | CC BY-SA 4.0 |
Error in formula for $X_n$ fixed.
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| Oct 4, 2020 at 3:27 | history | asked | Vincent Granville | CC BY-SA 4.0 |