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Statistical testing is used to estimate the likelihood of a hypothesis given a set of data. In cryptanalysis, statistical testing is commonly used to detect non-randomness in the data, e.g. distinguish the output of a PRNG from a truly random bitstream or to find the correctly decrypted message among several incorrect decryption attempts.

7 votes

Which test suit is better to say if PRNG is CSPRNG:TestU01 or NIST?

Please don't. TestU01 or NIST? Neither. Trust what they say on the xoshiro256+ website. A CSPRNG is not defined by it's speed. It's defined by security against predictability, i.e. the next bit tes …
Paul Uszak's user avatar
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5 votes

How to compute the dataset size required by dieharder tests?

I'll be so bold as to say that no one knows for sure how much data you really need. There is no guidance on the homepage, the manpage and this thread from Duke is equally unspecific. Anecdotal evidenc …
Paul Uszak's user avatar
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3 votes
Accepted

What problems with "random" data would cause this result from Ent?

I've seen this before in the true random number generators I've been working on. Look at the following test. I've ent'd two jpegs, one 10 times the size of the other. A jpg is highly compressed so …
Paul Uszak's user avatar
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3 votes
Accepted

Interpretation of certain results of NIST Test Suite

Randomness is pesky, and can wax and wane between samples. That's why there is no one specific categorical test that can validate an IID sequence. You need to statistically combine several (perhaps c …
Paul Uszak's user avatar
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2 votes
Accepted

Explanation of the EPC Gen2 randomness standard's first rule

All is revealed in the last paragraph of that section, repeated below:- A cryptographic suite defines RNG requirements and randomness criteria for cryptographic operations. These requirements and …
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2 votes

Sequence test for an image cipher

It's simple. Lena is 512 x 512 pixels with a bit depth of 8. So you simply export the raw image to a file that will be exactly 262,144 bytes long. It's critical that you export or save the image as …
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2 votes

What values constitute failing for ENT tests?

Failing ENT output is a little like the length of string; elusive. So I offer an anti-answer. The following is the output from running the code below and shows a random sequence passing ENT. You'll …
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2 votes

Is it possible to test 15-bit PRNG with the library TestU01?

This one? Generators of this form are called linear congruential generators. You can test them but by inspection you can see that it will fail a serious randomness test quite spectacularly. 32 bi …
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1 vote
Accepted

NIST STS incorrect results for sample files

Don't worry about it :-) The documentation is "Revised:April2010". The latest code implementation is (officially) dated July 9, 2014 and commented as "This update has a few minor corrections to the …
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1 vote

How can the 'randomness' of a finite sample of binary keys from a finite key space be estima...

The answer is that you're simply over thinking the problem :-) You do not have any special problem class, other than forgetting that randomness is a function of sample size. A bigger sample just m …
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1 vote

Why does mt19937 fail the universal test in NIST SP 800-22?

Your testing is wrong somewhere I'm afraid. MT is used throughout the world and is good enough for most scientists. Yes, it's not cryptographic and has some very minor defects in the higher dimensio …
Paul Uszak's user avatar
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1 vote
Accepted

Test the randomness of a random permutations, that was generated without Fisher-Yates?

One thing that comes to mind when evaluating random permutations is what happens if we shuffle an array that contains consecutive integers and just use the first index as a randomly generated number, …
Paul Uszak's user avatar
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1 vote
Accepted

NIST random excursion results

So, there are a few things here. 8 in the first case and 18 in the second Yes, that's correct but only if there is enough sample data. These last two tests need looads of numbers. In fact, in e …
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1 vote

exact meaning of ntup in dieharder tests

We can discern the following from the man page:- -n ntuple - set ntuple length for tests on short bit strings that permit the length to be varied (e.g. rgb bitdist). Clearly you know what a tu …
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1 vote
Accepted

NIST algorithm testing results

I'd ignore it. Maurer's test is a compression test. Does your file compress with pkzip, 7z or stronger stuff like PAQ8 or cmix? No? Does it pass ent (the most trustworthy test in my opinion)? Most ran …
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