# Questions tagged [statistical-test]

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.

64 questions
Filter by
Sorted by
Tagged with
73 views

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

Update: with the help of @SqueamishOssifrage and @PaulUzdak, we discovered that my NIST SP 800-22 has a broken universal test. So this becomes a moot question. Check this report. It seems to sail ...
203 views

### How can the 'randomness' of a finite sample of binary keys from a finite key space be estimated?

Given a set of bit sequences generated by an extractor, what would be a valid setting for estimating the randomness of these generated keys and what resolutions can be drawn for that extractor in ...
71 views

### Interpretation of certain results of NIST Test Suite

I am using NIST Test suite on a PRNG and have a confusion regarding some specific results. Following is the part of the results: ...
71 views

### NIST random excursion results

NIST specifies so-called random excursions test and random excursions variant test. From the description I can derive that the number of p-values should be 8 in the first case and 18 in the second. ...
248 views

### Randomness Testing

Let say I have three sequences: S1 = {1,2,3,4,5,6,7,8,9,10} S2 = {3,7,1,9,4,10,5,8,6,2} S3 = {8,3,10,2,6,7,1,5,9,4} i.e. S2 and S3 are just the permutations of S1. Is there any method to check how ...
71 views

### Randomness Test of Permuted Sequence

As we can generate a permuted sequence using KEY in KSA (Key Scheduling Algo) of RC4. Is there any way to check the randomness of the permuted sequence? Let say I created 100 different permuted ...
173 views

### How to actually compute the statistical distance?

I have an algorithm for discrete sampling that I've defined. This is to say that $A$, upon input some pdf $p(x)$, outputs samples from the pdf $p(x)$. There are some nuances (you have to make the ...
146 views

### Statistical Tests for Pseudorandom Functions

Say I have an implementation of a potential Pseudo-Random function and I want to test whether my implementation does at least not contain any obvious flaws. As far as I understand, in other ...
95 views

### How to make a hypothesis test for a simple statistical test for a certain RNG?

I'm self-studying about hypothesis test in the context of RNGs. I'm building a hypothesis test from scratch. I'm taking the simplest statistical test I can think of: how many $1$s are there in the ...
68 views

### Origin of the Chi-Squared test statistic for serial test (two bit test)

On page 181 of Handbook of Applied Cryptography Chapter Five, it states the following: The purpose of this test is to determine whether the number of occurrences of 00, 01, 10, and 11 as ...
80 views

### NIST STS incorrect results for sample files

So I wanted to check the outcome of a hardware TRNG and see if its entropy is good enough. I downloaded the source files for statistical test suit from nist.gov website, compiled them on my macOS ...
266 views

### Golomb's Randomness postulates

In Handbook of applied cryptography, Golomb's randomness postulates are given: Let $s$ be a periodic sequence of period $N$. Golomb’s randomness postulates are the following. R1: In the cycle $s_N$ ...
382 views

### Interpretation of (NIST) Non Overlapping Template Matching Test

Regarding the Non-Overlapping Template test, this test normally gives us a bunch of p-values (148 values). I would like to ask that how do we interpret those values into a single p-value for ...
108 views

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

The library TestU01 inconvenient for generators that don't produce 32-bit outputs. But is it possible to somehow test say a 15-bit generator with it? How could that be done? For instance, the ...
152 views

### Is it correct to concatenate (pseudo-)random byte values before testing them with the NIST suite or tools like dieharder?

Let's assume I have thousands of (pseudo-)random 4-byte values. The values are 4 byte random values which a blackbox device gave me. I got these values by requesting them. In between others might have ...
49 views

### Statistical test strange behaviour [closed]

Hi I'm running the dieharder test suite (this) to test an algorithm, but I've found somethings that I don't understand. This is the command that I run to test my binary file ...
123 views

### adaptation of NIST sp800-22 for short sequences

I would like to ask about the NIST test suite for randomness evaluation. The test suite consists of 15 subtests which evaluate the particular property of the sequence. In fact, each test has an ...
92 views

### Sequence test for an image cipher

I am reading a paper on security analysis of a cipher image using the paper at the following URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8306512&tag=1 It indicates some ...
625 views

### Is there are a metric based on collisions to compare bad hash functions?

Bad hash functions are not so perfect as in the "general collision probability" hypothesis... And a general concept of "collision resistence" not need the constraint of independence between the ...
53 views

### How to perform Black box testing of a key exchange protocol?

Though obviously not an alternative for proper cryptanalysis, I was wondering about statistical/black box analysis. Should I produce a new key exchange protocol. With the same shape as Diffie-Hellman: ...
202 views

...
300 views

### How can I calculate non-linearity of an s-box element wise?

First i transform the s-box into row matrix like if i have 4×4 s-box having 16 elements into 1×16 row matix then substitute the binary values in column . multiply the matrix by mobius trasformation ...
276 views

### How is the inter and the intra distance of a PUF calculated?

I was wondering, if I want to calculate the intra distance of a PUF, and I have already measured $n$ times a response to a challenge. Do I choose one reference value and compare the hamming distance ...
131 views

### Explanation of the EPC Gen2 randomness standard's first rule

When we read PRNG requirements of the EPC standard, first rule (page 57 in this link) in the documentation; Probability of a single RN16: The probability that any RN16 drawn from the RNG has ...
100 views

### LIL (PRNG) statistical test does not appear to be in a stable state [closed]

I am trying to run the LIL statistical testing tool that can be found here http://webpages.uncc.edu/yonwang/liltest/ When I execute the jar with: ...
695 views

### Quality test for an hardware source of randomness

Say that I developed an hardware source of randomness, which I would like to use to seed a cryptographically secure random number generator. How would I go about testing it? Are there standardized ...
788 views

### Estimated entropy per bit given P-value of a statistical test, and number of bits tested?

Assume that a certain statistical RNG test (say from the NIST Statistical Test Suite, Dieharder, etc..) gives us a certain P-value (per the definition [*] used in NIST Special Publication 800-22), ...
1k views

### NIST random test suite choosing bitstream length and count [closed]

First it asks for bitstream length. Usage: ./assess <stream length> <stream length> is the length of the individual bit stream(s) to be processed ...
130 views

### Plaintext for randomness evaluation of cryptographic algorithms?

I’m running an experiment to test the randomness output of many cryptographic algorithms based on INST test suite to measure the randomness of their outcome. However I’m searching to a sample data ...
263 views

### Statistical tests for PRNG that generates a sequence which is not binary

Is there a pratical application to PRNG that generates a sequence which is not a binary one? A ternary, quaternary sequence, for instance. If so, how can we test this? Is there any alternative test ...
71 views

### Determining the degree of freedom for a chi-squared test on a strict avalanche criterion matrix

I have read that the degree of freedom is calculated by subtracting 1 from the number of states a random variable can be in. I am performing a goodness of fit test on a 64*32 strict avalanche ...
290 views

### What problems with “random” data would cause this result from Ent?

I'm playing around with a novel kind of source of "random" data and Ent is currently giving me results like this: Entropy = 7.977080 bits per byte. Optimum compression would reduce the size of this ...
715 views

### Testing implementation of cryptography algorithms: Brainstorm

I wonder what kind of techniques can be used to validate implementation of cryptography algorithms? The obvious one is to run specific algorithms against publically known test vectors (i.e. from ...
37 views

### How were the diffusion statistics for norx calculated?

I was reading the norx specification and came across this section, which provides some kind of statistics about the diffusion of the norx round function. However, I don't see how these values were ...
551 views

### Is the RC4 keystream random or not?

I have cause to use the PRNG half of RC4, but am seriously confused as to the randomness of its output. (Only the PRNG half.) On the one hand, there is a large body of literature finding ever ...
66 views

### How to compare two CSPRNGs? [duplicate]

Let's say I am given to CSPRNGs: RNG1 and RNG2. I want to select the best one of the two for cryptography. How should I do it? Any of the two RNGs can be initialized with a secret key during tests and ...
432 views

### Avalanche effect sample size

With a fixed key size – key has 128 bits, while block size is 8 byte – how do I calculate how many different keys and texts I have to test for an cryptanalytic statistics study? Differently worded: ...
997 views

### What values constitute failing for ENT tests?

The dieharder tests give a clear PASSED, WEAK, etc and I'm wondering what those thresholds ...
613 views

### Why calculate pi to estimate randomness?

Why do testing suites calculate $\pi$ (pi) using the Monte Carlo method to determine if a series of numbers are random? As far as I can tell, the Monte Carlo method can be used to estimate $\pi$ ...
153 views

### Using machine-learning techniques for data-dependent operations in ciphers

From 'Methods of Symmetric Cryptanalysis' by Dmitry Khovratovich, The data-dependent operations are one of the most controversial design concepts. We say that an operation is data-dependent, if it ...
105 views

### Minimum number of independent trials needed to detect a bias [closed]

Suppose, I suspect that the probability of occurrence of a particular bit as $0$ is $.558$. Since, it is not $.5$, so this is possibly a bias. Now, my question is: What is the minimum number of ...
102 views

### Available programs that can verify the working of a simple substitution cipher

Is there any tool available that can test whether a simple substitution cipher is working. I will put my scenario in detail. Lets say I built a simple substitution cipher that maps 8 bit data to 16 ...
103 views

### Infer encoding mechanism from $n$-grams distance?

I have a series of obfuscated strings which across the set of strings have regions of high variance and regions of low variance – implying some encoding mechanism as opposed to an encryption procedure ...
2k views

...
559 views

### Chi-Squared Step of Vigenere Cipher Decryption [duplicate]

So, I have been assigned an assignment where I had to solve a Vigenere cipher. Following along with this webpage I managed to get all the way to the chi-squared step. But, that is the problem. Upon ...
6k views

### Shannon confusion and diffusion concept

I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that ...
132 views

### Statistical tests for pseudorandom permutations

I'm implementing a format-preserving encryption scheme similar to those described in the literature. I want to sanity test my PRP using some statistical tests like TestU01. However, I'm not sure how ...
186 views

### run length testing [closed]

Looking for guidance/references with/about calculations: I am designing a widget that creates N-bit binary sequences. My customers target spec for the sequence's minimum entropy is X bits/bit. I plan ...