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.

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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 ...
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195 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 ...
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1answer
55 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: ...
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42 views

Security analysis using Statistics

I have a security protocol, there are total z number of nodes in the protocol and a group of n random nodes is made each time, the attacker nodes can break the protocol if the for a particular group ...
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1answer
58 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. ...
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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 ...
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2answers
332 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 ...
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3answers
736 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), ...
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2answers
71 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 ...
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2answers
136 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 ...
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2answers
89 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 ...
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1answer
53 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 ...
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1answer
74 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 ...
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2answers
288 views

Differential privacy definition

Differential privacy defines "privacy" of a mechanism $A$ as the "closeness" of the two distribution $Pr[A(D) \in S]$ and $Pr[A(D') \in S]$ where $D,D'$ differ in one element. And the distance between ...
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1answer
587 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 ...
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1answer
205 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 $s_N$ ...
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1answer
236 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 ...
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2answers
102 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 ...
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3answers
148 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 ...
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0answers
48 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 ...
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1answer
112 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 ...
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1answer
91 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 ...
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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: ...
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1answer
276 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 ...
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1answer
124 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 ...
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2answers
532 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 ...
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0answers
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: ...
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2answers
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 ...
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1answer
638 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 ...
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1answer
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 ...
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508 views

Odds of false error detection in a randomness test using the chi-squared test?

Common Criteria classifies the requirements for true Random Number Generators, and specifies how these should be tested against failures (these can occur accidentally, or following deliberate attack, ...
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1answer
129 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 ...
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1answer
256 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 ...
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2answers
964 views

What values constitute failing for ENT tests?

The dieharder tests give a clear PASSED, WEAK, etc and I'm wondering what those thresholds ...
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1answer
287 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 ...
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1answer
70 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 ...
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2answers
5k views

Randomness test question from FIPS 140-1 and comparison with 140-2

In FIPS 140-1 there are 4 statistical random number generator tests (The Monobit Test, The Poker Test, The Runs Test and The Long Runs Test. Then FIPS 140-2 came along and supposedly tightened the ...
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1answer
683 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 ...
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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 ...
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1answer
65 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 ...
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2answers
603 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 $\pi$ ...
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1answer
422 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: ...
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0answers
516 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 ...
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151 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 ...
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1answer
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 ...
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1answer
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 ...
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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 ...
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1answer
131 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 ...