# Questions tagged [randomness]

Usage of randomness (i.e. non-predictable data, usually in the form of bits or numbers) for cryptographic purposes.

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### Reusing same source for single-source randomness extractor

Let $ext$ be a single-source randomness extractor which takes a $d$-bit seed and a $n$-bit source as input and produces a $m$-bit output. Suppose we have a source $X$ with min-entropy $k$. Is it ...
132 views

### Use of randomness in an Elgamal like encryption

Suppose I have the following encryption scheme: for a message $m\in\mathbb{F}_p^*$, I generate the ciphertext = $(g^r,f^mh^r)$ where $g$ is the generator of a cyclic group $G$ of unknown order $n$ and ...
209 views

### Feasible way to check n-dimensional equidistribution of PRNGs

I am currently gathering some test methods and test suites for random number generator qualities, and am a bit stuck at finding something feasible to test for n-dimensional equidistribution. As input ...
169 views

### Use of scrambler LFSR for randomness extraction of semi-random source

I am using a linear feedback shift register (LFSR) in a scrambler configuration as a randomness extractor for a weakly random source. This source is semi-random (aka. Santha-Vazirani source): the bits ...
61 views

### Computational Randomized Encoding in the hybrid proof

A computational randomized encoding scheme $(\textrm{RE.Encode}, \textrm{RE.Decode})$ works as follows: $\textrm{RE.Encode}(1^\lambda, C, x, r)$: takes as input the security parameter $\lambda$ in ...
52 views

### Fisher Yates on "faulted" random number generator cryptanalysis

For the sake of curiosity and fun, i have implemented a C# program that operate as deck dealer on 40 cards deck (following the Fisher Yates shuffeling algorithm https://en.wikipedia.org/wiki/Fisher%E2%...
448 views

### Can Verifiable Random Functions be used to pick a random node from a pool?

Let's say that I have a decentralized system and I have a list of nodes published on a public log like a blockchain. I want a node A to be able to connect to ...
71 views

### Is the number still a CSPRN if we only allow an interval from a CSPRNG?

tr -dc 0-9 < /dev/urandom | fold -w 3 | awk '$0>=100 &&$0<=200' What this line does: /dev/urandom (Linux) is proven to be a CSPRNG, that is ...
108 views

### Special random distribution algorithm

I am implementing ring signatures as a part of an authorization system. Since the number of users could get high enough to make computation on end-user devices infeasible, I am thinking of "...
112 views

### How to verify the claim of entropy available made by Linux 4.5?

The Linux kernel has an entropy source and it estimates its amount of bits in the device /proc/sys/kernel/random/entropy_avail. How can I verify that this number ...
36 views

### Sentinel ("trick") values for lattice attack on DSA with biased k (MSB)

I'm studying lattice attack using this sage script. There are 2 options in script: LSB and MSB. The most interesting option for me is MSB. It recovers private key with less then 100 signatures ...
73 views

### How does a pseudorandom generator produce a similar distribution to $U_{n}$?

According to Wikipedia, a function $G:\{0,1\}^{\ell }\to \{0,1\}^{n}$ with $\ell < n$ is a pseudorandom generator against $\mathcal {A}$ with bias $\epsilon$ if, ...
64 views

### Nth term for Linear Congruence Generators

We can get the N+1th term for a Linear Congruence Generator like this: x[n+1] = A * x[n] (mod m) by raising the A to the exponent of n like this: ...
64 views

### Min Entropy per Bit for Trevisan's Extractor/or An Extractor

We know that: trevisan's extractor based on min entropy of the relative system. For trevisan extractor, we need source, seed, min entropy value per bit and error rate for per bit I have the code for ...
32 views

### NIST STS randomness testing inconsistent results

I have generated the nine datasets according to this document for AES-128 and testing these for randomness using NIST STS. However, the results are inconsistent. Sometimes there appear a * in the ...
99 views

### What is a "set synchronized CSPRNG"?

I'm looking to implement a performant revocation method for JWTs. I'm reading a paper, in which the following section's second paragraph states: If we use the client hashing approach described ...
81 views

### libgcrypt and rdrand usage

For some reasons, I was looking into libgcrypt source code and found this. If I understand this correctly, while asking to use /dev/random for some bytes, it actually checks first if rdrand is ...
91 views

### Would the result of encrypting weak random data via AES-128 with a CSPRNG-generated key be considered strong/secure random data?

I am trying to understand the security implications of using a well known block (or stream but in this example block) cipher like AES-128 to produce pseudo-random data. My specific question is would ...
106 views

### Why does a "never-repeating" nonce limit a key to safely encrypt only a single block?

This questions comes from a section outlined in RFC 5297 on SIV-AES. The paragraph in particular outlines the idea of a never repeating nonce vs an "almost always" non-repeating nonce. If the nonce ...
77 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 ...
73 views

### What is fixed randomness and unfixed randomness?

I have found these notions recently in an article. What is fixed randomness ? What is unfixed randomness ? Link of the article : http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.431.9034&...
165 views

### How Are Linear Congruential Generator Multipliers Chosen?

There are several numbers that keep coming up when looking at certain random number generators, for example 6364136223846793005 is used in newer pcg-family algorithms and seems to draw it from ...
107 views

### Is there an algorithm or protocol that allows to securely generate random shuffles when two parties are not colluding without a sever side seed?

I am building an app that pits one party against another party in a gambling transaction – both parties have competing interests and have an incentive not to cheat the other party. I am looking for a ...
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### Beginners question about revealing randomness in probabilistic asymmetric encryption

I am encrypting "1" with probabilistic encryption with a foreign public key (I don't have the private key for it) which results in an encrypted file e. Can I prove to a third party, that e contains ...
68 views

### RIsk mitigation: block cypher vs xor

It sort of looks like to me that there is a kind of risk mitigation in the architecture of block cyphers vs the xor cypher. In XOR, the risk is entirely in the random number generator. The XOR ...
53 views

### Fuzzy Extractor: Order of elements in set

Does order of elements in two sets matters to authenticate using Fuzzy Extractor? Using extractor as proposed in https://www.cs.bu.edu/~reyzin/fuzzy.html it seems the set difference is zero for this ...
528 views

### Relationship between "Entropy" and "Security" in crypto functions

There is a lot of confusion between "entropy" and "security" of a cryptographic function. I like to visualize it as the entropy being the water, and the crypto function being a glass. So for ...
49 views

### Does RSA_PRBG security depend on keeping seed secret?

The HAC provides a PRBG using RSA (Chapter 5 p.185): It appears the seed must be kept secret if $e$ is a well known value. If $e$ is uniformly distributed between 1 and $\phi$, then the seed does not ...
221 views

### PHP predicting array_rand

Given the following PHP code (assuming PHP 5.6.x): ...
98 views

### To prove $r_2$ is a uniformly at random value in $Z_n$, where $r_2=r_1 . m$

$m$ is arbitrary value in $Z_n$, where n is RSA modulo. Then we do: $r_2=r_1 . m (modn)$, where $r_1$ is a random value such that $r_1\in Z^*_n$. ** Question(1): is $r_2$ a uniformly at random ...
48 views

### Cryptographic Random Beacon VS Random Oracle

Let's start with what I mean by cryptographic random beacon (RB). A RB is a protocol among some parties who generate a random value all together such that: these parties do not trust each other the ...
73 views

### Cryptographically correct way to roll a giveaway winner

I'm looking to create a fair selection of a giveaway winner, but I am versed enough in cryptography theory to determine if the below would hold up to public scrutiny if published on github. The reason ...
38 views

### Can disjoint distributions be Computationally indistinguishable?

As mentioned in these notes definition 2 We say that $\{Xn\}_n$ and $\{Yn\}_n$ are computationally indistinguishable if, for all $\mathsf{nuPPT}$ $D$, there exists a negligible function $ε$ such that ...
35 views

### Alter signature post signing without the private key

There a plethora of signature scheme's but I am wondering if there are scheme's with the following properties: Given that you know the message, alter the signature with the public key in such a way ...
56 views

### How do I retrieve a number which has been multiplied with a random number?

I have a 1024-bit number $n$ obtained by multiplying two 512-bit randomly generated prime numbers $p$ and $q$. Then there's $\phi = (p-1)(q-1)$, which is another 1024-bit number. I do not have $\phi$ ...
43 views

### Security analysis of encrypting a matrix after homomorphic encryption by the random mask

Problem Definition Alice has two private matrices $M_A$ ($N*M$), $M_a$, where $M_a$ is the binary matrix of $M_A$ Bob has a private matrix $M_B$($N*M$) Alice and Bob are semi-honest server and ...
134 views

### Randomness Testing of Block Ciphers with 256-bit Block/ Key length

NIST explained the process of "Randomness Testing of the AES Candidate Algorithms" in the document. The document explains the generation of 9 datasets for AES candidates with 128-bit block ...
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### Explaining the reason of radically more accuracy while using different set of hash functions instead of same set of hash functions on some operations

So I am looking for an explanation of an experiment. In this experiment, I took a set of k hash functions. Say the total number of data points I am working on is d. Call an algorithm A which used that ...
59 views

### RNG randomization strength for PRF seed

Consider a use case that requires the creation of multiple asymmetric key pairs. There are two options for generating random seeds for a PRF: Use a software based RNG and generate a new seed for each ...
61 views

### What is the probability that a random function is invertible?

Having a random function - $R\in{}\mathcal{R}$ s.t. $R:\{0,1\}^n\rightarrow{}\{0,1\}^n$. What is the probability that $R$ is invertible? I know calculating it suppose to be straight forward, but I'...