# Questions tagged [pseudo-random-generator]

In cryptography, a pseudo-random generator (PRG) is a deterministic procedure that maps a random seed to a longer pseudo-random string such that no statistical test can distinguish between the output of the generator and the uniform distribution. Pseudo-random generators have numerous applications in cryptography. For instance, pseudo-random generators provide an efficient analog of one-time pads.

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### Pseudo Random Generators

G is a PRG and takes in a seed s. Is G'(s) = [G(s)]' (i.e. the complement of G(s)) a PRG as well? My proof by contradiction: Suppose G' is not a PRG, then G''(s) = [[G(s)]']' = G(s) is also not a PRG ...
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### Prove a function G is not a pseudo random generator

A function G(x) = x || x (where “||” denotes string concatenation). It is given that G is not s pseudo random generator. Can someone describe how can we prove this. I am getting a bit confused in the ...
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### Relationship between LCGs and LFSRs

Here: https://en.wikipedia.org/wiki/Linear-feedback_shift_register they wrote: The linear feedback shift register has a strong relationship to linear congruential generators What this relationship ...
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### How to reproduce seeds in Random Number Generator like WELL, KISS etc

I am curious about Padding the seeds of Random Number Generator. (I am sure that terminology, padding the seeds, is not correct. If someone knows the proper word, please let me know :) ) What is ...
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### Getting the plaintext encrypting the ciphertext

Context: an encryption game from overthewire (the link to it: https://overthewire.org/wargames/krypton/krypton6.html, also good for more info) where given the ciphertext, one must obtain the plaintext....
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### PRNG based on GF?

Are there any pseudo random number generator based on Galois fields? The source of the AES randomness lies in the GF, so GF should be capable of generating random bits. Why are there no such ...
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### A source of randomness that anyone can independently, conveniently and robustly access?

Does there exist a source of randomness that anyone in the world can independently, conveniently and robustly access? For example, the 10th decimal place of the temperature in Mexico City is ...
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### Peusodrandom Generator Properites

I've learnt that a PRG is deterministic and an adversary must not be able to distinguish G(k) from a real random string. I'm asked which of the following derived generators are pseudorandom generators....
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### What are the fastest algorithms that sample from the uniform distribution?

Lots of cryptography algorithms rely on pseudorandom number generators. Sometimes, given a plaintext, you need to generate a pseudorandom number from it. What are some fast algorithms that do so? I've ...
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### Non-overlapping seeded numbers generator for small output range

Seen this, but it's sort of useless as it allows for trivial solutions by increasing the size of the output's space up to a point any hashing function will achieve non-collision. This question is ...
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### PRNG generator which could repeats blocks

Let's use AES as stream cipher, and let's use as an input numbers $1,2,3,...$. This way we should get the random blocks and every block will be different from each other. But I have a pseudorandom ...
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### How can I recover mersenne twister when only the part of the bits?

https://github.com/tna0y/Python-random-module-cracker Here, when we get 32*624 bits of outputs from Mersenne-twister we can recover Mersenne twister. My question is when we get the parts of the bits, ...
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### Can we combine two true random generators to obtain a new one?

It is well known that a true random generator exploits the randomness occurs in some physical phenomena. Also, the output of a true random generators can be either biased or correlated. Therefore, de-...
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### Is Fibonacci-XOR-rotate one-way-ish?

Fix $n\in\mathbb{N}$ with $n > 2$ and consider the following method. Pick relatively prime seeds $x_1, x_2 \in \{0,1\}^n$ (where $x_1, x_2$ are interpreted as binary numbers. Then proceed with the ...
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### What is the NIST recommended maximum bias for random number generators?

What is the maximum bias recommended by NIST for random number generators? This answer says that it is $2^{-64}$. Is it same for all applications? Does NIST have a publication with more information? I ...
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### Shift-rotating random number generator

Let $\omega$ denote the set of non-negative integers. For $n\in\omega\setminus\{0\}$ define the rotation function $$\text{rot}_n:\{0,1\}^n \to \{0,1\}^n$$ by $x \mapsto x'$ where $x'_k = x_{k+1}$ ...
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### How to combine $n$ 'less random' bits to generate one 'more random' bit?

Suppose we have a random number generator badrand() generating 1 with probability $0.9$ and 0...
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### In the reduction proof below, where OWF exists only if is a PRG. I am not able to understand the highlighted part

I am able to understand how G(x) id generated. But then what is the use of variable z. Also if the probability is >1/2 + e then the distinguisher wins! Then how is this still a OWF
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### How to prove that the given encryption scheme have ciphertext indistinguishability for all PPT adversaries?

I am not sure how to prove that the given two scheme is perfectly indistinguishable for all PPT adversaries!
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### Pseudorandom Generator Expansion

I have a question regarding the theoretic definition of Pseudorandom Generators. In Katz & Lindell's textbook (2nd edition), Definition 3.14 (p. 62), it is defined as follows: DEFINITION 3.14. ...
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### Is there a way to bound linear complexity of a sequence less than its period

Linear complexity of a sequence $s_0,s_1,\ldots$ over a finite field is the shortest length $n$ of linear recurrence of the sequence such that $s_{n+j}=\sum_{i=0}^{n-1}a_is_{i+j}$ for $j=0,1,2,\ldots$ ...
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### Is it guaranteed that all possible random numbers can be produced?

As far as I know PRGs get an input (seed) and generate a larger output value than the input. Therefore is it possible that some outputs will never be generated? based on the fact that input is smaller ...
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### A question regarding next-bit predictors

Consider a probability distribution $D$ over $n$ bit strings. Consider a next bit predictor $A$ as follows. \begin{equation} \underset{X \sim D}{\text{Pr}}[A(X_1X_2.....X_{k-1})=X_k] \geq \frac{1}{2} +...
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### Is this a good Pseudo-Random Number Generator? [closed]

I discovered what appears to be a good quality pseudorandom number generator, but I have not subjected it to any statistical tests beyond bit frequency, bit pair frequency, and least-significant bit ...
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### Why do some people believe that humans are "bad at" generating random numbers/characters like this?

I'm not even sure if they are serious, but I've heard many times that some people refuse to not only trust their computer to generate a random string (which is understandable) but also don't trust ...
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### K-dimensional equidistribution - how big are periods of PCG?

I'm trying to figure out what is period of PCG generator XSL-RR-RR: https://www.pcg-random.org https://en.wikipedia.org/wiki/Permuted_congruential_generator If we use just random multiplier and ...
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### Why should a distribution being pseudorandom strictly be a sequence of distributions being pseudorandom

According to Katz Lindell book, Let Dist be a distribution on l-bit strings. Informally, Dist is pseudorandom if the experiment in which a string is sampled from Dist is indistinguishable from the ...
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### 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, ...
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### 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: ...
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### Cryptographically secure linear congruential generator - is it possible?

Let's consider generator: $x_{n+1} = (a \cdot x_{n} + c) \mod m$ And let's assume we will meet three requirements known as Hull–Dobell Theorem. Also consider only $m=2^{i}$ (then $c$ has to be odd). ...
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### Questions about using PRF to construct PRG

Let F be a secure pseudorandom function with 128-bit key and 256-bit block length. Which are the following functions G are secure pseudorandom generators? (Select all that apply.) A. $G(x)=F_x(0...0)$...
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### Why this example about pseudorandom generators is performed like that?

Suppose Alice wishes to authenticate herself to Bob, by proving she knows a secret that they share. With pseudorandom number generators (PRNGs) they could proceed as follows. They both seed a PRNG ...
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### Deterministic Counter Mode with a PRF. What does evaluate at a point mean?

This is from Dan Boneh's Lecture where he talks about operating a PRF (AES, DES) in Deterministic Counter Mode. Dan Boneh says What we could do is we could use what's called a deterministic counter ...