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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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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How to pass the output of a function to itself a number of times in RNG? [migrated]
I'm trying to pass the output of a function in C to itself a number of times but I'm still getting the same answer each time (I tried to pass it by value and by reference I do not know which is the ...
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What kind of random algorithm is used in this game? [migrated]
I am playing a game for iOS that uses a deck of 48 cards and I would like to reverse engineer the kind of algorithm that is used to generate the random deck of cards such that I can predict which card ...
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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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1answer
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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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1answer
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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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1answer
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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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1answer
46 views
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 ${\displaystyle G:\{0,1\}^{\ell }\to \{0,1\}^{n}}$ with ${\displaystyle \ell < n}$ 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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1answer
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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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1answer
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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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1answer
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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 ...
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1answer
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Unable to understand the concept of a 1-bit PRF
In his lecture on building Block Ciphers from PRGS, Dan Boneh says this
Let’s start by finding out if we can build PRF from a PRG?
Let $G:\ K \to K^2$ be a secure PRG
Define 1-bit PRF $F:\ K \times \{...
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1answer
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Tests to distinguish between PRNG and a CSPRNG
What are the tests which a regular PRNG would fail but a CSPRNG would succeed? Is it just the next-bit test or are there multiple other tests which a PRNG which is not a CSPRNG would fail? Would a ...
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1answer
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Understanding the Inner State of a RNG
Based on the BSI evaluation criteria for quality of deterministic random number generators:
K4 – It should be impossible, for all practical purposes, for an attacker to calculate, or guess from an ...
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1answer
60 views
PRG exponential expansion
I am just beginning to read into pseudorandom generators and I came across this definition for a PRG:
$G_n : \{0,1\}^n \rightarrow \{0,1\}^{l(n)}, \quad \text{ where $l(n)$ is a polynomial}$
Is there ...
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1answer
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How to combine a PRG and a non-PRG to design a PRG?
I'm trying to solve the following exercise:
Let $G_1, G_2: \{0,1\}^\lambda \to \{0,1\}^{\lambda + l}$ be two deterministic functions mapping $\lambda$ bits into $\lambda + l$ bits (for $l \ge 1$). You ...
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Proof that PRG of itself is a PRG (composition)
I have this question and I am struggling to find a formal answer to this:
Given $G$ is a PRG, show that $H(s)=G(G(s))$ is also a PRG.
I know that a proof for this would assume that there exists a p....
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Why is breaking the Blum Blum Shub PRNG not an undecidable problem?
The Blum Blum Schub (BBS) pseudo random number generator (PRNG) is defined inductively by
$$
x_{i+1} = x_i^2 \mod N
$$
to generate the bit sequence $b_0b_1b_2...$ where the bits are taken to be the ...
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Bad pseudo-random number generator — any guesses?
I'm trying to diagnose a badly-implemented pseudo-random number generator. The two key features of the bit streams produced by this PRNG are: significant correlation of consecutive bits (approximately ...
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What is the advantage of guessing PRG impossible outputs?
Lets say we have a length-tripling PRG $$ G:\{0,1\}^l \to \{0,1\}^{3l}$$
What would the advantage of an adversary to guess one of the impossible outputs of G?
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Are there any universal PRG’s or PRF’s?
Leonid Levin constructed a universal one-way function, i.e. a function $f$ such that if any one-way functions exist, then $f$ is a one-way function. My question is, what universal pseudorandom ...
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Proving G(x)=x||[x^2 mod 2^N] is not a PRG
This was a question from my exam yesterday.
We have that $G:\{0, 1\}^n\rightarrow \{0, 1\}^{2n}$ and
$$G(x)=x\mathbin\|[x^2 \bmod 2^n]$$ with $x$ is uniform and $|x|=n$, give an efficient ...
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1answer
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PRF and deterministic polytime function implie PRG
I'm struggling while trying to resolve this exercise. I already read all questions about PRG and PRF here and some proofs around the internet but none of them helped me.
let's consider a function $C$ ...
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Fast cryptographic hash function for short inputs
I am looking for a cryptographic hash function optimized for speed on short inputs, in order to implement a pseudorandom generator with expansion factor 2 (e.g. takes 16 bytes of input and outputs 32 ...
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Pseudorandom Generator
In a cryptographic application, two types of (pseudo)random bit streams are needed:
a stream $A= a_{1}a_{2}a_{3}\ldots$ in which $\Pr[a_{i}=0]=\Pr[a_{i}=1]= 1/2\ \forall i$ and
a stream $B= b_{1}b_{2}...
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How does a hybrid argument work relating to PRG's?
How does a hybrid argument work relating to PRG's?
I am working on a homework assignment where the problems say to use a hybrid argument to prove/disprove that something is a secure PRG, and I can't ...
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Lehmer random number generator cipher scheme with moving bits
Let's consider linear congruential generator:
$X_{k+1} = a \cdot X_{k} \mod 2^{128}$
Such that $a$ is some number which for every 128-bit input $X_{k}$ from $0$ to $2^{128}-1$ will give us different ...
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1answer
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Cryptographically secure PRBGs and the previous-bit test
I am reading Junod's paper about the Blum-Blum-Shub PRBG (BBS) and I am having trouble following his reasoning at on page 15, where he argues that the next-bit test can also be peformed for the ...
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1answer
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Lehmer random number generator - cipher?
Let's consider linear congruential generator:
$X_{k+1} = a \cdot X_{k} \mod 2^{128}$
Such that $a$ is some number which for every 128-bit input $X_{k}$ from $0$ to $2^{128}-1$ will give us different ...
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How to calculate CPA attack complexity in bits manipulation
The following Forward Errors Correcting FEC is used in our daily devices. But I added a potential security measure.
In one of FEC systems the input is $K$ bits and the output code is $M$ bits where $M=...
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1answer
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Ranking “amount of randomization” in a sequence
I'm facing the problem of implementing pseudo random bit generator (PRBG) on a very low power device. NIST.SP800-22 "Statistical test suite for Pseudo Random Generators" suggests a suite of ...
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RNG and Mersenne twister learning resources for the amateur
I am a complete amateur in the area of random number generators. I would appreciate resources to begin learning.
Also I would also like to learn about Mersenne twister. Resources that are easy on the ...
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1answer
270 views
Is it possible to create a 128-bit UUID from a weak entropy source?
I am looking at a seemingly popular piece of JavaScript code to generate a UUID which is supposed to be a 128-bit number:
...
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Is $f(g)$ a PRG if $f$ is a OWF and $g$ a PRG?
If we have a PRG $g$ and a OWF $f$, can we say that $g' = f(g)$ is a PRG?
And what if $g$ stretches its input by a factor of 2?
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1answer
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Breaking a Mersenne-twister RNG with unsequential outputs
Pardon me for this newbie-ish question. I'm still a novice in cryptography . I have an application that outputs random numbers from 0 - 12 (endpoints inclusive) unsequentially (some outputs are thrown ...
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2answers
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How to construct a prg?
Does the adversary know the random seed s? If he does not, isn't one possible construction simply the random seed itself? if the output needs to be bigger than random seed s cant I just add a hardcore ...
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1answer
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How many 12 bit integers output are required to reverse the Mersenne Twister?
I am creating a web app that applies Python's random algorithm (Mersenne Twister) to generate random 12-bit integers. I am concerned as to how a user can predict ...
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1answer
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Would knowing the random seed help to break AES or similar?
Consider I knew the seed of the random number generator that Bob uses to send encrypted emails to Alice. Would I have an advantage in deciphering the message? Also, how does, for example, openssl ...
