# 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 this PRG secure?

$G$ is a secure PRG in range $\{0,1\}^n\rightarrow\{0,1\}^{n+1}$. Let us define $G'(S)=G(S\oplus G(S)_{1,...,n})$, s.t. $G(S)_{1,...,n}$ is the first n bits of $G(S)$. Is $G'(S)$ a secure PRG? ...
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### How can we formally define a Pseudo-Random Shuffle function?

My question is related to: When we turn Random shuffle to Pseudorandom Shuffle The idea is to permute the elements in vector $\mathbf{v}$ pseudorandomly, where $|\mathbf{v}|=n$; I am aware that we ...
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### Program to predict a 5-bit output from mersenne Twister random module from python

Is there a program to predict the mersenne twister random module in python for a 5-bit integer output, provided the consecutive 3994 outputs are available? The random module is not seeded so i guess, ...
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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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### composition of RLWE distributions

Assume we have the polynomial space $R_q$ defined as $R_q = Z_q/(X^n + 1)$. Additionally, we define the error distribution $\chi$ as a discrete centred Gaussian bounded by $B$. Let $s,t \in R_q$ be ...
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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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### 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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### 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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### 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 ...
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### Alternative AES key expansion for CTR based random number generator

Daniel J. Bernstein proposes an alternative to NIST AES-CTR based deterministic random number generator (AES-CTR-DRBG). Instead of a less performant complex construction, he uses an standard AES-CRT ...
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### Pseudo Random Generator (PRG) not deterministic

Usually a Pseudo Random Generator is supposed to be IND-CPA secure. But apparently, it is not in some cases such as the following: A PseudoRandom Generator $G$ has expansion factor $n + 2$. Encrypt ...
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### Dependence of a Pseudorandom Function's Security on its Input/Output Spaces

Let $n$ be a security parameter and $F:\{0,1\}^{\ell_{key}(n)} \times \{0,1\}^{\ell_{in}(n)} \rightarrow \{0,1\}^{\ell_{out}(n)}$ be a keyed function which forms a family of Pseudorandom Functions (...
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### Construction PRF from PRG

As discussed here, a classic and secure construction of PRF from PRG is: $F_k(x_1x_2\cdots x_n) = G_{x_n}(\cdots(G_{x_2}(G_{x_1}(k)))\cdots)$ where $G$ is a secure pseudorandom generator. I was ...
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### Which 'info' and 'salt' parameters to use in HKDF for TLS 1.3?

all the following discussion is for HKDF in TLS1.3: Regarding the 'salt' parameter in - HKDF-Extract(salt, IKM) as written in RFC 5869: HKDF without having to protect the secrecy of the salt. In a ...
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### show that G' is not a secure PRG even if G is

Hello I'm trying to show that the function G'(s) = G(s) || G(G(s)) is not a secure PRG even if G is. My first question is that in this case, how do I know what G ...
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### A modification of the Blum-Micalli construction

Consider the following modification of the Blum-Micalli construction (denoted by BM): $G_l(x) = f^l(x) || BM^l(x)$ I am asked the following questions about it: Show it is a PRG of fixed stretch ...