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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is a MAC defined by a pseudo random generator secure?

Let $ G:\{0,1\}^*\rightarrow\{0,1\}^*$ be a length doubling PRG, and let $ \Pi=(Gen,Mac,Vrfy)$ be the following MAC scheme: $ Gen $ on input $ 1^n$ uniformly samples and outputs $ k\leftarrow \{0,1\...
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192 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 ...
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302 views

Can we construct a PRF directly from a one way permutation function?

In Introduction to Modern Cryptography first a pseudo random generator (PRG) is constructed from a one way function (OWF). After that the PRG is used to to construct pseudorandom functions (PRF). Is ...
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179 views

Finding the cycle sets of an LCG

My LCG has the form: $$S_0 = k$$ $$S_{n+1} = S_n \times a + 1 \pmod m$$ Each choice of $k$ generates a different sequence but in some cases a sequence may just be a cyclic shift of another. In this ...
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272 views

Is a PRG that reveals the first bit of the input secure

Let $G:(0,1)^n \rightarrow (0,1)^{n+1}$ be a secure PRG. Define $G'(s):=s_1 ||G(s)_{2,...,n+1} $. ($||$ is concatenation, and the subscript $ _{2,...,n+1}$ means the last $n$ bits of $G$) I claim ...
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209 views

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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312 views

On the Definition of a PRG and a CSPRG

I've been looking at the definition of a PRG, here. This is a broader notion than a cryptographically secure PRG ("CSPRG"), which is described here. I am realizing that I am very confused by this ...
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232 views

Integer factorization based password authentication

After looking at this security issue at DjangoProject, I started to think in a password-based authentication that places the burden of PBKDF2 (or whatever is the hashing function) on the client. So I ...
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How many bits of cryptographic security do these XOR Mid-Square random numbers have?

This pseudo-random number generator uses only XOR and Mid-Square operations: Get one secret 128-bit truly random seed $R_0$ Generate a million secret $R_j$ by the recurrences (for $1\le j\le 1000000$)...
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215 views

Decentralized consent over a random number

Maybe, some of you remember having to pick one person during playing as kids. That person would than have to catch the others for example. The methods to pick given person often would either depend on ...
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229 views

Showing a generator based to pseudorandom function is also pseudorandom

First of all sorry for the bad title, this is an exercise I'm struggling with: Let $F_k$ be a pseudorandom keyed function (abbreviated to PRF) with key, input and output of length $n$. Define the ...
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62 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 ...
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91 views

Polynomial restriction for PRG

Say we have a PRG $G(l,x)$ that expands a random string $x$ to length $l$ and is pseudorandom for any $l$ polynomial in $n$ (where $n = |x|$). Is $G$ pseudorandom for any $x$ of arbitrary length? I'm ...
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563 views

Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?

If $F$ a PRF, and we construct $G$ using $F$ in the following way: $$G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$$ where $|s|= n$. Is $G$ then a PRG? If so how can I prove this? If not how can $G(s)$ ...
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262 views

How can I construct a distinguisher given an inverter?

Let $ PRG: \{ 0, 1\}^n \rightarrow \{ 0, 1\}^{n+s}$ be a pseudo random generator and let $A$ be an inverter that runs in polynomial time, specifically: $\large \mathbb P_{d \leftarrow PRG(U_n)}[ A(d) ...
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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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41 views

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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1answer
78 views

Question about the Proof of “Pseudorandom generators imply one-way functions” in “Foundations of Cryptography”

In "Foundations of Cryptography, Volume 1" by Oded Goldreich, chapter 3.3.6 states the following theorem: Let $G$ be a pseudorandom generator with expansion factor $l(n) = 2n$. Then the function $f\...
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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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284 views

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 ...
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213 views

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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107 views

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 ...
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Pseudorandomness based on homomorphic multiplication property of Paillier cryptosystem

Given the instance $(n, g, \lambda)$ of Paillier cryptosystem with $\text{ord}(g) = n \lambda$ (symbols have their usual meaning), and $c = g^{na}$, is it possible to distinguish (computationally) $c' ...
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122 views

Indistinguishable encryptions and CPA-secure example

Let $ F $ be a PRF and $ G$ be a PRG with expansion factor $n \to n +1 $ For the following encryption scheme, decide whether it has indistinguishable encryptions and whether it is CPA-secure. ...
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Never design your own crypto…how to design a PRG

As a new learner of cryptography I have learnt from online tutorials and lectures not to design your own crypto. What I am trying to understand is the fundamental to designing PRGs to a given context ...
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113 views

Calculating t and epsilon for a computationally indistinguishable pseudo random generator

I have a PRG $G : \{0, 1\}^n \rightarrow \{0, 1\}^{2n}$. How would you go about calculating the optimal size of $n$ given that you have $$\epsilon = \cfrac{1}{2^{80}}$$ and, $t = 2$ years for a ...
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143 views

$G_f(x) = x \|f(x)$ is not a PRG with $\operatorname{DPT}$-computable function $f$

Let $f:\{0,1\}^* \rightarrow \{0,1\}$ be any $\operatorname{DPT}$-computable function. Show that $G_f(x) = x \|f(x)$ is not a PRG. Can anyone help me on understand how to prove this?
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Mersenne Twister's vulnerabilty with small-size distributions

C++ rookie here, trying to wrap his head around (CS)PRNGs. I (assume that I) already understand the concept of the Mersenne Twister being "broken" (i.e. not cryptographically secure) due to its ...
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139 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 ...
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309 views

Assume G(s) is a PRG, is the following also a PRG?

Let s be a n-length binary word and not_s its negation. Let G be a PRNG with expansion 2n. Prove that H1(s) = G(not_s) is also a PRG? Prove that H2(s) = G1(s)||G2(not_s) is also PRG. Given ...
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202 views

Pseudo-random function where the output is inverted using XOR

I'm looking to know whether or not this PRF is secure : $$F'(k, x) = F(k, x) ⊕ 1^n$$ knowing that $F$ is already a secure PRF for $$\{0, 1\}^n × \{0, 1\}^n → \{0, 1\}^n$$ with, for example, $n= ...
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Assume $G$ is a PRG. Proof that $G'$ is PRG?

Let $G: \{0,1\}^s \rightarrow \{0,1\}^n$ be a pseudorandom generator (PRG). Are the following PRGs? $G'(x) = G(x)_{0,\ldots,n-2}$ ($G'(x)$ drops the last bit of $G(x)$) $G'(x) = G(x) \oplus ...
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how to prove by reduction correctly?

some times when see a problem like : if some G is a PRG then G' is also a PRG. we prove this by reduction in the following way: we assume there is a Distinguisher A for G' and we construct ...
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Does using pseudorandom generator more than once cause security loss?

Everytime we use the generator with itself there is security loss. Even if this loss is not enough to loose all cryptographic security, there is still some small loss in security. Is there any way to ...
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45 views

HMAC for provable server distributed randomness

I have an application in which a user must use a high-entropy salt to salt a message. Due to the fact that I can not rely on the user to actually provide a strong salt, the server must provide this ...
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377 views

Proving pseudorandom generators

Can anyone please help me on how to prove or disprove (by counterexample) whether the following function $G'$ is a PRG (Pseudorandom Generator) given that $G$ is a PRG. $$G'(s) = \operatorname{trunc}...
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PRG variant as a commitment scheme

I would like to use a PRG in order to achieve the commitment properties (i.e. Hiding and Binding), however, if we look at a general PRG we cannot state that it has the Binding property. First I show ...
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336 views

Is F' a pseudorandom function when F is composed with G, a pseudorandom generator?

If $F$ is a pseudorandom function, is $F'$ also a pseudorandom function in the following: $$ F'_k(x)=F_k(G(x)) \space \space \text, $$ where $G$ is $a$ pseudorandom generator? Also, does the other ...
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safe concating PRP and PRG

Suppose it is necessary to build a safe PRG. You have one PRP with $\epsilon = \frac{1}{2} ^ {45}$, and one PRF with $\epsilon = \frac{1}{2} ^ {55}$. There is no mathematical relationship in the PRP ...
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29 views

How are implementations of PRF and PRG via AES-CTR different?

I heard that AES-CTR can be used for implementation of PRF and PRG. What is the difference between these implementations?
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How to shuffle a number between a range in a reversible manner

I have to generate identification number plates from a database ID. These ID are composed of three letters and three numbers e.g. BAC 212, I already have a function ...
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87 views

Oracle version of the IND-PRG game with q queries

Consider the following oracle-based game: $O_0$: Init: $1^n$; Query: output $y \stackrel{u}{\in} \{0,1\}^{l(n)}$ $O_1$: Init: $1^n$; Query: output $G(x)$ with $x \stackrel{u}{\in} \{0,1\}^{n}...
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131 views

Making PRFs out of PRGs

Is it possible that we take a $PRG$ $G(k)$ of stretch $n\cdot2^n$, and read its output as the table of a $PRF$ $F(K)$ with input and output size of $n$? Intuitively it sounds possible however I read ...
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247 views

Is there a password hash function with a human component?

Sort of Related: Is there a cryptographic hash function that can be performed with pencil and paper? One problem with hashing passwords is that the attacker has more of everything it seems. More ...
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Random UUID PRNG source

I have been fiddling around with UUIDs for a while (background info: http://gh.peabody.io/uuidv6/, https://github.com/bradleypeabody/gouuidv6, and am working on: this) and am starting on a prototype ...
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219 views

Random number generator in a 2p2 Network

for my thesis I am trying to develop a system where nodes from a peer to peer network agree in generate a random number every tot seconds. I am stocked in this problem since almost 1 week anyone can ...