Questions tagged [pseudo-random-function]

A pseudo-random function (PRF) is a family of deterministic functions indexed by a parameter, such that a randomly selected instance is computationally indistinguishable from a uniformly random function with the same input and output spaces.

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2answers
32 views

Mathematical definition of deterministic and non-deterministic random bit generators

Can anyone give the mathematical definition of deterministic and non-deterministic random bit generator? Providing a reference will also be very helpful.
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Is this a PRF? Fk(x) = G(k⊕x) where G is a PRG

This is not homework, but a random thought. Let $G(x)$ be a PRG. We define the following function: $$F_k(x) = G(k\oplus x)$$ My intuition is that it shouldn't be a PRF but I couldn't come with an ...
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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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Which is faster, PRF based on AES-CTR and PRF based on BLAKE{2,3}?

Recently Blake3 has been announced, which can be used as PRF. I'm wondering which PRF is faster, namely PRF based on Blake3 or the one based on AES-CTR?
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How can we implement a PRF with 1bit input space and 1024bit output space using AES securely?

I'm considering an implementation of PRF $F:\{0,1\} \times \mathcal{K} \rightarrow \{0,1\}^{1024}$ with a key space $\mathcal{K}$ in particular with AES-128 in counter mode. Since output space is ...
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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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1answer
48 views

Why is it not ideal to rely on interactive assumption to build PRF?

I understood the meaning of interactive assumption from What is the notion of an interactive assumption? . However, I am not sure why there exists a research field of constructing PRF from standard ...
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1answer
65 views

Do 'nonsequential' PRNGs exist?

It is my understanding that PRNGs typically use a seed and can then generate random values one after the other. This is what I mean by being 'sequential'. How about a PRNG which allows me to retrieve ...
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Sponge with PRF instead of PRP

In most uses of Sponge mode of operations such as SHA3 and many of the round-2 candidates in the NIST lightweight cryptography project, the underlaying primitive is a cryptographic permutation - that ...
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Is changing-key $F_1$ a secure PRF?

Let $F(k,x):\{0,1\}^n\times \{0,1\}^n\rightarrow \{0,1\}^n$ be a secure PRF. Prove or disprove whether $F_1(k,x)=F(F(k,0^n),x)$ is a secure PRF. My guess would be that it is PRF, and the part of ...
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Is there a cyclic RNG without an explicit form for $i$'th element which is guaranteed to have a sum of zero (subset of elements, $\mod P$ possible)

Let $X$ be a sequence element list of (pseudo) random values generated by a RNG and $x_i \in X$ a member of it. The period length is $k = |X|$ and it is a cyclic generator. For $i>k$ the value $x_i ...
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Random oracle : Replay

What I understand about the random oracle game: The adversary can query the oracle polynomial many times with the same (secret but unknown) key. From the output returned by the oracle, the ...
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203 views

Any speed up methods for finding the index of a random value produced by the Inversive congruential generator?

The Inversive congruential generator produces random values with: $$x_{n+1} = a\cdot x_{n}^{-1} + b \mod P$$ (special case if $x_n=0$ -> $x_{n+1}=b$) starting with an initial value $x_0$ With well ...
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Wrong Proof of Secure PRF

Disclaimer, this is not homework; I found the question statement here: Security of this PRF To restate the question: Given $F$ a secure PRF with input size $\lambda$. Define $F'$ as $F'(k,x\...
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Necessary conditions for construction of $n$ to $p(n)$ pseudorandom generators from $n$ to $n+1$ generators?

Given a polynomial time deterministic algorithm $G_1:\{0,1\}^n \rightarrow \{0,1\}^{n+1}$, consider the function $G:\{0,1\}^n \rightarrow \{0,1\}^{p(n)}$ constructed as follows: Let $s \in \{0,1\}^n$ ...
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What is the difference between pseudorandom permutation/pseudorandom function/block cipher?

What is the difference between; pseudorandom permutation pseudorandom function block cipher? Very confused with the 3 terms and I am not good at advanced math. Can someone explain in plain word?
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Can Trivium be used as a PRF?

The Trivium encryption algorithm has two inputs, key and IV, both of which are 80 bits long. Let's call it Trivium(key, IV) → keystream. My question is whether doing Trivium(key, input) and taking the ...
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Is F_k_1(x) \xor F_k_2(x) a pseudorandom function?

I'm trying to determine if $F_{k_1, k_2}(x) = F_{k_1}(x) \oplus F_{k_2}(x)$ ($k_1 \neq k_2$ because that would be lame) is a pseudorandom function. My hunch is that it is. My reduction proof proceeds ...
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Proving a function is or is not a pseudorandom function F_k(x) = F_k(x)||0

I have 4 functions to analyze. I need to determine if they are or are not pseudorandom and give a proof/counterexample. I'm having trouble just determining if they are - let alone proving or giving ...
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1answer
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Post-Quantum security of Pseudo-Random Functions

I am wondering what is the exact post-quantum security of a PRF. I know that for most symmetric mechanisms, it is assumed it is sufficient to double the key size, but I am looking for a more precise ...
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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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What is the most secure/reliable CSPRNG currently available? [closed]

In terms of period length, uniformity/distribution, what is the most secure/reliable CSPRNG currently available?
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Help, Feedback and Solutions to a problem on a PoC CSPRNG

Background I do not recommend trying to roll your own crypto. This is just a for-fun PoC, which won't be used in any public or private scenario. I am creating a PoC nearly-true random number ...
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What is the practical impact of using System.Random which is not cryptographically random?

I recently noticed a .NET software using PBKDF to derive an encryption key from a password string. This password string was ...
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1answer
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Fundamental difference between the constant, key, nonce, and counter bits in Salsa20/ChaCha20 or AES-Encrypt?

The Salsa20 core function takes a 128-bit constant, 256-bit key, 64-bit counter, and 64-bit nonce and produces a 512-bit value. Or more generically, it is a mapping from 512-bit values to 512-bit ...
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Security of this PRF [closed]

Given $F$ a secure PRF with input size $\lambda$. Define $F'$ as $F'(k,x||x') = F(k, 0||x)\oplus F(k, 1||x')$ with $x$ and $x'$ of $\lambda-1$ bits. Is $F'$ a secure PRF?
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Output a pad (un-keyed, variable length) from an input seed (fixed value for same seed)

I want a function $y = f(x, len)$: $x$ is the seed. $y$ is the output. $len \in \mathbb{Z^+}$ is the length (bytes) of $y$ Select a seed string $x$ to generate a string $y$. For each same pair of $x$ ...
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189 views

Is $f(K, f(K, x))$ a pseudorandom function?

Given a PRF $f : \{0, 1\}^n \times \{0, 1\}^n \rightarrow \{0, 1\}^n$, is $f(K, f(K, x))$ a PRF, too? My hunch is to construct a PRP similar to Feistel ciphers but with the property $f(K, f(K, x)) = ...
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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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1answer
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A hash-based pseudorandom function

Let $H()$ be a cryptographic hash function. Question: Can we consider $c= H(r||i)$ as a pseudorandom value, where $i$ is a public value, $1\leq i\leq n$, and $r$ is a large uniformly random value/...
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1answer
88 views

Can you defeat AES-CTR's birthday boundary with a 2nd AES?

This follows on from How do I produce a stream of secure random numbers from AES-Counter mode? Consider then the generator:- $$ \operatorname{AES_{k1}}(n) \oplus \operatorname{AES_{k2}}(n) $$ ...
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1answer
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PRP vs PRF for the F-function of a Feistel network

A Feistel network is generally defined with a PRF for its F-function, but PRPs have been used as well. What are the theoretical cryptographic implications of using a PRP instead of a PRF? Does it ...
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1answer
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PRP, PRF change at next selection?

This is probably a silly question, and similar question was asked before; but I can not figure out what actually is PRP/PRF. For example, it is commented that: A Pseudo Random Function is a ...
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Do you really need a KDF when you have a PRF?

My understanding is that a KDF is like a PRF, except that it has a preliminary step that "extract" entropy. It is thus needed when the entropy is non-uniform (for example the output of ECDH is modulo ...
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1answer
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How does changing input size affect The Goldreich-Goldwasser-Micali Construction?

If we want to construct a PRF that is length preserving, it is easy to show with hybrid proof that the resulting construction is a PRF. But what happens when we have longer input. Supose that the ...
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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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Does a regularly reseeded PRNG provide backtracking resistance?

I'm currently discussing a security topic with some of my classmates. A cryptographic PRNG typically provides backtracking resistance if an adversary that compromises the internal PRNG state cannot ...
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A well known hash function?

Name a well-known and standardized function $F : \{0,1\}^{256} × \{0,1\}^{128} → \{0,1\}^{128}$ that is believed to be a pseudorandom permutation. I was thinking SHA256, but I am not sure. Can ...
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Tool to find non-linearity, resiliency and algebraic degree of a boolean function?

Is there any program or software to find out cryptographic properties like non-linearity, algebraic degree, balancedness and resiliency of a large boolean function?
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1answer
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Constructions of PRF (Pseudo Random Function)

I was taught only GGM based PRF construction in class. It's very inefficient. I am just curious about various PRF constructions from standard assumptions. Please provide a few PRF constructions from ...
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Which functions can be used as Pseudo Random functions? Can block Ciphers be used for this purpose with our own encryption function?

Since the cloud security algorithm I am trying to implement says that for a PRF, any secure encryption algorithm or a keyed hash function can be used. The security parameter I have chosen is 15 bits ...
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Statistical Tests for Pseudorandom Functions

Say I have an implementation of a potential Pseudo-Random function and I want to test whether my implementation does at least not contain any obvious flaws. As far as I understand, in other ...
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How to prove security of scheme constructed by Hash then PRP

Suppose there is a scheme where a message is first hashed and then sent to a PRP. If the hash is done using an $\epsilon$-bounded universal hash function and the PRP $K\times \{0,1\}^n\rightarrow\{0,1\...
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Patarin’s H-Coefficient Technique

I have come across many paper that applies Patarin’s H-Coefficient Technique in various cryptographic securities (KPA, CPA, CCA,...). I am asking kindly if someone could explain it simple with ...
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1answer
176 views

The role of IV when AES is used as $PRF$

We want to use AES as a pseudorandom function. Given a random master key, we want to derive a set of pseudorandom values/keys, e.g say $n$ keys. Then from each of those derived keys, we want to derive ...
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1answer
100 views

Formal definition PRNG

I tried to look for a book that presents cryptographic concepts(specially PRNG) in a formal way but what I find is an intuitive approach. So my question is what is the formal definition of Psuedo-...
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3answers
660 views

Truncating the output of AES-128

I'd like to use the output of a pseudorandom function (PRF) as a one time pad. I want to use AES-128 (as it's commonly used as a PRF). As we know AES-128 output 128 bits. Question: Would be secure ...
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1answer
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Give a distinguisher to differentiate between PRP and RPO

I have understood the proof that shows that a PRP is a PRF except for negligible probability $\frac{q(n)^2}{2^{-l(n)}}$. My computations suggest me that the same argument, perhaps with minor ...
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1answer
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Amplifying PRF Advantage

I am trying to solve this question and I have no idea how to find the value for $q$. I know that I am supposed to find the probability of $q>3q/512$ in terms of the equation $q$, but not sure how? ...
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Computing a probability

Let $(w_1,\cdots,w_l) \in (\{0,1\}^\lambda)^l$, and $r_1,\cdots,r_l $ are chosed as uniformly random from $Z^*_q$ such that $r_1+\cdots+r_l=0$ and $q$ is a large prime number. Also, Let $F$is a ...

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