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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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4
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2answers
168 views

Is $F(x) =Ax+b$ a pseudorandom function or not?

Consider the following keyed function $F$: For security parameter $n,$ the key is an $n\times n$ boolean matrix $A$ and an $n-$bit boolean vector $b$. Define $F_{A,b} : \{0, 1\}^n->\{0, 1\}^n$ by $...
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1answer
51 views

Instead of sending a set of random values, send a key for a PRF

Some Protocols require one party to send $n$ random challenges (or random values) to another party. For communication efficiency purpose, one can pick a random key for a pseudorandom function, and ...
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1answer
290 views

How is a PRP different from PRF? Both can be inverted to get the same input

PRP is said to be a bijective function which means that there is a one-to-one mapping with the output. And hence the output can be inverted using the decryption algorithm to get the same input. ...
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0answers
131 views

Is $F_k(x)=H_k(x \oplus H_k(x))||H_k(x)$ a PRF, where $H$ is a PRF?

Let $H_k(x)$ be known to be a PRF from the family of PRFs defined by $H_k(x): \{0,1\}^{n} \times \{0,1\}^{n} \rightarrow \{0,1\}^{n}$, and then define $F_k(x) = H_k(x \oplus H_k(x))||H_k(x)$. Here,...
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0answers
39 views

Use derived keying material as key for stream cipher

Section 7.3 of SP 800-108: To comply with this Recommendation, the derived keying material shall not be used as a key stream for a stream cipher. Footnote: The level of security provided by ...
3
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1answer
159 views

Key derivation: Does it make sense to use KDF and PRF consecutively?

I'm in a project, where the output of a Key Agreement algorithm (uses ECC) is used as input for a KDF, and the output of the KDF (X9.63 KDF) is consecutively used as input for a PRF (CMAC) to ...
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1answer
410 views

Given a secure PRF $f(k, x)$, is $f(x, k)$ also a secure PRF?

Let $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}^n$ be a secure PRF. Define $F(k, x) = f(x, k)$. Is $F(k, x)$ also a secure PRF?
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1answer
54 views

Unsure of syntax used in Searchable Encryption

This image is taken from Algorithm 1 from "Σoφoς – Forward Secure Searchable Encryption, CCS '16". On line 4 there seems to be a new variable, M, that is never defined throughout the rest of the ...
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1answer
107 views

Can we use Pohlig-Hellman Exponentiation Cipher with a PRG to achieve an oblivious PRF

The Commutative Cipher Setup Alice and Bob agree on a 2048-bit safe-prime $p$, where $(p-1)/2$ is also a prime. Both parties have an encryption exponent $e$ in the range $(1, p-1)$ with $gcd(e, p-1) =...
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1answer
206 views

Can we convert a pseudorandom function (PRF) to an Oblivious PRF (OPRF) through an Oblivious Transfer (OT) protocol?

I'm a software engineer, so I generally think in building blocks. And I'm not so familiar with the Math notation in Crytography, so I'll stick with function calls and function blueprints (which I ...
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2answers
128 views

Does PBKDF2 reveal any knowledge about the salt?

DK = PBKDF2(PRF, Password, Salt, c, dkLen) When PBKDF2 is used for key derivation (not password hashing), is it possible for an adversary who doesn't know ...
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2answers
454 views

Relationship between PRF/KDF/MAC?

It seems that not every MAC is a KDF. But would any PRF also work as both KDF and MAC? Could someone explain the relationship between these 3 definitions?
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0answers
45 views

Question on inputs of PRFs and HKDF KDF

I've read a lot of information about PRNGs, PRFs and KDFs. As far as I know: PRNG: The seed for the PRNG must be a uniform string. It transforms a short real uniform string into some bits of pseudo-...
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1answer
310 views

Is $F'_k(x) = F_k(x) \oplus k$ a pseudo random function?

Let $F_k$ be a pseudo random function. Is $F'_k(x) = F_k(x) \oplus k$ necessarily a pseudo random function? I think that it is a PRF, but I just can't find a reduction that works with it.
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1answer
127 views

When will a function $f$ be a truly random function?

I'm familiar with a definition of a truly random function: $f$ is a truly random function if it was selected uniformly from the set of all the functions $f(x):\{0,1\}^{n} \to \{0,1\}^{n}$ But I'm ...
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2answers
247 views

PRF from hash function?

Let $G=\langle g \rangle$ be a cyclic group of prime order $Q$. Let $H_1:\{0,1\}^*\to G$ be a hash function. Is the following a family of PRF for $s \in \mathbb{Z}_Q^*$? $$f_s(x)=(H_1(x))^s$$ Or ...
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1answer
149 views

is XOR-hash difference-unpredictable

Let $F$ be a PRF. The $XOR\text{-hash}$ is defined as: ...
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2answers
79 views

Why isn't exponentiation in a prime order group a random function?

Give a prime order group $\mathbb Z_p$, let's take a generator $g$ and raise it to $x$, now, is $g^x$ a random number and indistinguishable from any other element in the group? What am I missing?
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0answers
83 views

Are all commitment schemes pseudo-random functions?

I am interested in understanding whether or not we can use commitment schemes that are both hiding and binding as pseudorandom functions. My reasoning is that if a commitment is hiding, then an ...
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2answers
453 views

Proof that MAC and hash composition is insecure

Let $F$ be a secure PRF and $H$ a universal hash function. How can I exhibit a pair $(F,H)$ whose composition $$S'((k_1, k_2), m) = F(k_2, H(k_1,m))$$ is an insecure MAC (or an insecure PRF, since a ...
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1answer
733 views

How to prove a function is negligible?

My question essentially concerns how to prove if a function is negligible. As a matter of fact, though this question might seem very basic, it seems that most of the "proofs" of negligible concern ...
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0answers
70 views

why isnt E a secure block cipher

Let $\pi : \{0,1\}^n \rightarrow \{0,1\}^n$ be a permutation. Let $E(k, x) = \pi(x \oplus k)$ where $x,k \in \{0,1\}^n$. Why isn't $E$ a secure block cipher? My idea: Suppose $E$ is a secure block ...
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2answers
196 views

Are the following functions pseudorandom?

Given a PRF $F $, such that for each $k \in \{0,1\} \ ^ n$ , $F_k:\{0,1\} \ ^ n \to \{0,1\} \ ^ n$ , is the function defined by $W_{k_1,k_2}(x) = F_{F_{k_1(0 \ ^n )}}(x) || F_{k_2}(x)$ also a PRF? I'...
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0answers
60 views

Did “The Catena Password-Scrambling Framework” make an error in the reduction of its pseudorandomness?

I was reviewing the most recent version of the Catena paper and they made some claims that I find questionable in their reduction of the pseudorandomness of the output of Catena (p. 32). First I will ...
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1answer
246 views

Why do we use (pseudo) random permutations and not (pseudo) random functions for en- and decryption?

Why do we use pseudo random permutations and not pseudo random functions for encryption an decryption?
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2answers
167 views

Building adversary to show a PRF is not secure

Let $F(k,x)$ be a secure PRF over $(\mathcal{K},\mathcal{X},\mathcal{Y})$ where $\mathcal{K} = \mathcal{X} = \mathcal{Y} = \{0,1\}^n$. Let $F'(k, x) = F(F(k, 0^n), x) \; \Vert \; F(k, x)$. $a \; \...
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0answers
362 views

secure PRFs and XOR

Let $F(k,x)$ be a secure PRF over $(\mathcal{K},\mathcal{X},\mathcal{Y})$ where $\mathcal{K} = \mathcal{X} = \mathcal{Y} = \{0,1\}^n$. Why is the function $F_1(k, (x_1, x_2)) = F(k, x_1) \oplus F(k, ...
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1answer
299 views

Relationship between CCA/CPA-security and PRFs

I'm a bit confused about the relationship between CCA/CPA-security and PRFs and particularly when do we think of encryption and decryption as a PRF. Assume we have an encryption scheme $\Pi = (Enc, ...
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2answers
117 views

why isn't G a secure Pseudo-Random Function?

let $F(k,x)$ be a secure Pseudo-Random Function defined over $\{0,1\}^n$, that means: $F: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}^n$ define a $G(k,x) = F(k,x) \; \Vert \; 0$ how can one ...
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1answer
164 views

Interpolation in the Exponent (Shamir Shared PRF)

Trying to implement the Diffie-Hellman distributed PRF mentioned by Cachin : https://cachin.com/cc/papers/abba.pdf. It makes sense to me... just use the same Lagrange coefficient I'm using to combine ...
4
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1answer
791 views

Can someone explain how OPRF (Oblivious pseudo-Random Function) is based on OT (Oblivious Transfer)?

Can someone explain to me how OPRF is based on OT extensions? I'm currently reading papers about private set intersection problem that uses efficient OT-based protocols based on OPRF, the link of the ...
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1answer
73 views

Is there a property comparable to IND-CPA for hash functions taking a random value?

I would like to have a function $F(x, rnd)$, where $rnd$ is a fresh random value, such that it is hard, given $x_0$ and $x_1$, to distinguish $F(x_0, rnd)$ from $F(x_1, rnd)$, EDIT: but the values ...
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0answers
123 views

Does there exist a highly irreversible hash function or a highly irreversible pseudo-random number generator?

In my previous question, I asked about potential symmetric cryptosystems which are designed to be computed by a reversible computer. I am now wondering if there are any cryptographic hash functions ...
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1answer
205 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 ...
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0answers
364 views

Can Verifiable Random Functions be used to pick a random node from a pool?

Let's say that I have a decentralized system and I have a list of nodes published on a pubic log like a blockchain. I want a node A to be able to connect to another ...
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0answers
162 views

Define a DEC algorithm for a problem

Given $F$ , a PRF family and $F_{n,k}$ a permutation over the set $\{0,1\}^n$. In addition, each permutation (as usual for PRF) and their inverse (not usual) has an efficient calculation. Define: ...
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1answer
143 views

Security of OFB mode if PRP is used instead of PRF

In the cryptography lecture at my university, we had the theorem that (randomized) OFB mode is IND-CPA secure if the used pseudorandom function (PRF) is IND-PRF secure. Afterwards, we investigated ...
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0answers
58 views

Is there any OPRF (oblibivious pseudo random random functions) between one receiver (1 input) and n senders (n inputs)? any references to read?

I am looking for some references for multi-party / distributed Oblivious pseudorandom Functions. I found two party OPRF protocols between a sender $S$ and a receiver $R$ for securely computing a ...
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0answers
122 views

Luby-Rackoff theorem for Generalized Feistel

I was reading about Luby-Rackoff theorem from various sources: [1], [2], [3], which says you need at least 3 rounds of a $2$-branch Feistel network to get a PRP if the underlying $f$ function is a PRF....
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3answers
632 views

Is a PRF always collision resistant?

Context: We usually assume that the hash functions we use in practice are both: collision resistant and pseudorandom. I wonder what's the relation between those properties. Question: Is a pseudo ...
6
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1answer
336 views

Homomorphic Evaluation of Pseudo Random Function

I'm looking for a special Pseudo Random Function (PRF) $F_k()$ which follows the below. For fully homomorphic encryption (FHE), $\mathit{FHE}(F_k(x)) = F_k(\mathit{FHE}(x))$. Or is there any ...
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0answers
165 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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0answers
64 views

Does a distinguisher for an PRF based on a hash make the hash function insecure?

I recently found a distinguisher for the PRF $f(s, i) = H(s || i)$ where $s$ is the seed and $i$ is a counter and $H$ is a cryptographic hash function, which is able to distinguish $f(s, i)$ from true ...
3
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1answer
614 views

Existence of PRF $\implies$ existence of PRG

Let $F:\{0,1\}^n\times \{0,1\}^m \to \{0,1\}^l$ be a PRF. I want to show that $G(-)=F(-,x_0)$ is a PRG for every $x_0\in \{0,1\}^m$. Proof attempt: Let $D$ be an efficient distinguisher against $G$...
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2answers
154 views

Is this scheme multi-message secure? [closed]

Let $G$ be a pseudorandom generator. Is the scheme with encryption $$\text{Enc}_k(m) = s \| \left( m\oplus G(k) \oplus s \right),\quad s\in\{0,1\}^n \text{ uniformly sampled},$$ and decryption $$\...
2
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0answers
711 views

Showing the concatenation of pseudorandom functions is a pseudorandom function [closed]

The definition of a pseudorandom function is: Let $F:\{0,1\}^*\times \{0,1\}^* \to \{0,1\}^*$ be an efficient, length-preserving, keyed function. $F$ is a pseudorandom function if for all ...
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1answer
3k views

How to calculate entropy of a random number?

I am having a set of random numbers and I want to calculate entropy of them. I searched many entropy calculation formula, but I didn't get it. Can you elaborate a little bit?
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4answers
1k views

The difference between MACs vs. HMACs vs. PRFs

I have some confusion regarding the difference between MACs and HMACs and PRFs and when to use which term. If the function is computed using a hash and secret key like the following, is this a HMAC ...
8
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2answers
646 views

Why is this function pseudo random (PRF)?

First, I want to clarify this is not homework. I encountered this question (here How can I prove that a function F isn't a pseudo random function?) while studying for a test coming soon. $F'_k(x) ...
3
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1answer
160 views

Security proof for CBC as a prefix-free PRF

I am currently trying to fully understand Dan Boneh's/ Victor Shoup's proof in their excellent crypto book draft, that the raw CBC construction is a secure pseudo random function family for prefix-...