A pseudo-random function is an efficiently-computable function which emulates a random oracle.

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Permuted vectors

Consider we have two vectors $v_1, v_2$ of size $n$, and each vector contains $n$ elements. We permute the vectors as: $\pi (k_1,v_1), \pi (k_2,v_2)$. Where $\pi (k_i,v)$ denotes a permutation of a ...
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Swap $x$ and $k$ in GGM construction

I'm studying the Goldreich-Goldwasser-Micali construction from pseudo-random generators to pseudo-random functions. In this specific construction, assume $G:\{0,1\}^n\rightarrow \{0,1\}^{2n}$ is a ...
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Is $f\colon x\mapsto g(x+1)$ necessarily a pseudorandom function?

Let $l\in\mathbb N$ and suppose $$g\colon\;\{0,1\}^l\to\{0,1\}^l$$ is a pseudorandom function. Is $f$, defined as below, necessarily a pseudorandom function as well? $$f(x)=g((x+1)\bmod2^l)$$
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Pseudorandom Function Proof

Given a set of pseudorandom functions $F=\{f_s^i\}_i$ for each $s\leftarrow\{0,1\}^n$ generated at random; moreover each $f_s^i$ uses a specific PRG $G^i:\{0,1\}^n\to\{0,1\}^{2n}$, where: ...
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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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Pseudorandom function library [closed]

I'm wondering if there is any library supporting pseudo-random function, so I can specify the key length and output domain. Is it correct that I need to use a block cipher for this purpose? Any ...
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PRF based on the GGM construction

What's the differences between the concepts “pseudorandom generator” and “pseudorandom number generator”? In fact, I want to implement a pseudorandom function based on GGM's construction at ...
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What is the difference between a hash function and a pseudorandom function? [duplicate]

Read the title. I've seen in RFCs that some MAC functions are called "pseudorandom functions". What are those? How are they different than hash functions? Why can't a hash function be used instead?
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Pollard's Rho - Restricting the random function to the exponents

Pollard's Rho is usually constructed using a function $f:G \rightarrow G$ which behaves 'random enough' in order to detect a collision with Floyd's cycle detection trick. It is easy enough to observe, ...
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Difference between Pseudorandom Function vs randomly chosen function

I am currently going through a course in cryptography. In this, I stumbled upon Pseudorandom Functions. I got a little idea of Pseudorandom Generators which map an input string (key) to an extended ...
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Proving the existence of a pseudorandom function

I've been reading the Introduction to Modern Cryptography book by Katz and Lindell as part of my own learning and have come across this exercise which I am not sure how to approach. The exercise is: ...
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Implementing a pseudo random function in practice

Can anyone point me to a C++ crypto library with an implementation of a pseudo random function (PRF)? I don't have much background in crypto theory, but I am in the middle of a graduate course ...
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INT_32_BE in PBKDF2

Trying to understand PBKDF2 in detail. It is clear that the password and the salt is given to the PRF (which is HMAC-SHA-1 in the specification). But what is the role of the INT_32_BE(i)? What does it ...
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118 views

CBC-MAC based on PRF

Why is the block cipher in the CBC-MAC taken to be a pseudo random permutation (PRP) and not a pseudo random function (PRF)? We don't need the bijective property of the PRP. So why go with it?
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Luby-Rackoff theorem confusion

The Luby-Rackoff theorem states that if a round function is a secure pseudorandom function (PRF) then 3 rounds are sufficient to make the block cipher a pseudorandom permutation (PRP). PRPs are ...
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CTR mode encryption using PRG

In CTR mode encryption, the encryption block is not required to be invertible. Thus, a PRF can be used instead of a PRP. However most of the implementations of CTR mode are based on AES which is a ...
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Skein or Keccak stream cipher construction

I am wondering if using Skein or the Keccak hash algorithm in this construction (as a stream cipher) is secure: $H$ = Keccak or Skein hash with a 256 bit output $K$ = The main 256 bit random key, ...
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Turning PRPs in PRGs with a counter

I am following the Coursera Cryptography I course and I have the following question, I am a bit perplexed by the statement, in week 2 lecture "What are block cyphers?" that a counter-mode PRF is a ...
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Is a keyed PRF a MAC?

I remember I read that a MAC can be considered as a PRF. Can a variable-length input keyed-PRF be considered as a MAC?
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Cryptographic pseudo-random generation of address subsets

Suppose I have devices which broadcast, on an insecure channel, 32-bit addresses. I want to make these devices untraceable - one way to do so is to allocate for each device a distinct subset of ...
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Special random distribution algorithm

I am implementing ring signatures as a part of an authorization system. Since the number of users could get high enough to make computation on end-user devices infeasible, I am thinking of ...
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PRF and hash functions

Is there a difference between PRF and a hash function? For example: Creation of a secret key is using PRF and creating a secret key is using hash function.
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How to implement a Cryptographic Pseudo Random Function

I need three pseudo random functions which all take a seed S (t-bits long). The functions should map from $d$ bits to $d$ bits $d$ bits to $1$ bit $d$ bits to $t$ bits $d$ is $10$ bits $t$ is ...
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Security of KDF1 and KDF2 (hash based KDF's)

It's still common to come across implementations of KDF1 and KDF2. Basically these are KDF's that simply derive multiple keys from the key seed and a counter: $K_i = KDF(K_{master}, i) = H(K_{master} ...
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Exchanging Keyspace and Message space in PRF

Suppose there is a secure PRF $F: K \times X \to Y$. Then is $F': X \times K \to Y$, defined by $F'(x,k):=F(k,x)$, a secure PRF? In my opinion it should be because exchanging the keyspace with ...
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What is the difference between PRF and a Random Oracle?

What is the difference between Pseudo Random Functions and Random Oracles? Is the difference only about the domain of PRFs and Random Oracles, former having a fixed domain and latter can act on any ...
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TLS Key Block calculation - What is a PRF?

In Section 6.3 of the RFC for TLS 1.2, it is written that the key_block is derived from the following formula: ...
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HKDF vs TLS PRF. Which of the one is better? [closed]

Which of the one (HKDF or TLS1.1+ PRF) is more secure and why?
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What might be assumed about a PRF if the key has been chosen?

The defining feature of a PRF $f:\{0,1\}^k\times\{0,1\}^s\mapsto\{0,1\}^*$ is that, if the first parameter is selected at random, it should be indistinguishable from a function ...
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Traitor-tracing PRF

I'm looking for a pseudorandom function (PRF) with "traitor-tracing" properties. More specifically, I'd like there to be multiple equivalent keys, so I can give different parties different keys, but ...
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Private set intersection, using a semi-trusted server

Alice has a set $S$ of words. Bob has a set $T$ of words. They want to compute the intersection $S \cap T$ of their words, with the help of a semi-trusted third party Trent. Trent runs a central ...
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Is this a pseudo random function (PRF)? F(k,x) = f(k,x) - f(k,x-1)

I have a question about Pseudo Random Functions. Let $f:\{0,1\}^m \times \{0,1\}^n → \{0,1\}^n$ be a secure PRF. Define $F(k,x) = f(k,x) - f(k, x-1 \bmod 2^{n}) \bmod 2^{n}$. Is $F$ is a secure ...
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Prime factors of non-random keys

I have been working on a challenge i found on the internet. It is as follows: You've stumbled onto a significant vulnerability in a commonly used cryptographic library. It turns out that the ...
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PRP, PRF and modular arithmetic

Are there any arithmetic or mathematical functions that can be used as PRPs or PRFs ? Since, Conventional block ciphers like AES are that are proven to be good PRPs are not based on mathematics but ...
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Prove that two MACs with incremendal PRF application are not secure

How do I prove the following MACs are insecure?                                                        1                                                                                   2
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What is the impact of different modes on pseudo randomness of AES?

AES in CBC-MAC mode is proven to be good PRF . But is there any study done on other modes ? how good is ECB mode as PRF ?
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Why is this MAC based on secure PRF with ordering and randomization insecure?

Is this MAC secure: To authenticate a message $m=m_1||\ldots||m_l$ where $m_i \in \{0,1\}^{n/2}$, choose $r \leftarrow \{0,1\}^n$ at random, compute $$t:=F_k(r)\oplus F_k(\langle 1\rangle || ...
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how to truncate a PRF on n bits to PRF on t bits where t < n? [closed]

Dan Boneh's courersa lecture on format preserving encryption at 5.50 mins , talks about truncating a PRF on $n$ bits to PRF on $t$ bits. The approach is by appending $(n-t)$ zeros to input $t$ bits ...
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Security based on PRF

I've seen that there is several kinds of PRF, and sometimes people speak about strong PRFs. When proofs of a protocol or algorithm are given based on the assumption of the use of a PRF, are they ...
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Why is it important to generate a pseudorandom permutation from a pseudorandom function?

Most of the papers on block cipher constructions, especially the ones which discuss constructing block ciphers of arbitrary lengths or small domains, the techniques are designed based on building a ...
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Protocol/algorithms based on a variable-length input PRF

Are the proofs based on a PRF assumption still valid when using a variable-length input PRF ? The answer might be obvious, but I have a doubt.
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Is this EAX extension weakening the (provable) security of EAX?

I would like to insert a key deriving function into EAX mode, in order to hamper brute-force attacks for a key-size restricted cipher (56 bits). The modification inserts an identical multi-block ...
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1answer
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The Goldreich-Goldwasser-Micali Construction with bad PRGS

I understand that if we have a secure PRG then the Goldreich-Goldwasser-Micali construction gives us a secure PRF. However, what I've not been able to find much material on is how will the GGM ...
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Is there any existing analysis for this construction to turn a tweakable blockcipher into a PRF?

I'm basically looking at this construction to turn a tweakable blockcipher $E_c(x)$ taking a key $k$, nonce $n$, counter $c$ (forming tweak $t = c||n$) and an input $x$ into a PRF on an ...
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Estimating bits of entropy

Best ways to estimate average bits of entropy in a byte stream. I know there are different statistical tests out there (NIST, Dieharder, etc), which all do different ways of analyzing entropy. What ...
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Salsa20 in Davies-Meyer mode with a fixed key (message): is it one-way?

Say I have a function that calculates a pseudo random permutation and this function is easy to invert. For example $P(i) = AES_k(i)$ where $k$ is a publicly known key. So anyone can compute $P(i)$ ...
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Hash function based on pseudorandom functions and security

Are there hash functions that make use of pseudorandom functions. Precisely, I'm looking for a specification of a hash function based on PRF (and based on the security of such a primitive).
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security amplification

Reading some papers on security amplification of weak-PRP written by Stefano Tessaro, I noticed the use of notion "epsilon-PRP" and the notion of "security amplification". These notions, in ...
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Why is it said that if we know few bits of pseudo random sequence we can predict the whole of it?

I am new to this cryptography and in the source from which i study it is said that if we know the first few bits of a pseudo random sequence we can predict the whole of it.How is it possible? The ...