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

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Let $F$ be a PRF, is the following $G(x)=F_{0…0}(x)∥F_{0…1}(x)|| … ||F_{1…1}(x)$ a PRG?

$F$ is a PRF with $n$ bit key, input, and output length. I know the answer is "NO it isn't!", but I can't understand why. Is that because on any input $x$, the keys for every $F$ in the concatenation ...
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90 views

How to prove that a function is not pseudorandom?

I am currently enrolled in a cryptography course, which uses the book by Katz and Lindell. I'm struggling with the exercies which ask for proofs, like the following one: Let G(k) be a PRG with ...
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Proving existence of an encryption scheme that has indistinghuishable multiple encryptions in the presence of an eavesdropper, but is not CPA-secure [duplicate]

I got stuck in trying to find a solution to the 3.7 exercise of the Katz-Lindell book. The exercise also assumes the existence of a pseudorandom function. The problem is that a multiple messages ...
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32 views

Does pseudorandom secret sharing require a central dealer?

I'm trying to figure out whether pseudorandom secret sharing (as described in this paper) requires a central dealer, i.e. one party who doles out keys to the other players and thus who would be able ...
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41 views

Shuffleless PRNG function with non-repeating values?

I need a simple PRNG function of type: Integer = PRNG(n, maxval) as I would like to count from 0 to maxval, not in a linear manner, but in a pseudorandom manner where I still use every value, but ...
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37 views

Pseudorandom functions: how are functions stored?

I am wondering about the setup for testing if a function family is pseudorandom. We step into a room, and query the black box with $x$, which yields $f(x)$, etc... We don't know if $f$ is a random ...
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1answer
29 views

What is the difference between a PRF and a PRF+?

What is the difference between a PRF and a PRF+? I am understanding them to mean the same thing, but I imagine that is because I don't understand their differences. The IKE RFC defines a PRF as: ...
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46 views

Pseudo Random Function

The definition of pseudo randomness that leads to pseudo random function talks about indistingishability of a key-ed function and a random function. i.e. The key-ed function family $\{F_k\}$ is PRF ...
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53 views

Cryptanalysis of Marvin32

So I am curious about the security analysis of Marvin32, the randomized hash algorithm used in .NET (to prevent hash-table DoS). I found the source code here: ...
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1answer
59 views

Is it OK to substitute a PRF for a random oracle?

Random oracles don't exist, but aren't PRFs essentially indistinguishable from them? So why can't we substitute pseudorandom functions wherever we use random oracles? And if we can do this, why is ...
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69 views

What is the difference between H(M) and H3(M, s, IDA)? [closed]

What is the difference between H(M) and H3(M, s, IDA)? I am aware of Hash function with a Message and a Key, but there are three parameters in: H3(M, s, IDA). Here M is the message, s is the key, ...
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145 views

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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1answer
34 views

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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1answer
50 views

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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71 views

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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82 views

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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1answer
105 views

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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1answer
234 views

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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56 views

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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4answers
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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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1answer
173 views

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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120 views

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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132 views

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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128 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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823 views

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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1answer
117 views

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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1answer
100 views

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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1answer
109 views

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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114 views

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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473 views

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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160 views

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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79 views

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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156 views

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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1answer
735 views

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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222 views

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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199 views

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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167 views

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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125 views

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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282 views

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 ...