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

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What is difference between PRG, PRF, and PRP

Until what I have gotten is: A PRG is generator is a part of PRF that produces pseudo-random values for the function. PRF is semantically secure and has no worries of being invertible. Fine, then ...
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How to construct a good PRF from a block cipher?

We want to explicitly construct a good (as tentatively defined below) Pseudo-Random Function $F$ with $b$-bit input and output, from (preferably just) one Pseudo-Random Permutation $E$ of $b$-bit, as ...
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186 views

State recovery of Micalli-Schnorr random number generator modulo a prime

Let $p$ be a public prime of $n$ bits. Define the sequence $x_i=z_{i-1}^e \bmod p$, where $z_i$ is the $k$ high-order bits of $x_i$, and $r_i$ the remaining $n-k$ bits of $x_i$ (thus $z_i=\Big\lfloor\...
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Cryptographic security of PHP mt_rand() function using Mersenne Twister algo

At stackoverflow this question has been asked. It uses additional random entropy and a hash method (among others) to try and create a cryptographically secure pseudo-random number generator for PHP. ...
8
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1answer
658 views

Are there any authoritative definitions of “key stretching”?

This is mostly a terminology question, but I suppose that it is best asked and answered here. After browsing the Internet I have come across a fair number of completely different definitions of the ...
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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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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 ...
6
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1answer
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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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1answer
653 views

Goldreich-Goldwasser-Micali Construction

The Goldreich-Goldwasser-Micali construction allows to build a (cryptographically secure) pseudo-random function from of a (cryptographically secure) pseudo-random generator. More formally, let $G: \...
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1answer
96 views

Is IPsec IND-CCA secure provided the used block cipher is a pseudorandom function?

I am trying to solve the question whether "IPsec is IND-CCA secure provided the used block cipher is a pseudorandom function" (with IPsec using a variant of Encrypt-then-MAC) As a resource I am given ...
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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 PRF?...
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Questions about Key Derivation Functions

My understanding is that a KDF is a function that takes a master secret and generates multiple keys. It is secure as long as the keys are "independent". If this is true, the following definition would ...
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Does a hash function in chaining mode or in counter mode make a better pseudo-random number generator?

I have two pseudorandom generators: $f_1$ takes a random seed $l_0||r_0$ $\in \{0,1\}^{160}$ as input and outputs $r_1||r_2|| \dots ||r_k$, where $l_i||r_i = \operatorname{SHA-1}(l_{i-1}||r_{i-1})$ ...
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1answer
118 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
117 views

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 arbitrary-...
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Best differential characteristic for this PRF

Consider the following construction of a PRF $F: \{0,1\}^{128} \times \{0,1\}^{64} \to \{0,1\}^{64}$ on 64-bit messages and 128-bit keys. Define $f:\{0,1\}^3 \to \{0,1\}$ by $$f(c,x,y) = \begin{...
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1answer
568 views

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 ...
4
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1answer
197 views

PBKDF2 PRF: HMAC or just hash?

I understand the way $\textrm{PBKDF2}$ can be used to 'stretch' a password/passphrase that does not provide full entropy. My question: how does one choose the PRF? A common choice is any well-known ...
4
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1answer
189 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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A periodic PRNG based on hash function?

I need a PRNG which provides 128 bytes numbers. Let's say that given a symmetric key $K$ and an internal state $s$ I use the PRF HMAC-SHA512 this way: The output is PRNG($K, s$) = HMAC-SHA512$_K$($s$...
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1answer
214 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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1answer
54 views

Prove that the following MAC is insecure

I am trying to prove that the following MAC is insecure, but I don't know how to exploit the properties of the pseudorandom function $F$ involved: Gen generates a uniform $k \in \{0, 1\}^n$. To ...
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1answer
126 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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1answer
72 views

Statistical tests for PRNG that generates a sequence which is not binary

Is there a pratical application to PRNG that generates a sequence which is not a binary one? A ternary, quaternary sequence, for instance. If so, how can we test this? Is there any alternative test ...
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1answer
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How to prove a function is pseudorandom function?

I am currently enrolled in a cryptography course, which uses the book by Katz and Lindell. I am using a function having $F_{k}$ = $A_{k}(B_{k}(r,m),r)$, the random number is generated using the ...
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How to prove that a function F isn't a pseudo random function

Let $F$ be a length-preserving pseudorandom function. For the following constructions of a keyed function $F' : \{0, 1\}^n \times \{0, 1\}^{n−1} \to \{0, 1\}^{2n}$, state whether $F'$ is a ...
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1answer
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Question about the definition of a secure PRF

I'm taking a cryptography introduction course, and we're covering the definition of a secure PRF. I understand the test goes as follows: A challenger picks a function $f$ such that $f \leftarrow \...
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2answers
125 views

Does CTR mode yield a PRF?

Can the keystream generated by CTR mode be considered a pseudo-random function? I give more information. Assume $f$ is a PRF. We define a function which takes 2 inputs, the desired length, and an ...
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1answer
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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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Construct a random permutation from a random function?

How can we construct a (pseudo) random permutation from a (pseudo) random function ? I've seen a method from Luby-Rackoff which allows to construct a PRP of length $2N$ from a PRF of input/output ...
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386 views

Proof that a function constructed from a PRP is, or is not a PRF?

Let $E$ be a family of Pseudo-Random Permutations of $b$ bits, with $E_K$ indistinguishable from random permutation with effort less than $O(2^b)$, easily computable as well as the inverse permutation,...
3
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2answers
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secure PRF or not

I am new in Cryptography and I saw this question in a note I solved it but I'm not sure about my answers. Let $F : \{0, 1\}^n × \{0, 1\}^n→ \{0, 1\}^n$ be a secure PRF (i.e. a PRF where the key ...
3
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1answer
565 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 |k|...
3
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1answer
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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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1answer
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Can Pseudorandom values be used as secure keys?

I want to derive $n$ keys from a master key. I pick a master key $mk$ and use pseudo-random function (PRF) to generate $n$ pseudo-random values, $v_i=PRF(mk,i)$ where $1\leq i \leq n$. Next, I use ...
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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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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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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 $g:\{0,1\}^s\mapsto\{0,...
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1answer
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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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2answers
335 views

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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2answers
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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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Realize a MAC using a Pseudo-random function?

Given a pseudo-random function and assuming that we do not have any other tools, How can we construct a MAC? I believe this can be done. Would like to know if there is more than one way of doing ...
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Is pseudorandom function also a one-way function?

Can I assume this? Specifically, I want to know if the following two cases are valid. Suppose $prf_k(m)=c$ One-wayness: Only given $c$, we cannot reveal $m$. Without key $k$, even given $m$, cannot ...
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1answer
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Crypto-period for keys used in PRF

I am wondering about the crypto-period for keys used in pseudo-random functions. For example, let's say I am using HMAC-SHA256 with a secret key $K$. After how many computes do I have to update $K$?
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1answer
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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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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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1answer
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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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Pseudorandom functions

The usual case to distinguish a pseudorandom function from a random function is to assume that the adversary can choose the plaintext blocks. Is there another case (game) in which the adversary can ...
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1answer
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Cryptographically strong pseudo-random seq. generators

If a pseudo-random sequence generator is built so that it uses an n-bit seed and outputs a string that is of length x. Let's say one wants to generate a bit string of length y and uses the previous ...
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1answer
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Why is $Mac_k(m_1||m_2) = ⟨F_k(m_1), F_k(m_1 \oplus \overline{m_2})⟩$ not a secure MAC?

I am preparing for an exam and trying to solve the following question I found on the internet: Let $F_k$ be a pseudorandom function. Show that the following MAC for messages of length $2n$ is ...