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.

Filter by
Sorted by
Tagged with
4
votes
2answers
1k views

What is the purpose of Pseudorandom Function Families (PRFs)?

I'm currently in a course in Cryptography, and was wondering why pseudorandom function families exist at all. If there existed one pseudorandom function f(x), based on its definition, could that not ...
4
votes
2answers
881 views

Given a pseudorandom function F, is $(F_k(r) \; | \; F_k(r + 1))$ also a PRF?

Given: F is a pseudorandom function, G is a pseudorandom generator with $l(n) = n+1$. The following schemes should be classified as being insecure, IND-COA secure, IND-CPA secure. To encrypt $m \in \{...
1
vote
1answer
212 views

how to prove sequence y uphold golomb's third axiom

given $\{ x_k \}$ is a m-seq of order $n$, we define $\{ y_k \}$ to be a $m$ digits number: $$ y_i=x_ix_{i+1}...x_{i+m-1} $$ for every integer $n \ge m \ge 1$ how can I show that $\{ y_k \}$ upholds ...
4
votes
2answers
195 views

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 ...
2
votes
1answer
322 views

Key Derivation Function (KDF): Can a key derived from KDF be considered as a secure key?

Consider a case where we have a master key MS that is used in pseudo-random function to generate a set of pseudo-random values. Then we use key derivation function to derive a key from each of pseudo-...
4
votes
2answers
2k views

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 ...
4
votes
2answers
1k views

Given PRNG $G(s)$, why is $G(s) || G(s+1)$ not a PRNG?

I have given a pseudorandom Generator $G(s)$, $|s|=n$ whose expansion $l(n)$ is $>2n$. I also know that $G^\prime(s) := G(s_1,\ldots,s_{\lfloor\frac{n}{2}\rfloor})$ is a pseudorandom generator. Now ...
0
votes
1answer
98 views

Key derivation function in theory & practice

I am implementing a cryptographic protocol and I'd like to generate a set of seeds using a seed for a pseudo-random function. The reason is that I can pass on only one seed and it can be used to ...
1
vote
1answer
142 views

Help with pseudorandom functions

I started a new lecture this year about crypto and I've had a few problems in the first few weeks with the exercises we got. I would appreciate a "guide" on how to solve problems like the following ...
4
votes
1answer
410 views

If a PRG is constructed by iterating a PRF, is it backtracking-resistant?

Say we construct a pseudo-random generator from a pseudo-random function $f$ (using some constant key $k$ and some initial value $v_0$). We do this by feeding the output block of the PRF back into the ...
0
votes
1answer
401 views

If PRF is non invertible, why does Ctr-mode work?

I am currently taking Dan Boneh's Cryptography I course online. I have just finished the segment discussing the Cipher Block Chaining and Counter-Mode. I am having difficulty understanding why Ctr-...
1
vote
1answer
162 views

PRF that can be distinguished after $k$ queries?

In adaptive attacks, if we design poorly, adversary can modify his queries and break the given pseudo random function (that is being able to distinguish it from uniform randomness). Is there a poor ...
4
votes
2answers
1k views

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 ...
1
vote
1answer
58 views

Deriving a Set of Seeds from a Seed

I need a set of seeds $S=\{s_1,..., s_n\}$, for pseudo-random function where seed $s_i$ is used to generate a set of pseudo-random values. Obviously I need to be able to regenerate the sets of pseudo-...
2
votes
1answer
52 views

Data Switching and Information Leakage

Hypothesis: Let $z,a$ be uniformly random elements of a field $\mathbb{F}_p$ where $p$ is a large prime number. Also, let $(-z)$ be additive inverse of $z$. I have a fixed secret value $x$. I mask it ...
2
votes
1answer
262 views

Modified version of a CPA-secure encryption scheme

The following encryption scheme: choose a random string $r \leftarrow \{0,1\}^n$ and compute the ciphertext $c= \thinspace <c_0, c_1>= \thinspace <r, F_k(r) \oplus m>$, assuming $F$ a PRF; ...
2
votes
1answer
165 views

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 $K$?
4
votes
2answers
315 views

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$_K$($s$...
3
votes
2answers
456 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 ...
1
vote
1answer
215 views

Random Function size

I am new to cryptography. I have question regarding the size of the set of random functions. I found the text from "Introduction to modern cryptography" by Katz and Lindell, in another thread which ...
2
votes
3answers
556 views

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

This exercise comes from Coursera's "Cryptography" course. 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 ...
5
votes
2answers
4k 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
votes
0answers
72 views

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 ...
2
votes
1answer
160 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 ...
-1
votes
1answer
173 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 ...
2
votes
2answers
154 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 ...
3
votes
1answer
2k 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: ...
1
vote
1answer
120 views

The encryption scheme is secure?

I have a scheme and I don't know that this scheme is semantic security or not. Secret keys $\{s_1,s_2, x_1,x_2\}$ and public parameter $p$ (large prime number). Encryption E(m): $C_1 = s_1m + x_1k \...
2
votes
1answer
244 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 ...
3
votes
2answers
658 views

Cryptanalysis of Marvin32 compared to SipHash

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: ...
3
votes
1answer
561 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 ...
0
votes
1answer
263 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, ...
2
votes
1answer
171 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 ...
0
votes
1answer
212 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 PRG,...
0
votes
1answer
104 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? $$f(x)=g((x+1)\bmod2^l)$$
2
votes
0answers
375 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: $G^i(s)=x_1\...
0
votes
0answers
131 views

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 ...
1
vote
2answers
916 views

Is Pseudo-Random Generator (PRG) in OpenSSL uniformly distributed?

I need to know can we use PRG of OpenSSL as a PRF?
1
vote
1answer
415 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 ...
1
vote
1answer
794 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 http://...
1
vote
1answer
4k 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?
3
votes
0answers
102 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, ...
3
votes
4answers
2k views

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 ...
5
votes
2answers
1k 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: (...
1
vote
0answers
605 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 ...
1
vote
1answer
441 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 ...
4
votes
1answer
635 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?
10
votes
1answer
5k 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 ...
2
votes
1answer
433 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 PRP....
2
votes
2answers
855 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, pre-...

1 3 4 5 6 7