A Pseudo-Random Permutation (PRP) is a function that cannot be distinguished (with practical effort) from a permutation selected at random with uniform probability from the family of all permutations on the function's domain.

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Non-iterative cryptographic hash functions

Consider the following cryptographic hash function $H$ which maps a message $m$ of variable size to $b$ bits: $$H:\{0,1\}^{*} \mapsto \{0,1\}^b$$ $$y = H(m) = SPRP(IV||m||padding)\mid_{b}$$ , where: ...
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Is the inverse of a secure PRP, also a secure PRP?

If a block cipher is a secure PRP, is it's inverse a secure PRP as well? My intuition says yes but I'm not exactly sure. On a related note, if a block cipher is a secure sPRP, is it's inverse a ...
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What is the most computationally efficient way of generating pseudo-random permutations?

I have an application in which I need to create up to J randomly shuffled-copies of an array of length N. Then I will have millions or even billions of iterations such that, in each iteration, I will ...
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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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State of the art low memory arbitrary-domain PRP?

I am wondering what the state of the art is on low memory arbitrary-domain PRPs. That is, I'm looking for an algorithm that implements bijective function $PRP : \mathbb{Z}_n \times \{0, 1\}^b ...
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help with cryptanalysis of a sponge permutation

I have been studying and researching hash functions. So far my research has led me to the sponge construction. It appears that the permutation used in the sponge to stir the state is more or less ...
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Example of a PRP that is not a strong PRP

The exact definition of security for a pseudorandom permutation is straightforward - for some encryption scheme $E\,\colon\,\mathcal{K}\times\mathcal{D}\rightarrow\mathcal{D}$, it must be the case ...
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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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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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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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Pseudorandom permutations on domains of arbitrary (i.e. not a power of 2) size

The Feistel cipher algorithm produces a pseudorandom permutation with domain size equal to $2^{2m}$ (for some $m \in \mathbb{Z}^+$). That is, a one-to-one function $\pi$ of the set $\{0, 1, 2, \dots, ...
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Is there any more asymetric-time permutation than x^3 (mod p)?

I've been using "asymetric-time bijective functions (or permutations)" for several practical uses. I've applied them to solve problems in software-attestation and proof of unique blockchain storage. ...
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Statistical tests for pseudorandom permutations

I'm implementing a format-preserving encryption scheme similar to those described in the literature. I want to sanity test my PRP using some statistical tests like TestU01. However, I'm not sure how ...
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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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How do you create a large PRP from a small one?

How can you efficiently create a pseudorandom permutation with a large domain given a PRP with a small domain? Meaning: given an $n$-bit PRP, how can I create an $n k$-bit PRP? I'm only interested in ...
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Impact of distinguishing between random text and cipher text?

In theory, distinguishing cipher text from random text is considered insecure for any PRP algorithm. Say for example - due to Patarin's proof with about six rounds of Feistel Network - the attacker ...
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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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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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Permuting Small Sized Set in Practice

Imagine we have a set $S$ of $m$ elements and we wants to permutes the set elements. Thus the original position of each element should be unknown after permuting. If we define a permutation function ...
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Pseudo random permutation for arbitrary size domains

Popular block ciphers like AES or Twofish are keyed pseudo random permutations on the domain $\{0,1,\dots,2^{k}-1\}$ with $k\in\{128,192,256\}$ or similar. I'm interested in pseudo random ...
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Are pseudorandom permutation really permutation in mathematical sense?

In security, and specifically Block Cipher (AES, DES, etc), when we talk about pseudo random permutations, is the term "permutation" refer to the same meaning as in discrete mathematics. That is, the ...
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Random Permutation polynomial

I need to know, please: (1) Is there anyway to pick uniformly at random permutation polynomial in a field of prime order? (2) Are there many permutation polynomials in a field? (3) In a finite ...
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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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What is the difference between PPE and SPPE?

Can somebody explain, in simple terms, the difference between Pseudo Random Permutation Ensemble and Super Pseudo Random Permutation Ensemble?
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Unkeyed, fast, one-way PRP

Are there any fast, secure, one-way, unkeyed almost-pseudorandom permutations? I am looking for something that can hide a MAC, without requiring a secret key and while being much faster than public ...
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Generating a 30-32-bit PRP

I want to generate a small 30 or 32 bit PRP. I am going to use that PRP in an open web service and anyone will be able to get any number of plaintext-cyphertext pairs. I've found an algorithm called ...
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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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When we turn Random shuffle to Pseudorandom Shuffle

It's well known that a simple but efficient random shuffle algorithm can permute a vector of $n$ elements in $O(n)$ time. In the algorithm, we need to pick a value $U$ uniformly at random where ...
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Indistinguishability game hop

I am trying to prove that changing an input in a security game from a randomly permuted set to a set that is permuted using a pseudorandom permutation (PRP) results in a negligible distinguishing ...
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How to show that a function is not a PRP?

So I have to answer these questions, but I honestly have no idea what I am doing or where to begin. Can I get some advice on how to tackle these? Consider a PRP candidate function $f$ on $K = X = ...
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Determine if encryption is safe against CPA

The following encryption scheme encrypts each block of length $n$ of the plaintext separately: $c_i = k_1 \oplus F(k_2 \oplus p_i)$ Where $F$ is a strong pseudo-random permutation (i.e. it is easy ...
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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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Forward pseudorandom permutation [closed]

Please consider the following scenario: The user A and B use their keys, K1 and K2 respectively. Each client have a vector of elements. Each client separately permutes his vector using his key and ...
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Hashing/encrypting an integer to produce an unique integer in the same range

I'm looking for a function or set of functions that can produce a pseudo-random permutation on an input set of arbitrary size. Given a set of $M$ values in range $0..M-1$, where $M$ is positive ...
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Probability of $D_k(a*k+b) =p$ for a PRP

I'm wondering what the probability of a PRP having numerous keys (say 3 or more) with the same simple idempotent, or near identity, function. For example, does there exist values of $p, a, b, x_1,$ ...
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Is AES's parity key-dependent?

Is the parity of the permutation of the set $\{0,1\}^{128}$, defined by AES encryption for a certain fixed key, dependent on this key? DES, and any pure Feistel cipher, has even parity for any key. ...
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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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CPA-security of a pseudorandom permutation encryption scheme

Let $F$ be a pseudorandom permutation, and define a fixed-length encryption scheme $(Gen, Enc, Dec)$ as follows: on input $m \in$ $\{0,1\}^{n/2}$ and key $k \in \{0,1\}^n$, algorithm Enc ...
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Is algorithm with more than $2^{word size}$ words secure? [closed]

Let's say we have a feistel cipher or feistel pseudo-random permutation with 8-bit function (S-box) similar to Treyfer, but with much bigger block size like 16MB. Here is example of such pseudo-random ...