# Tagged Questions

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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### 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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### 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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### 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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### 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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### 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 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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### Proving CCA security for scheme constructed from secure PRP

We have a $PRP : \{0,1\}^{3n} \rightarrow \{0,1\}^{3n}$ and encryption scheme constructed from this $PRP$. $E_k(x\|r\|0^n)$, where $r$ is randomly chosen from $\{0,1\}^n$ and $0^n$ is a block of ...
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