Questions tagged [pseudo-random-permutation]

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 there a constant-overhead PRP construction based on PRPs for large inputs?

Somewhat recently I learned that there's a separation between an encryption scheme being CCA2 secure and being AE secure, namely PRPs. So if we would use AES as an encryption scheme for fixed-size ...
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Is $f(K, f(K, x))$ a pseudorandom function?

Given a PRF $f : \{0, 1\}^n \times \{0, 1\}^n \rightarrow \{0, 1\}^n$, is $f(K, f(K, x))$ a PRF, too? My hunch is to construct a PRP similar to Feistel ciphers but with the property $f(K, f(K, x)) = ...
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Dependence of a Pseudorandom Function's Security on its Input/Output Spaces

Let $n$ be a security parameter and $F:\{0,1\}^{\ell_{key}(n)} \times \{0,1\}^{\ell_{in}(n)} \rightarrow \{0,1\}^{\ell_{out}(n)}$ be a keyed function which forms a family of Pseudorandom Functions (...
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PRP vs PRF for the F-function of a Feistel network

A Feistel network is generally defined with a PRF for its F-function, but PRPs have been used as well. What are the theoretical cryptographic implications of using a PRP instead of a PRF? Does it ...
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Aside from Keccak, are there any keyed/unkeyed permutations where the choice of all rotation constants is not based on heuristic methods?

I am interested to see examples of cryptographic algorithms (namely, keyed or unkeyed permutations that transform an $n$-bit input to an $n$-bit output) where the choice of all rotation values is not ...
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PRP, PRF change at next selection?

This is probably a silly question, and similar question was asked before; but I can not figure out what actually is PRP/PRF. For example, it is commented that: A Pseudo Random Function is a ...
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A well known hash function?

Name a well-known and standardized function $F : \{0,1\}^{256} × \{0,1\}^{128} → \{0,1\}^{128}$ that is believed to be a pseudorandom permutation. I was thinking SHA256, but I am not sure. Can ...
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How to prove security of scheme constructed by Hash then PRP

Suppose there is a scheme where a message is first hashed and then sent to a PRP. If the hash is done using an $\epsilon$-bounded universal hash function and the PRP $K\times \{0,1\}^n\rightarrow\{0,1\...
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Predicting value of E(k,0) for Block cipher with random and secret key

Some mode of operation of block ciphers rely on the fact that E(k,0) is an unpredictable value when k is random and secret (with 0 denoting the all-zero binary string). Why is this a reasonable ...
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Can multiple Pearson permutation tables be reduced or merged?

There was a recent question answered where the accepted solution was a double Pearson hash. It consisted of the following pseudo code:- h = T1[h ^ x[i]] followed ...
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Show that the CBC-MAC construction applied to a PRP is not collision resistant

I'm trying answer the following question. Yes, it is a homework question, so I'm not asking for the answer directly but would like to get some pointers on how to solve it. So far I have spent several ...
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A modification of the NMAC construction

Consider the NMAC construction: This is a proposed exercise in my notes: Assume F is a PRP with $n = l(n)$. Is it secure to replace $k_0$ by $F_{0^n}(k_0)$ and $k_i$ by $F_{0^n}(k_i)$? In ...
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Give a distinguisher to differentiate between PRP and RPO

I have understood the proof that shows that a PRP is a PRF except for negligible probability $\frac{q(n)^2}{2^{-l(n)}}$. My computations suggest me that the same argument, perhaps with minor ...
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Random permutation of bit strings of length $n$, where $n$ can be any positive integer?

I need an efficient, invertible random permutation of $n$-bit strings, defined by a $128$-bit key. $n$ can be any positive integer from $6$ to $128$. I have no requirements on the security of the ...
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Strong pseudo random permutation implies CCA-security

Let $F$ be a strong pseudo random permutation and define a fixed-length encryption scheme $(\operatorname{Enc,Dec})$ as follows: On input $m \in \{0,1\}^{\frac{n}{2}}$ and key $k\in \{0,1\}^{n}$, ...
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Locally computable random permutation

Let $A$ be a set of size $n$. Given a random seed $s$, I am looking to build a pseudo-random random permutation $\pi_s: A \rightarrow A$ such that $\pi_s(a)$ is fast to compute for every $a \in A$. By ...
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Is tweakable block-cipher based on the Merkle-Damgård construction secure if $F$ is a PRP

Assume $F$ is a pseudo-random permutation (PRP) then the tweakable block-cipher based on the Merkle-Damgård construction (take this as the way I understand, here is the equation): $F_k[t](m) := F_{...
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Can we use a PRF as a PRP?

Leaving aside the problem of how to compute the inverse of a PRF F, may we use it also as a PRP? The reciprocal of this statement is true, see for instance Katz and Lindell, Proposition 3.27, when ...
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Is it possible to apply a pseudo-random permutation (a keyed permutation) to construct a sponge function?

The description of the sponge function on Crypto.Stackexchange contains the following text (source): The cryptographic sponge is a construction scheme for hash functions (and other symmetric ...
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Is it possible to make use of a pseudo-random permutation to construct a one-way compression function?

Let $f_k(B)$ denote the underlying function (a pseudo-random permutation) of a block cipher: it uses an $x$-bit key $k$ to encrypt an $y$-bit block $B$. The question: is it possible to make use of $...
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Is this a PRP? How can I create a distinguisher to show it isn't?

Consider the keyed permutation $F_k : \{0,1\}^2 \to \{0,1\}^2$ with two-bit keys defined as $F_k(x) = k\oplus x$. Is this F a PRP? How can I create a distinguisher D and calculate the difference ...
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Does encryption using PRP mean indistinguishable encryption against an eavesdropper?

I am a student studying cryptography by reading "Introduction to Modern Cryptography". I have some confusion about encryption using PRP (e.g., AES). Briefly speaking, a keyed deterministic ...
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How to prove the PRF, $F(k,x) = (k \wedge x ) \oplus k$ is PRP?

I am trying to understand PRF's and PRP's. I have got a question where I have to decide whether $F(k,x) = (k \wedge x ) \oplus k$ (where $k$ and $x$ are simple $1$ bits (1 or 0)) is PRP or not. I am ...
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Permutation for which an inverse is a hard problem

Is it possible to construct (even if we don't know how) a permutation for which an inverse must exist but is difficult to find (brute force required)? The one way permutation contains no hidden ...
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How is a PRP different from PRF? Both can be inverted to get the same input

PRP is said to be a bijective function which means that there is a one-to-one mapping with the output. And hence the output can be inverted using the decryption algorithm to get the same input. ...
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Using a PRP $\pi: \{0,1\}^{16} \to \{0,1\}^{16}$ to construct an ideal cipher

Say we have an ideal 16-bit PRP. Since it appears that a permutation with a small domain can be used to turn it into a PRF, which can then be used in a Feistel network. On the surface, it makes it ...
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Reproducable pseudorandom permutation

I there a way to calculate two similar pseudorandom periodic sequences by exchanging some sort of initial value and generator polynomial? Like a linear-feedback shift register but with a finite ...
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why isnt E a secure block cipher

Let $\pi : \{0,1\}^n \rightarrow \{0,1\}^n$ be a permutation. Let $E(k, x) = \pi(x \oplus k)$ where $x,k \in \{0,1\}^n$. Why isn't $E$ a secure block cipher? My idea: Suppose $E$ is a secure block ...
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Why do we use (pseudo) random permutations and not (pseudo) random functions for en- and decryption?

Why do we use pseudo random permutations and not pseudo random functions for encryption an decryption?
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Security of OFB mode if PRP is used instead of PRF

In the cryptography lecture at my university, we had the theorem that (randomized) OFB mode is IND-CPA secure if the used pseudorandom function (PRF) is IND-PRF secure. Afterwards, we investigated ...
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A strange phenomenon of the composition of permutations of order 2

Suppose that $f,g,h:X\rightarrow X$ are permutations such that $f^{2}=g^{2}=\textrm{Id}_{X}$ (i.e. $f,g$ have order 2). Let $F=f\circ g$. Let $D_{f,g}$ be the distribution that takes the value $n$ ...
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Luby-Rackoff theorem for Generalized Feistel

I was reading about Luby-Rackoff theorem from various sources: [1], [2], [3], which says you need at least 3 rounds of a $2$-branch Feistel network to get a PRP if the underlying $f$ function is a PRF....
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Are there any pseudo-random permutation algorithms for any number of words in the input independently of the word size (as in MD6 core function)?

I am interested in fixed pseudo-random permutation algorithms that are defined for any number of words in the input (but there might be some minimal number of words, e.g. 8), where the word size may ...
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How to show that the following function is not a OWF?

Given F, which is a Pseudo Random Permutation, I need to prove that the following function f is not a OWF: f(x, y) = Fx(y) My first thought would be to create an adversary which tries and compute Fx-...
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Can we always find a key to map a given plaintext block to a given ciphertext block in AES?

I am revising for my exams and I have come across this question in a past paper and I am not confident about it at all. Assuming that only the smallest permissible key and block sizes can be used I ...
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Security properties of an encryption scheme built from a PRP and a PRG

Note: This was my in-class problem last week and potentially will be on the exam tomorrow. Thus, I want to reconfirm my thoughts so that I'll be ready to face this type of question (if appear) ...
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Pseudo-random function where the output is inverted using XOR

I'm looking to know whether or not this PRF is secure : $$F'(k, x) = F(k, x) ⊕ 1^n$$ knowing that $F$ is already a secure PRF for $$\{0, 1\}^n × \{0, 1\}^n → \{0, 1\}^n$$ with, for example, $n= ...
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A Construction of a Cipher from a Single Pseudorandom Permutation

A paper from 1997 A construction of a cipher from a single pseudorandom permutation proposes a cipher in which The message block is XORed with K1 before applying F [a single random permutation], and ...
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CCA-Security Proof of a particular scheme

Suppose to have a scheme that works so: $\mathcal{P}_k =:\{P_k\colon \{0,1\}^{2n} \to \{0,1\}^{2n} \}$ is a strong PRP family. Encryption: $\operatorname{Enc}(k,m)=P_k(m\mathbin\Vert r)$, where $\...
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What are the properties of a function based on multiple iterations of a pseudo-random permutation?

Let $F(S) = \text{Keccak-}f[1600](S)$. Assuming that the length of $S$ is equal to $1600 \times k$ and if $k$ is greater than $1$, we define a function $F_{k}(S)$ as follows. We note that $S$ is ...
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Security implications of plaintext-padding in an AEAD-scheme

Let's say I have a secure AEAD-scheme like ChaCha20/HMAC and my encrypted blobs need to match a fixed size: Is it OK to apply some padding to my plaintext to match the block-size? Can I use any ...
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What is the expected number of different sequences of bits in the collection that contains $2^{800}$ elements?

Let $F$ denote a function that returns the first $800$ bits of the input. Let $G(N)$ denote a function that returns the last $800$ bits of the binary encoding of the given number $N$. For example, ...
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Can we protect PRESENT from the Statistical Saturation Attack if we change the permutation layer to a random permutation layer?

This is continuation-question based on: If PRESENT had different permutations s would that protect it against Statistical Saturation Attack? Can we protect PRESENT from Statistical Saturation Attacks ...
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Creating single-cycle permutations

There was this one time I came up with a small permutation that had a block size of 16 bits. This was small enough to compute every mapping. I then iterated the mapping starting with zero to see how ...
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(Impossibility of?) Associative Pseudorandom Permutation

I'm not sure whether this had been a long-standing open problem in cryptography. Definition An associative pseudorandom permutation $f(k,m)$ is a permutation such that: $f(k_1, f(k_2, m)) = f(f(...
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How to build disk encryption system using forward permutations like Gimli?

First of all, this is purely a thought experiment. The width of Gimli isn't even a power of two (384 bits), and secondary storage bus speeds aren't even worth using a high performance permutation like ...
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How to pick up random number within range using pseudo-random number sequence

I want to generate PRP using Fisher–Yates shuffle for array [1,2,3,4,5,6,7,8,9,10,11,12]. I implemented NLFSR_25bit with specific seed for PRNG. (for picking up pseudo-random number in every ...
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Arbitrary width pseudorandom permutation

An arbitrary width pseudorandom permutation seems like a very versatile secret-key cryptographic building block. It allows for trivial (nonce-misuse-resistant!) authenticated encryption, among other ...
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Does there exist a deterministic, invertible function $\{0,1\}^n \rightarrow \{0,1\}^n$ that is not a bijection?

One of the requirements for a function to be a PRP is For any $K \in \{0,1\}^s$, $F$ is a bijection from $\{0,1\}^n \rightarrow \{0,1\}^n$. Taken from Wikipedia Does this have to be ...
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A novel encryption method using only a (huge) lookup table. Is this remotely secure? [closed]

So I've come up with an (admittedly impractical) encryption method using a lookup table. The table is a shuffled list of all unsigned 32-bit integers, effectively making it a 32-bit unkeyed PRP. I ...