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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Shuffling: Purpose and formal definition

To my understanding, shuffling means simply to permute the elements in vector $\mathbf{v}$ pseudorandomly, using a PRP $\pi (\mathrm{seed},\mathbf{v})$. A secure PRP should yield a permutation ...
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Compositions of specific pseudorandom permutations

Let's consider some specific pseudorandom permutations (PRP). Most of their bits cannot be distinguished from a random permutation, but there is one exeption. If number of the set is divisible by $2^{...
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Is there a Pseudo Random Permutation Generator that can output all values of the length of N

Is there a pseudo random permutation generator that produces all permutation of any bit length of the plaintext (this may not be clear, please let me know and I will explain). It must be fast, and ...
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What makes AES look like an ideal cipher?

There are 2128! permutations on 128-bit inputs. AES supports a maximum key length of 256 bits, therefore offers at most 2256 permutations. The total number of 128-bit permutations is much larger than ...
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Is it possible to compute permutations of a sequence of bytes by using exactly one pseudo-random number?

Suppose I have a certain sequence of bytes, for example 0102F4829hex, and I can pick from a pseudo-random number generator exactly one number. Is it possible, by using exactly one pseudo-random number ...
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How random are permutations generated from Feistel networks with a small number of rounds?

I wrote a toy pseudo-random permutation out of a Feistel network using blake2b. However, looking at the distribution of permutations for small n = 6, it's clearly not uniform unless many rounds are ...
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Provably secure way of expanding permutations

Gimli is a 384-bit permutation that makes use of an internal 96-bit permutation which works on columns. Every 4 rounds starting from the 1st a "small swap" is performed and every 4 rounds ...
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Any formal proof or reference that pseudorandom permutation can be used as pseudorandom function

Assume that a DRBG passes all statistical tests. We use that DRBG to shuffle(Fisher-Yates) an array that contains $\{0,1,\ldots,2^n-1\}$. Now get a pseudorandom permutation $\{0,1\}^n\rightarrow \{0,1\...
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Implementing MAC with PRF family $f$, why do we need $f_k$ to be invertible?

As per the title, say we have $\text{MAC}(k,m) = (m,f_k(m))$ where $f$ is a PRF family and every function $f_k$ is PRP, where $f_k(m)$ and $f_k^{-1}(m)$ are efficiently computable. I proved that this ...
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Regarding XEX mode

Wikipedia claims that given an unkeyed permutation $p$ (presumably of the same size as the key) this is safe: $p(m \oplus k) \oplus k$ Why isn't this construction used instead of XEX? Surely unkeyed ...
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safe concating PRP and PRG

Suppose it is necessary to build a safe PRG. You have one PRP with $\epsilon = \frac{1}{2} ^ {45}$, and one PRF with $\epsilon = \frac{1}{2} ^ {55}$. There is no mathematical relationship in the PRP ...
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Why is the internal chacha20 permutation vulnerable to attacks if used in a sponge construction?

The user Forest in here claims that the internal chacha20 permutation is "vulnerable to attacks if it were used in a sponge construction". My question is as follows: What are these attacks? Would ...
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Is there a method to encrypt relations in between values of a cyclic value set and generate values out of this set with pseudo RNG? (all at user PC)

Is there a pseudo RNG and function $f$ with 1.) The RNG produces a value $v_0$ out of $N$ different values (set $S$). 2.) Independent of the RNG the function $f$ generates $v_{i+1}=f(v_i)$ ...
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Sponge with PRF instead of PRP

In most uses of Sponge mode of operations such as SHA3 and many of the round-2 candidates in the NIST lightweight cryptography project, the underlaying primitive is a cryptographic permutation - that ...
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memory-hard KDF that's just a giant permutation?

Why aren't there memory-hard KDF functions that simply build a 1GB permutation and permute it? Then hash the 1GB result. For example, use a hash function (unfixed output mode) on the key+salt and use ...
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Is there a cyclic RNG without an explicit form for $i$'th element which is guaranteed to have a sum of zero (subset of elements, $\mod P$ possible)

Let $X$ be a sequence element list of (pseudo) random values generated by a RNG and $x_i \in X$ a member of it. The period length is $k = |X|$ and it is a cyclic generator. For $i>k$ the value $x_i ...
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Any speed up methods for finding the index of a random value produced by the Inversive congruential generator?

The Inversive congruential generator produces random values with: $$x_{n+1} = a\cdot x_{n}^{-1} + b \mod P$$ (special case if $x_n=0$ -> $x_{n+1}=b$) starting with an initial value $x_0$ With well ...
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How to check whether the permutation is random or not

Imagine that my friend gives me the permutation $\pi$. He pretends that the permutation was generated completely random. I'm suspicious and worried, because the permutation (for instance) looks like: ...
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What is the difference between pseudorandom permutation/pseudorandom function/block cipher?

What is the difference between; pseudorandom permutation pseudorandom function block cipher? Very confused with the 3 terms and I am not good at advanced math. Can someone explain in plain word?
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'random' function $r_{n+1} = f(r_n)$, $|\{r_i,\forall i\}|=N$, $r_N = r_1$ where a function $g(r_k)=k$ is harder than in ECC?

Is there a deterministic pseudo random function $f$ with $r_{n+1} = f(r_n)$, $|\{r_i,\forall i\}|=N$, $r_N = r_0$, (for given random initial value $r_0$) where a function which derives the index of a ...
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Question about the definition of Associative Pseudorandom Permutation [closed]

In question about associative pseudo-random permutation the definition uses: $f(k_1, f(k_2, m)) = f(f(k_1, k_2), m)$ What is defined by that? No luck with google so far. As far as I know a ...
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Pseudo Random Generator (PRG) not deterministic

Usually a Pseudo Random Generator is supposed to be IND-CPA secure. But apparently, it is not in some cases such as the following: A PseudoRandom Generator $G$ has expansion factor $n + 2$. Encrypt ...
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Efficient way of generating a random number of N (less than 64) bits with exactly M bits equal to one [closed]

Would there be an efficient way to implement a function with the following signature: unsigned long long int random_word(size_t n, size_t m) that would generate ...
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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 ...