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Questions tagged [permutation]

A way, esp. one of several possible variations, in which a set or number of things can be ordered or arranged.

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Randomness Testing

Let say I have three sequences: S1 = {1,2,3,4,5,6,7,8,9,10} S2 = {3,7,1,9,4,10,5,8,6,2} S3 = {8,3,10,2,6,7,1,5,9,4} i.e. S2 and S3 are just the permutations of S1. Is there any method to check how ...
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What can be said about the self-power map on groups based on DLP?

I've been playing with group representation theory some time, concretely representing groups as permutation groups (Cayley's theorem), where the group $G$ has an embedding into the symmetric group. ...
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Keyed Permutations [on hold]

I need some Keyed permutations names just like RC4 cipher, in which we can generate a pseudo random sequence based on the key. For example: If I enter key=abc123 it will generate a random sequence of ...
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modified substitution permutation networks

I have a model of substitution permutation networks, modified as follows: instead of iterating $n$ times a round(each of which is composed of the key mixing phase, substitution S-BOX) and ...
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AES: Why ShiftRows() before MixColumns()? [duplicate]

In above picture you can see a AES state array over 2 rounds through the S- and P-Boxes of AES. It's taken from here and intends to show how 2 rounds of transformation are necessary to achieve full ...
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Is a random permutation “hiding”?

Let's say I tell you $G: \mathbb{F} \rightarrow \mathbb{F}$ is a random permutation (some finite field). Does that mean: $G$ is one-way, so that if I give you $G(x)$, it is infeasible to determine ...
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Proving at most one affine permutation mapping $x$ to $u$ and $y$ to $v$ with $x,y \in \mathbb{Z}_n$ and $\gcd(x−y,n) = 1$

Suppose that $x,y \in \mathbb{Z}_n$ with $\gcd(x−y,n) = 1$. Prove that for any $u,v \in \mathbb{Z}_n$ there is at most one affine permutation mapping $x$ to $u$ and $y$ to $v$.
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Does there exist trapdoor permutation from lattices?

It seems that the lattice functions are either surjective (SIS) or injective (LWE), due to the error that is basically intended to destroy the structure and provide security. I was wondering whether ...
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Key, plaintext block and ciphertext block permutations question

Question: If a cipher’s key size is $k$ bits and its block size is $b$ bits, how many possible keys are there, how many possible plaintext blocks are there, and how many possible ciphertext blocks are ...
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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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404 views

What's the difference between confusion/diffusion and mode of operation?

I understand the concepts of confusion (substitution) and diffusion (permutation). My understanding of what a mode is that it's an algorithm that lets us encrypt arbitrary message size. i.e. AES is ...
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68 views

Permutation and modes of operation

I'm reading the book "Serious Cryptography A Practical Introduction to Modern Encryption" from Jean-Philippe Aumasson, and in the first chapter, it is written this : We can try to abstract out the ...
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For a hash over a finite space without size reduction, is a public permutation sufficient?

Suppose the application is a Lamport signature scheme. Is the following a secure hash $\{0,1\}^n \rightarrow \{0,1\}^n$? $$ H(x) = x \oplus P(x) $$ where $P$ is a public permutation that permutes an ...
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Mixing x into permutation through XOR vs. modular addition

Block ciphers mix key material into the permutation through XOR. Also do pre and post whitening this way. Chacha/Salsa finishes by 32-bit modular adding key and iv material (among other bits but ...
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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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105 views

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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What is the time complexity of the basic components of a symmetric cipher?

I have a very basic knowledge on time complexity and even less on programming, so please bear with me. I am interested to know the time complexity in big-O notation of some of the basic operations in ...
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60 views

Operation Table for Permutation Group

I cannot seem to figure out how the operation table for this permutation is formed. Is it multiplying each index and doing modulus? I can't seem to figure out. This is a Table 4.2 found in "...
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permutation cipher definition unclear

I have an assignment to decode a permutation cipher based on a key. But on the internet I found only ONE website talking about it. Things are not very clear. I understand that I have to reorder the ...
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Why do block ciphers use key schedules instead of round constants? (Even-Mansour)

Let's take AES as an example. What would be wrong with just having a 256 bit key that you XOR into your input and then XOR into your output? No key expansion at all. I believe it's even known as the ...
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Can both substitution and transposition ciphers be thought of as permutations?

I came across this problem to 'explain why both substitution and transposition ciphers can be thought of as permutations' and I cannot come up with an explanation to how substitution ciphers can be ...
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Can you rely on the permutation of a ciphertext for secrecy?

Say you have a message and you run it through an all-or-nothing transform. A transform that requires every single block in the correct order in order to recover any data. Each block is ...
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Composition of weak one way function is not a strong one way function

Given $f(x)$, a weak one-way permutation, how to prove that $f^T(x)$ is not a strong one-way function? Here $f^T$ denotes $T$ times self composition of $f$ and $T$ is a polynomial in input length.
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DES: how does Richard Outerbridge's Initial Permutation operate?

I know how initial permutation works, but I've never heard of this part. People say it's Richard Outerbridge's initial permutation and that it's faster than usual IP (initial permutation) and simple. ...
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133 views

Using multiple permutations to strengthen the security of a cipher

In one book it says a set of permutations with the composition operation is a group. This implies that using two permutations one after another cannot strengthen the security of a cipher, ...
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100 views

Is it possible to permute a binary vector obliviously?

Lets say A has a binary vector of length n, B has a permutation matrix of size n. Is there a way for B to permute A's vector so that A only learns about the result of permutation and B does not learn ...
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101 views

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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337 views

What are the subsequent inputs to the DES key schedule after round 1?

I've just been studying the DES crypto algorithm as presented by Christof Paar in his book entitled, Understanding Cryptography as well as his lecture. There is a diagram on page 68 of the text where ...
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460 views

How does Permutation and Substitution work?

I'm a little confused on how permutation and substitution works, I've been reading about S-DES and how it goes through P-Boxes and S-Boxes but what goes on inside P or S in the algorithm? Are these p ...
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Problem with a reduction using Hybrid Argument

I have an issue with this proof. We define two games: $$H'(\lambda):$$ 1) Pick $R \in \mathcal{R}(n,l)$ (the space of truly random functions from $\{0,1\}^n$ to $\{0,1\}^l$ 2) we define $\mathit{Enc}...
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Practical OWP of the set of $k$-bit bitstrings for low $k$

Down to what $k$ and how can we devise a practical, public, efficiently computable One Way Permutation $P$ of the set $\{0,1\}^k$ of $k$-bit bitstrings, if possible without involving a trusted party ...
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441 views

Proving RSA is a permutation

I am trying to prove that RSA is a permutation. All I can find is places where it is stated that it is a permutation because the function is bijective. I know that it is, but would like to see a ...
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152 views

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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Method for creating any involutive permutation

The Fisher-Yates shuffle can produce any permutation of a set of $n$ elements. Is there anything that can do the same for creating an involutive permutation of $n$ elements where $n$ is an even number?...
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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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If PRESENT had different permutations s would that protect it against Statistical Saturation Attack?

The block cipher PRESENT is vulnerable to the Statistical Saturation Attack for up to 15 rounds (PDF) and a simple example is here. So my questions are, if some (or all) of the permutations were ...
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What affect does the permutation layer have on the avalanche effect?

If the permutation is not well thought out, how will this effect the cipher's avalanche effect. For example, if the permutation in PRESENT was in some way different (just made up without any thought) ...
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What does it mean when 1 bit goes into an s-box but two (or more) come out?

I am trying to understand how bits are spread in the PRESENT cipher. The bits that enter the permutation of PRESENT return to their original position after only three rounds. But I am told that in ...
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How does the PRESENT cipher's permutation affect all rounds when it repeats after every three rounds?

I heard that the permutation in PRESENT affects all bits after only a few rounds. However, when I looked at it the bits return to their original position after only three rounds. For example, in round-...
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Relationship between existence of OWFs and OWPs

OWPs are bijective OWFs, so every OWP is a OWF, but not the other way around. However, I'm wondering what the relationship between the existence of both types of functions is. Obviously if one ...
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Is there a public key encryption for permutations which is homomorphic under permutation composition?

I'm brainstorming an idea for extending our Latin square autotopism secret sharing scheme (proposed here [open access]) to a repairable scheme. I seek a cryptographic method, which may or may not ...
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Total password count, given length and pool size

First, if my password is exactly 8 characters long, derived from a pool of 95 characters, then is the total amount of passwords I can create simply $95^8$ ...
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520 views

Pseudo-random permutation of a range

I have this set: {0,1,2,3,...,15}. I would like to create a pseudo-random permutation from elements of this set, for example ...
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96 views

Can a random permutation be restored / decrypted?

Say you have a 1,000,000 random bytes file and you split it into 1000 x (1000 bytes) pieces. You then pick two random pieces and swap them writing down the position of the pieces (eg. swapped piece ...
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How to generate a permutation of n numbers using secret sharing scheme?

Consider $n$ parties having their private inputs $s_1,\cdots,s_n$. How can they compute a public function $f(s_1,\cdots,s_n)= \pi$, where $\pi$ is a permutation of numbers between $1,\cdots,n$, using ...
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Mathematical structure for Sbox

Recently, when I studied the permutation cipher, I saw a matrices structure which is same as permutation cipher. This method was so simple and interesting for me. Let $m$ be $n$-bit plain text and $P=...
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Apply a permutation cipher by hand

I did the following problem from the book "Cryptography Theory and Practice" as I am doing some self-study. Problem: a) Suppose that $\pi$ is the following permutations of the set $\lbrace 1,\dots,8 ...
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265 views

What is the importance of $f_k$ in a feistel network being a permutation

I was doing some cryptography exercises, one of which was an example of a feistel network. It said that the function $f_k$ was a permutation for all k but didn't explain why that makes a difference. ...
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519 views

substitution-permutation network construction

I want to understand more about substitution-permutation network, if we modify it instead of carrying out the key-mixing, substitution, and permutation steps in alternating order for r rounds, the ...
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465 views

Number of combinations required to brute force

I am trying to encrypt a password in a program. Here is the process: Let us assume that I have a string $p$ ($n$ characters long) which contains the password. Now the program reverse the string and ...