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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45
votes
3answers
15k views

What are the benefits of the two permutation tables in DES?

Why do we use a permutation table in the first step of DES algorithm and one at the end of the algorithm?
18
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2answers
6k views

Shannon confusion and diffusion concept

I read the document(not the whole document) from Shannon where he speaks about the concepts of confusion and diffusion. I read in many places(not in the document but around the internet) that ...
15
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1answer
2k views

Replacing the Rijndael S-Box?

The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?
6
votes
1answer
605 views

One-way permutation over a small interval?

I am wondering what concrete computable functions we know that are a permutation over an integer interval of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{...
6
votes
2answers
604 views

Can we exchange the permutation of a sponge construction?

Part of a sponge construction (like SHA3 uses) is a fixed permutation $p$; which is clearly not one-way. Could we, theoretically, exchange the permutation $p$ with any other permutation? What basic ...
4
votes
1answer
426 views

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 ...
12
votes
1answer
1k views

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 ...
5
votes
1answer
338 views

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 ...
2
votes
4answers
341 views

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 ...
10
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1answer
1k views

Block cipher and parity of permutation

Can anyone explain the following text passage to me? Most real-world block ciphers build even permutations, because it's hard to build odd ones using small operations (32 bit) on larger (128 ...
4
votes
1answer
212 views

When all shares of a secret are given to adversary as a permuted matrix

Suppose we have a secret $\sigma$. The secret comes from a universe in which the elements are not necessarily distributed uniformly. We split $\sigma$ into $n$ shares $[\sigma_1,...,\sigma_n]$ (...
3
votes
1answer
585 views

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. ...
13
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4answers
3k views

Why is the permutation in AES (and other ciphers) not random or key-dependent?

If the permutation in AES (or other ciphers) were randomly generated or dependent on the key, would it not be stronger against differential attacks? If this is so, then might we need fewer rounds for ...
2
votes
2answers
211 views

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) ...
7
votes
5answers
4k views

What is the difference between a hash and a permutation?

As defined by Wikipedia a hash function is [...] any algorithm or subroutine that maps large data sets of variable length to smaller data sets of a fixed length. For example, a person's name, ...
15
votes
3answers
14k views

Why is AES not a Feistel cipher?

I am studying for an exam right now. And I wanted to make sure I got this point correct. AES is not a Feistel cipher because the operations in AES are not invertible. Is the above statement correct?...
3
votes
1answer
130 views

What can be said about the self-power map on groups based on DLP?

Introduction 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 ...
3
votes
2answers
309 views

Is there a theoretical maximum useful keysize given the block-size?

Consider a block-cipher $F$ with a $N$-bit block-size and a $M$-bit key-size. That is, if $k$ is a $M$-bit key, $p$ is a $N$-bit block of plain-text and $c$ is a $N$-bit block of cipher-text, then: $$...
2
votes
0answers
101 views

Permutation parity after cycle-walking

Let $E$ be a random even permutation of the set $\{0\dots n-1\}$. We construct a permutation $P$ of the set $\{0\dots m-1\}$, for some $m\le n$, using cycle-walking; that is, computing $P(x)$ is as ...
2
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1answer
177 views

What is the difference between a bijective random oracle and a random permutation?

Assume $S$ be a finite set $O$ be a random oracle from $S$ to $S$, such that $O$ is bijective $f$ be a random permutation of $S$ Is there any difference between $O$ and $f$? Does it makes any ...
5
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1answer
186 views

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 ...
4
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2answers
287 views

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 ...
3
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1answer
785 views

Is SHA-256 a one way permutation when restricting the domain to {0,1}^256? [duplicate]

Suppose we consider the space of $\lbrace 0,1 \rbrace^{256}$ as the domain and SHA-256 as our hash function. Does SHA-256 become a one way permutation? Has anyone tried to prove this? Or can it be ...
3
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1answer
540 views

How do substution-permutation networks work?

I understand what's going on in higher level. But i don't understand what's really going on in page 3 and 4 of this slide. Specifically, How S0 and S1 is used? What goes in what goes out? How ...
3
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1answer
110 views

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 ...
1
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2answers
92 views

From the product of two permutation matrices raised to the same power, is it easy to find the power?

Let $A$ and $B$ be two public permutation matrices. If $r$ is a secret power of large number, can we easily find $r$ from $A^rB^r$?
1
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1answer
231 views

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. ...
0
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1answer
116 views

Is Permutation conjugate problem hard?

Let $x$,$y$,$z$ be permutations. Then public key is $z=xyx^{−1}$ and $y$. Is permutation conjugate search problem easy? if yes, how to find $x$ from $z$ and $y$? Let be a is Alice's secret key as ...
-1
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1answer
107 views

Can we use merely permutation to hide a message?

This question is related to this: When all shares of a secret are given to adversary as a permuted matrix I think the below question is a simplified version of that. Assume we have a 40-bit ...