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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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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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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?...
15
votes
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?
14
votes
2answers
2k views

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: ...
13
votes
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 ...
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 ...
10
votes
1answer
360 views

Santa Claus' secret permutation

This December, $N$ friends play secret santa: they select a random permutation $\sigma$ of $N$ (without fixed point). For Santa Claus, everyone has to bring a gift to the next person in the ...
10
votes
2answers
970 views

Shared secret: Generating Random Permutation

-- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ...
9
votes
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 ...
7
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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, ...
7
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1answer
1k views

Permutations of pseudorandom data

Assuming a bit string is deemed cryptographically secure, e.g. PRNG using AES in counter mode, can we equally assume any permutation of said bit string is also cryptographically secure? In a more ...
6
votes
2answers
602 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 ...
6
votes
1answer
601 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
3answers
147 views

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 ...
5
votes
4answers
667 views

Get permutations from password

Are there any "good" ways to get a permutation from a password/pass-phrase? If one, for example, wanted to get a permutation of letters from a password, how might one do that in a smart way? I would ...
5
votes
3answers
2k views

Can I make a cipher (ex: Vigenère) harder to break?

The Vigenère cipher can relatively easy be broken when the key size is small compared to the size of the message. One first finds the length of the key, and then uses frequency analysis to actually ...
5
votes
1answer
335 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 ...
5
votes
1answer
117 views

Are any block ciphers provably free of equivalent keys?

There are $2^n!$ possible permutations of an $n$-bit block cipher $E_k:\{0,1\}^n \rightarrow \{0,1\}^n$, and any given key $k$ selects one of these permutations at random. Define equivalent keys as a ...
5
votes
2answers
109 views

What does it mean that $BW_N$ is a permutation over the squares mod N?

Let $BW_N$ be a function such that $BW_N:\mathbb{QR}_{N} \mapsto \mathbb{QR}_{N}$ and let if be defined as follow: $BW_N(x) = x^2 \pmod N$ where $N=pq$ and p and q are primes and $p=q=3 \pmod 4$. I am ...
5
votes
1answer
672 views

Is it possible to generate a secure permutation F over 32-bit integers even if F(0) … F(n) is public knowledge?

I'm currently interested in the problem of generating random-looking URLs from sequential database IDs, like how they do it in link shorteners. One way to do this is to encrypt the sequential database ...
5
votes
1answer
182 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 ...
5
votes
0answers
114 views

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 ...
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 $[\sigma_1,...,\sigma_n]$ (...
4
votes
1answer
486 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 ...
4
votes
2answers
285 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 ...
4
votes
1answer
139 views

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=...
4
votes
2answers
12k views

How to solve Columnar Transposition Cipher without a key

I have been given a 77 character message for decryption, but no matter where I look all the Columnar Transposition scripts out there are all requiring of a key. I believe the number of columns to be 7,...
4
votes
1answer
505 views

How secure is bit level permutation?

Could anyone explain how secure is bit level permutation? What is the most serious threat against the security of this kind of cipher?
4
votes
1answer
317 views

NP complete problems related to permutations of binary vectors or block ciphers

Recently, T.Gowers wrote a blog entry called "How not to prove that P is not equal to NP" about the Razborov/Rudich Natural Proofs paper. He has a construction where he talks about compositions of 3-...
4
votes
1answer
150 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, ...
4
votes
1answer
127 views

Using a round function intended for an SP network in a Feistel network?

If I use the round function from a secure SP network (such as AES) and use it in a Feistel netwok, is this a good starting point for the second cipher? My thought is "yes" because: it already has ...
4
votes
1answer
425 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 ...
3
votes
2answers
101 views

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 ...
3
votes
1answer
365 views

Periodic One Way Function

Is there any notion of a periodic OWF? I.e. an OWF $f$ that on every input $x$ in its domain it holds that $f(f(f\ldots f(x))\ldots )=x$ when $f$ applied many times, each time on the previous output....
3
votes
1answer
613 views

Simple proof that shows AES is not a uniform permutation on any n-bit string?

Is there a simple proof that shows AES is not a uniform permutation on any $n$-bit string? Since I'm just starting with crypto, I'd like to see a simple yet elegant proof for the said property. ...
3
votes
1answer
590 views

Revealing random bit permutation

I am new in cryptography. I want to determine the complexity of revealing a random bit permutation which is used as block cipher for plaintexts (bitstrings of length n). An adversary catches different ...
3
votes
3answers
412 views

Construct a random permutation from a random function?

How can we construct a (pseudo) random permutation from a (pseudo) random function ? I've seen a method from Luby-Rackoff which allows to construct a PRP of length $2N$ from a PRF of input/output ...
3
votes
1answer
573 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. ...
3
votes
2answers
4k views

DES: How to find the Inverse of the Initial Permutation?

I am doing a DES problem by hand and I want to know how you calculate the inverse of the initial permutation. I know what the permutation is, but how do you find it based off the given initial ...
3
votes
1answer
141 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 ...
3
votes
1answer
631 views

How does Feistel cipher create diffusion between blocks?

From what I've read about Feistel ciphers, I can understand that within each block, there is both confusion and diffusion. But it is unclear to me how a Feistel cipher permutates among blocks of data. ...
3
votes
1answer
88 views

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 ...
3
votes
1answer
358 views

derangements and permutations in cryptography

Given a partial key for a mono-alphabetic substitution cipher (missing 11 letters), calculate the number $N$ of possible keys, given that no plaintext letter can be mapped to itself. Ordinarily, ...
3
votes
1answer
782 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
votes
1answer
310 views

Salsa20 in Davies-Meyer mode with a fixed key (message): is it one-way?

Say I have a function that calculates a pseudo random permutation and this function is easy to invert. For example $P(i) = AES_k(i)$ where $k$ is a publicly known key. So anyone can compute $P(i)$ ...
3
votes
1answer
104 views

How do we find the last two correspondences in an otherwise known even permutation?

A secret even permutation $P$ of the set of non-negative integers less than $n$ is chosen. That might be a Feisltel cipher with a random key. We are given in sequence the $P(x)$ for $x$ from $0$ to $...
3
votes
1answer
154 views

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 ...
3
votes
1answer
513 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
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 ...