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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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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: ...
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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 ...
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1answer
55 views

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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Is there a 'chain-function' which allows computing the value for the index which is next, previous, +/- some constants but has no shortcut for other?

Looking for an algorithm which has a cyclic 'chain'-function which only allows the computation of next, previous element and in addition to that also a shift by a small amount of constants. Example 1 ...
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1answer
83 views

How are the four 8-bit permutation tables of Present cipher calculated?

the fast implementation of present cipher for 8-bit register uses four 8-bit lookups tables for permutation. Table 3 & 2 are : ...
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99 views

What is the intuition behind the strength of unstructured symmetric cryptography?

Consider a single round of a cryptographic permutation, what is so special about it that lacking some bits of information that either get mixed into it as a subkey or omitted at the end (sponge ...
5
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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 ...
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1answer
732 views

No of keys used in Triple DES Algorithm

I am studying Triple DES. I have got two basic questions. One, why are we following a sequence like encrypt(decrypt(encrypt)); what is the problem using a sequence encrypt(encrypt(encrypt))? Second,...
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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 ...
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1answer
133 views

How strong is XooDoo vs AES?

What is Gimli, and how does XooDoo compare to symmetric ciphers such as AES or ChaCha? I am looking at this library, called charm. Interesting paper here. I also ...
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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 $A^rB^r$?
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1answer
114 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 ...
3
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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 ...
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40 views

Examples of extended trapdoor permutations

I am interested in Extended Trapdoor Permutations (ETP). An Extended Trapdoor Permutation (ETP) is a collection of permutations $\{f_{\alpha}\}_{\alpha}$ along with four algorithms $I$ (index), $S$ (...
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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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2answers
76 views

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 $v$.
2
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1answer
536 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 ...
3
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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
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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. ...
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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 ...
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1answer
82 views

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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64 views

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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3answers
620 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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1answer
79 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 ...
3
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1answer
39 views

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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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 ...
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71 views

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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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 ...
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3answers
321 views

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 ...
5
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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 ...
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1answer
104 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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0answers
51 views

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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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 ...
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0answers
60 views

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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0answers
34 views

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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3answers
123 views

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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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 ...
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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 ...
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1answer
105 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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1answer
106 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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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, ...
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1answer
373 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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1answer
578 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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1answer
97 views

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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1answer
109 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 ...
4
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1answer
488 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 ...
2
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1answer
127 views

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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1answer
170 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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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 ...