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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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 ...
2
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1answer
101 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
91 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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107 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 ...
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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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196 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
111 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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84 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 ...
2
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0answers
47 views
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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1answer
66 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
449 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
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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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1answer
37 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
123 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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0answers
68 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 ...
3
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1answer
117 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
262 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 ...
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1answer
71 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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1answer
173 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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49 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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33 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
94 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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1answer
518 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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1answer
141 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
103 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
103 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
351 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
489 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
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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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1answer
106 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 ...
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1answer
447 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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1answer
162 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
120 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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2answers
265 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 ...
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1answer
420 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 ...
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2answers
199 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) ...
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1answer
71 views
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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1answer
138 views
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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1answer
323 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 ...
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74 views
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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2answers
122 views
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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1answer
556 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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1answer
100 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 ...
3
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1answer
137 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 ...
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133 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=...
