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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What is the inverse of this variant of the Gimli SP-box?
Consider a slightly modified variant of the Gimli SP-box:
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What is the AEGIS design rationale for one way rounds and slow diffusion?
The AEGIS reference document doesn't specify why the authors chose a slow diffusion process and a one way round transformation.
As you can see the previous state is XORed with AES applied to itself ...
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How is the Full-State Keyed duplex useful?
In the Full-State Keyed duplex (sponge construction AEAD), plaintext is absorbed into the entire state of the sponge permutation but only a portion of the output can be used else the scheme breaks (...
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Why doesn't ChaCha use a 512bit key and xor parameters into it?
ChaCha has clear delineations between key, nonce, counter and constants.
What is the reason for not using a XEX-like ($k=0$) approach such that the ChaCha key is 512 bits and all the other things are ...
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A 5-bit S-Box whose differential branch number is equal to 4 and the linear branch number is not less than 3
The last paragraph of Section 1 (Introduction) of the paper “On the Relationship between Resilient Boolean Functions and Linear Branch Number of S-boxes” [S. Sarkar, K. Mandal, D. Saha] contains the ...
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Worst-case one-way permutations under P different from NP
This is probably obvious, but I cannot find it anywhere, since all textbooks define OWFs for average-case hardness.
Do we known if worst-case one-way permutations exist assuming $\mathbf{P} \neq \...
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Sponge construction versus Merkle-Damgard For Hashing based on the very same primitive
I am a bit confused about Sponge construction and Merkle-Damgard-style ones for hashing. The only advantage I see for sponge construction is that they are secure against length extension attacks. So ...
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Comparison of distinguishing attack against blockcipher and permutation
In a previous question, we explored various security definitions of encryption schemes, such as IND-CPA, IND-CCA{1,2,3,etc.}
These indistinguishability games can roughly translate to blockciphers, as ...
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Secure ciphersuite from security-wise sub-optimal unkeyed permutation?
Hypothetically,
IF we were to create a SSL/TLS or QUIC ciphersuite from a single (unkeyed) permutation operating in sponge mode to provide hashing and duplex mode to provide AEAD cipher,
AND IF the ...
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Getting permutation box and S-box for AUT64 block cipher
Want to get 32 bits from 0x8000 address as 8 bytes (perm box)
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Vigenere Cipher Collision
I have been reading the book "Serious Cryptography" by Aumasson to begin learning about Cryptography. There was a part where the author suggested how encryption using permutation should have ...
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Is there any relationship between avalanche and permutation in block ciphers?
Avalanche is one of the characteristics of S-Box or SP network(S and P boxes are used together).Is it possible for the permutation module, when tested alone, to show avalanche effect.? reference SP ...
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Does a self-build random 256-key based on substition and permutation have the same power as an AES-key?
As far as understand AES takes 16 bytes, shuffles them and replaces every of the 256 bits via XOR.
Then the same procedure applies to the next 16 bytes, and then again - until the entire file is ...
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Security of the encryptions, using a PRG for the keyGen
I recently got doubtful to the usefulness of psuedorandom generators(PRG) in cryptography.
Based on Kereckhoff's principle, we always assume that the used algorithms are made public.
So, when we use a ...
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How one can combine shift row and mix column to form a single matrix?
I am trying to combine the effect the shift row and mix column into a single matrix. The cipher that I am working with is skinny64 (untweaked version). I know that combining the effect of these two ...
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Why not use a random permutation as a block cipher?
The purpose of a block cipher is to act like a random permutation, and indeed a common security definition is one in which the block cipher is taken to be indistinguishable from a random permutation (...
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Example of enhanced trapdoor perrmutation (Enhanced TDP)
I am currently reading about Trapdoor Permutations (TDP). While I can totally understand and think of examples of TDP. I cannot think of any examples of Enhanced TDP. The definition of both TDP and ...
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Even-Mansour Cipher: Efficient algorithms for sampling a random permutation
My understanding of the Even-Mansour cipher is the following:
We draw a random permutation $P$ from the set of all permutation $P: \{0,1\}^n \rightarrow \{0,1\}^n$. This permutation is public.
We ...
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How to know if a power is a permutation of an inverse group?
Consider the group $$ℤ^*_{55}$$
Is exponentiating to the 3rd power a permutation of: $$ℤ^*_{55}$$ And exponentiation to the 5th power?
I'm trying to solve this problem related to groups, but I don't ...
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Connecting, joining or merging Substitution Permutation layer
I am trying to identify how the SP Network is constructed. I am looking for plausible solutions that help to connect these layers together and what are the ways that exist in literature other than Kam ...
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How difficult is finding $i$ for sequence $s_{i} = g^{s_{i-1}} \mod P$ with $s_0 = g$ for given value $v\in [1,P-1]$
Assuming we found a constant $g$ and a prime $P$ which is able to produce all values from $1$ to $P-1$ with it's sequence
$$s_{i} = g^{s_{i-1}} \mod P$$
$$s_0 = g$$
How many steps are needed to ...
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How difficult is finding $i$ in tetration $^{i}g = g\uparrow \uparrow i = \underbrace{g^{g^{\cdot\cdot\cdot^{g}}}}_i\equiv v \mod P$ for $v\in[1,P-1]$
EDIT: I messed up something (see comments at answer). This question contains some false statements EditEnd.
For tetration modulo prime $P$
$$^{i}g = g\uparrow \uparrow i = \underbrace{g^{g^{\cdot\cdot\...
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Could we use permutation polynomials for Shamir's secret sharing scheme?
Could we use permutation polynomials for secret sharing scheme like Shamir's? The say that they induce a bijection over $\mathbb{Z}_p$ what does this mean and how does it helps?
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Substitution-Permutation Network (SPN) Example
I came in contact with an algorithm that deals with SPN in an example, first I'd like to give a definition of what it is:
Let $l, m, $ and $N$ be positive integers, let $\pi_s: \{0,1\}^l \to \{0,1\}^...
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Can anybody explain the proof of Rabin and Ben-or of secure multiparty computation?
Can anybody explain the proof of Rabin and Ben-or of secure multiparty computation?
The idea is that every player $i$, of $N<+\infty$ players, holds a secret say $s_i$. All of them want to share ...
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Number of Involuntory Keys in Permutation Cipher
I've came with the following problem from the Theory and Practice book by Stinson-Paterson. It states the following:
2.17
(a) Prove that a permutation $\pi$ in the Permutation Cipher is an
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What's the difference between permutation and transposition?
I am trying to understand the difference between permutation and transposition. I have seen a similar question in the forum but I would like to ask you for proper definitions and examples of each. I'm ...
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Structure of composition of permutations
If $P_1, P_2$ are finite permutations, what can we say about $P_3 = P_1 \cdot P_2$? That is, what properties of the composition of permutations can be inferred from the properties of the permutations ...
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How to find k evenly-distributed elements from the set of all n！ permutations over n alternatives?
Let $C=\{ c_1, c_2, \cdots,c_n \}$ be a set of $n$ alternatives and $T$ be the set of all strict complete orderings on $C$. For any two $t_1$ and $t2$ in $T$, their (Kendal-tau) distance $d(t_1, t_2)$ ...
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Why is a fixed permutation not oneway?
This may not be a good question, but I am just start to learn cryptography.
I would like to ask why a fix permutation is not one way.
An adversary is given y=f(x) and try to invert y, x and y are n ...
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Can modular exponentiation with a public index be considered a secure permutation?
Secure permutation can be used in Sponge and Duplex constructions to build hash functions and encryption. To potentially use them in public-key cryptography, some arithmetic properties is desired.
Can ...
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How to generate keys from a 56 bit using DES
First I just want to apologize for my lack of knowledge in this system.
The professor kind of gave us an exercise to solve before even going through the lessons. I tired to look at videos online but ...
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How to cryptanalyze the message using permution cipher
The message is:
ACAUI MMGRC AILEE HKREG EAISW OSTHDS
With a grid size of 6 x 6. The forbidden cells are in different rows and different columns, so there are no two forbidden cells in the same line.
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Permutation polynomial
I want to find a linearized polynomial as my permutation polynomial in GF(2^n). I know that the only root should be 0. So, is there any way to find such polynomial instead of choosing a random one and ...
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How does this generate a permutation?
In the process of trying to answer this question, I ended up getting stuck. I found a paper which seems to solve their issue: its authors define a process which yields a pseudorandom permutation ...
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Assistance with Permutation Cipher (Columnar Transposition) [closed]
I was wondering if someone could provide some assistance with understanding a permutation cipher. I have both the cipher text as well as the plaintext but am having some difficulties trying to find ...
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Test the randomness of a random permutations, that was generated without Fisher-Yates?
Overview of the problem
Before this gets immediately flagged as duplicate, I'm not interested in testing the Fisher-Yates shuffle for randomness, since this can simply be done by testing the ...
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How can I determine the number of times I have to reapply the Scytale until the original plaintext comes back?
Given "①②③④⑤⑥⑦⑧⑨⑩⑪⑫" as plain text and a 4 rows Scytale inscription with 3 as the length of the longest row, the original plaintext is back after 5 runs:
①④⑦⑩②⑤⑧⑪③⑥⑨⑫
①⑩⑧⑥④②⑪⑨⑦⑤③⑫
①⑥⑪⑤⑩④⑨③⑧②⑦...
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What Permutation Entropy really is?
I was wondering about what is permutation entropy(PE). Then, I came to know this paper which describes PE. Now, let's assume that we have a pseudorandom permutation that is generated using an entropy ...
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Why I can't permutate an email and get away with it?
I can understand why a simple substitution cipher can be broken easily using English letter frequencies, and even English digrams like th can be used. Also a ...
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What's a random involution?
What are the properties of random involution? What is the difference between random involution and random permutation?
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Does there exist a universal one-way permutation?
Leonid Levin constructed a universal one-way function, i.e. a function which is one-way as long as there exists at least one one-way function.
But my question is, does there exist a universal one-way ...
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Parity attack on block cipher
My misunderstanding is all about the parity attack mentioned in "Cryptography Engineering by Ferguson, Schneier and Kohno".
Most modern block ciphers have a 128-bit block size, but they ...
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Double permutation patterns for transposition ciphers, how to crack
I'm reading from Cornell , I know for a single permutation, I can find the ciphertext length (100), divide in some key lengths (10x10, 5x20), then try all permutation (10x9x8... 5x4x3x2x1). then find ...
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collision resistance with added permutation
Suppose we have an $n$ bit ciphertext $c$ protected by a $k$ bit $MAC$, with $k < n$.
Generally, we expect collisions after $O(2^{k/2})$ ciphertext/MAC pairs are seen.
Consider the following ...
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Is this permutation secure?
Let vector ${\bf d} \in \{ \pm 1 \}^n$ be the message we want to send. In my system, ${\bf d}$ is multiplied by an $n \times n$ Fourier matrix ${\bf F}$, as follows
$$ {\bf x} = {\bf F} {\bf d} $$
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Proving that RSA encryption function with non-square free modulus is not a permutation
Here is a backgroung for the question on hand. While studying RSA I came up to the question about what happens if $p$ and $q$ involved in modulus computation are not actually primes? There is already ...
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Some questions on building permutations from boolean functions
I've seen multiple examples of boolean functions being used as a permutation.
For example the Keccak Chi : 2.3.1 function:
from https://keccak.team/figures.html
Or as a formula: for $i=\{0..4\}$ $A_i=...
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Shuffling: Purpose and formal definition
To my understanding, shuffling means simply to permute the elements in vector $\mathbf{v}$ pseudorandomly, using a PRP $\pi (\mathrm{seed},\mathbf{v})$. A secure PRP should yield a permutation ...
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One way permutation and its inverse
Is the following statement correct?
Let $F$ be a OWP. Then the inverse $F^{-1}$ of $F$ is also a OWP.
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