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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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I'm curious on what the downsides of the public-key encryption method from my research project could be

As part of my final BS degree research project, I had to work with an encryption method based on research done in my university. What surprised me, is that while the method is very simple, I can't ...
H-a-y-K's user avatar
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How to attack the shuffling of correlated numbers?

Suppose I have a function that accepts vector input $x$ and outputs vector $y=f(x)$. I want to protect the output $y$ through shuffling numbers in it. I hope the shuffling can confuse the attacker by ...
Zhengyi Li's user avatar
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Inverse Permutation in Sequential Manner Per-XOR (𝑃𝑥−1)

I'm trying to understand a protocol proposed in a research paper. There is a step that involves computing inverse Per-XOR. The explanation along with solved example is given below: "Perform ...
Fakhr Ali's user avatar
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1 answer
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Per-‌XOR computation

I have an assignment where I have to understand a protocol proposed in a research paper. The first step involves computing Per-XOR, but I can't seem to understand the explanation given. Below is the ...
Fakhr Ali's user avatar
2 votes
1 answer
67 views

Rationale for BLAKE2 message schedule?

BLAKE2 uses a message schedule I did not see before. It uses permutations of pieces of the message block. The BLAKE2 book did not state the rationale for such a choice and how it contrasts with the ...
LightTunnelEnd's user avatar
4 votes
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107 views

Impossibility of uniform generation in random world

I was reading Limits on the provable consequences of one way permutations by Impagliazzo and Rudich when I got stuck on a sentence. First of all, they define a polynomial relation that is any relation ...
Pur2all's user avatar
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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: ...
lyrically wicked's user avatar
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108 views

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 ...
LightTunnelEnd's user avatar
4 votes
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138 views

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 (...
LightTunnelEnd's user avatar
2 votes
1 answer
237 views

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 ...
Loraine Toorla's user avatar
3 votes
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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 ...
lyrically wicked's user avatar
1 vote
1 answer
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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 \...
Noel Arteche's user avatar
1 vote
2 answers
211 views

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 ...
A.Solei's user avatar
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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 ...
DannyNiu's user avatar
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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 ...
DannyNiu's user avatar
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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) ...
dev's user avatar
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2 answers
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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 ...
John Pham's user avatar
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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 ...
user103130's user avatar
1 vote
1 answer
211 views

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 ...
user103089's user avatar
1 vote
1 answer
157 views

Security of the encryptions, using a PRG for the keyGen

I recently got doubtful about the usefulness of pseudorandom generators (PRG) in cryptography. Based on Kerckhoffs's principle, we always assume that the used algorithms are made public. So, when we ...
m123's user avatar
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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 ...
Muhammad Awais's user avatar
2 votes
1 answer
788 views

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 (...
user918212's user avatar
1 vote
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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 ...
tur11ng's user avatar
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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 ...
cryptobeginner's user avatar
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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 ...
Aleix Martí's user avatar
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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 ...
Muhammad Awais's user avatar
2 votes
1 answer
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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 ...
J. Doe's user avatar
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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\...
J. Doe's user avatar
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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?
Hunger Learn's user avatar
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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\}^...
João Víctor Melo's user avatar
2 votes
1 answer
231 views

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 ...
Hunger Learn's user avatar
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1 answer
538 views

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 ...
João Víctor Melo's user avatar
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1 answer
565 views

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 ...
Baldovín Cadena Mejía's user avatar
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1 answer
110 views

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 ...
SRobertJames's user avatar
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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 $d(t_1, t_2)$ ...
Joe Zhou's user avatar
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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 ...
js wang's user avatar
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1 answer
243 views

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 ...
DannyNiu's user avatar
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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 ...
Hakim Cheheb's user avatar
1 vote
0 answers
71 views

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.
Rose's user avatar
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1 vote
2 answers
378 views

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 ...
dilot's user avatar
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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 ...
JamesTheAwesomeDude's user avatar
1 vote
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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 ...
Mike's user avatar
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2 votes
1 answer
206 views

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 ...
camel-cdr's user avatar
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1 vote
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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...
Rodrigo Panchiniak Fernandes's user avatar
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1 answer
438 views

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 ...
Radium's user avatar
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3 votes
2 answers
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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 ...
KMG's user avatar
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1 vote
1 answer
147 views

What's a random involution?

What are the properties of random involution? What is the difference between random involution and random permutation?
wurst's user avatar
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7 votes
1 answer
178 views

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 ...
Keshav Srinivasan's user avatar
5 votes
1 answer
524 views

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 ...
killertoge's user avatar
1 vote
1 answer
617 views

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 ...
pianobegginer's user avatar