# 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 are advantages/disadvantages of an invertible tweak schedule in a tweakable block cipher?

I have been doing research on a tweakable block cipher called BipBip. This is a rather niche cipher so I'll give a few facts about it for background before asking my question: The structure is based ...
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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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
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### 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 ...
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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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1 vote
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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 ...
1 vote
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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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1 vote
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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 ...
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 ...
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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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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...
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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 ...