# 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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### 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 $d(t_1, t_2)$ ...
58 views

### 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 ...
186 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 ...
168 views

### 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 ...
59 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.
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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 ...
70 views

### 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 ...
19 views

### Working of Algorithm on SP network by Kam and L. Davida

I am reading the paper titled "Structured Design of Substitution-Permutation Encryption Networks". by John B. Kam and Georges I. Davida (1979) They have presented and algorithm for ...
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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 ...
97 views

### 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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### calculating the branch number/ active bundles of a cipher

I have read the papers Wide Trail Strategy and Wide Trail Design Strategy for Binary MixColumns. These papers describe the need for a good linear transformation in a cipher, a provable mechanism to ...
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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 ...
2k views

### 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 ...
358 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 ...
184 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 ...
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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 ...
257 views

### 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 $${\bf x} = {\bf F} {\bf d}$$ ...
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 ...