Questions tagged as ['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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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 involuntory kei iff (if and only if) $$\pi(i) = j$$ implies $$\pi(j) = > i$$, for all $$i,j \in \{1,...,m \}$$.

(b) Determine the number of involutory keys in the Permutation Cipher for $$m = 2,3,4,5,$$ and 6.

I've prove ...

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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 trying to understand the DES algorithm and I'd like to understand if the halving of the initial block and eventual swapping of the halves would be permutation or transposition. Thank you in advance.

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Securely and Deterministically select a combination of objects from hash (cryptographic seed)

I am working on a project that is using a bit-commitment concept to authenticate information.

I need to select a combination of objects securely from a secure hash, then distribute that hash later. Then a client knows that only the authenticated server selected that combination of objects before distribution of the hash the combination derived from. In other words, I need to select a combination  ...

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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 which are composed?

Since permutations form a group, for any $$P_2$$ and $$P_3$$, there exists a $$P_1$$ that when composed with $$P_2$$ gives $$P_3$$. So there range of composition spans the entire space of ...

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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 $$d(t_1, t_2)$$ is defined as the number of pairwise disagreements between $$t_1$$ and $$t_2$$.

My Question: How to find $$k$$ (much smaller than $$n!$$) different elements from $$T$$ such that they are "evenly ditributed" in  ...

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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 bits

In my opinion, an efficient adversary could only make polynomials query to the permutation. And it could only succeed if it made a query of x to f().

So the probability of the adversary to success is on ...

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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 modular exponentiation with a public index be considered a secure permutation? What public attacks are available? Are there constructions proven to be insecure?

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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 what I only know how to use a 64 bit initial key.

initial 56-bit hexadecimal key: 'B092EBA02E3798' Give the key K16 (on the last turn) to 64 bits in hexadecimal.

So my question is, do I have to turn my 56 b ...

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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.