# 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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### 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 ...
1 vote
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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 ...
1 vote
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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 ...
66 views

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\... 0 votes 1 answer 29 views ### 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? 0 votes 1 answer 81 views ### 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\}^... 2 votes 1 answer 133 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 ... 0 votes 0 answers 24 views ### Rational secure multiparty computation with permuatation secret sharing scheme? Taking a look in this economic paper they use cryptographic tools to implement correletaed equilibria in the case of two plaeyrs. They use permutations for the exchange of information between the ... 0 votes 1 answer 64 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 ... 0 votes 1 answer 88 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 ... 0 votes 0 answers 23 views ### 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. ... 0 votes 1 answer 59 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 ... 0 votes 0 answers 23 views ### 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) ... 0 votes 1 answer 66 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 ... 4 votes 1 answer 198 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 ... 0 votes 3 answers 423 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 ... 1 vote 0 answers 60 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. 1 vote 2 answers 84 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 ... 0 votes 1 answer 98 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 ... 1 vote 0 answers 20 views ### 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 ... 1 vote 1 answer 94 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 ... 1 vote 0 answers 101 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... 0 votes 1 answer 127 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 ... 3 votes 2 answers 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 ... 1 vote 1 answer 100 views ### What's a random involution? What are the properties of random involution? What is the difference between random involution and random permutation? 5 votes 1 answer 119 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 ... 4 votes 1 answer 393 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 ... 1 vote 1 answer 275 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 ... 0 votes 1 answer 56 views ### 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 ... 2 votes 2 answers 275 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 ...