# 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 does it mean that $BW_N$ is a permutation over the squares mod N?

Let $BW_N$ be a function such that $BW_N:\mathbb{QR}_{N} \mapsto \mathbb{QR}_{N}$ and let if be defined as follow: $BW_N(x) = x^2 \pmod N$ where $N=pq$ and p and q are primes and $p=q=3 \pmod 4$. I am ...
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### Shared secret: Generating Random Permutation

-- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ...
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### PRP representation size

I'm now studying the block cipher substitution-permutation network construction and realized that it uses several small pseudo-random permutations instead a big one for saving memory (or that is one ...
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### What is the difference between a bijective random oracle and a random permutation?

Assume $S$ be a finite set $O$ be a random oracle from $S$ to $S$, such that $O$ is bijective $f$ be a random permutation of $S$ Is there any difference between $O$ and $f$? Does it makes any ...
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### Is SHA-256 a one way permutation when restricting the domain to {0,1}^256? [duplicate]

Suppose we consider the space of $\lbrace 0,1 \rbrace^{256}$ as the domain and SHA-256 as our hash function. Does SHA-256 become a one way permutation? Has anyone tried to prove this? Or can it be ...
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### NP complete problems related to permutations of binary vectors or block ciphers

Recently, T.Gowers wrote a blog entry called "How not to prove that P is not equal to NP" about the Razborov/Rudich Natural Proofs paper. He has a construction where he talks about compositions of 3-...
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### Why is AES not a Feistel cipher?

I am studying for an exam right now. And I wanted to make sure I got this point correct. AES is not a Feistel cipher because the operations in AES are not invertible. Is the above statement correct?...
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### Is the inverse of a secure PRP, also a secure PRP?

If a block cipher is a secure PRP, is it's inverse a secure PRP as well? My intuition says yes but I'm not exactly sure. On a related note, if a block cipher is a secure sPRP, is it's inverse a ...
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### Salsa20 in Davies-Meyer mode with a fixed key (message): is it one-way?

Say I have a function that calculates a pseudo random permutation and this function is easy to invert. For example $P(i) = AES_k(i)$ where $k$ is a publicly known key. So anyone can compute $P(i)$ ...
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### Can I make a cipher (ex: Vigenère) harder to break?

The Vigenère cipher can relatively easy be broken when the key size is small compared to the size of the message. One first finds the length of the key, and then uses frequency analysis to actually ...
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### Permutations of pseudorandom data

Assuming a bit string is deemed cryptographically secure, e.g. PRNG using AES in counter mode, can we equally assume any permutation of said bit string is also cryptographically secure? In a more ...