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# 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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I am wondering what concrete computable functions we know that are a permutation over an integer interval of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{... 2answers 109 views ### What does it mean that$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$. I am ... 2answers 969 views ### Shared secret: Generating Random Permutation -- or: How to Play Poker Without a Dealer I know this question is long but it's a really interesting theoretical problem about shared secrets and multi-party computation. General Problem: "Shared ... 1answer 82 views ### PRP representation size I'm now studying the block cipher substitution-permutation network construction and realized that it uses several small pseudo-random permutations instead a big one for saving memory (or that is one ... 1answer 176 views ### What is the difference between a bijective random oracle and a random permutation? Assume$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$? Does it makes any ... 1answer 781 views ### Is SHA-256 a one way permutation when restricting the domain to {0,1}^256? [duplicate] Suppose we consider the space of$\lbrace 0,1 \rbrace^{256}$as the domain and SHA-256 as our hash function. Does SHA-256 become a one way permutation? Has anyone tried to prove this? Or can it be ... 1answer 317 views ### NP complete problems related to permutations of binary vectors or block ciphers Recently, T.Gowers wrote a blog entry called "How not to prove that P is not equal to NP" about the Razborov/Rudich Natural Proofs paper. He has a construction where he talks about compositions of 3-... 3answers 14k views ### Why is AES not a Feistel cipher? I am studying for an exam right now. And I wanted to make sure I got this point correct. AES is not a Feistel cipher because the operations in AES are not invertible. Is the above statement correct?... 1answer 1k views ### Is the inverse of a secure PRP, also a secure PRP? If a block cipher is a secure PRP, is it's inverse a secure PRP as well? My intuition says yes but I'm not exactly sure. On a related note, if a block cipher is a secure sPRP, is it's inverse a ... 1answer 310 views ### Salsa20 in Davies-Meyer mode with a fixed key (message): is it one-way? Say I have a function that calculates a pseudo random permutation and this function is easy to invert. For example$P(i) = AES_k(i)$where$k$is a publicly known key. So anyone can compute$P(i)$... 2answers 309 views ### Is there a theoretical maximum useful keysize given the block-size? Consider a block-cipher$F$with a$N$-bit block-size and a$M$-bit key-size. That is, if$k$is a$M$-bit key,$p$is a$N$-bit block of plain-text and$c$is a$N$-bit block of cipher-text, then: $$... 3answers 411 views ### Construct a random permutation from a random function? How can we construct a (pseudo) random permutation from a (pseudo) random function ? I've seen a method from Luby-Rackoff which allows to construct a PRP of length 2N from a PRF of input/output ... 5answers 4k views ### What is the difference between a hash and a permutation? As defined by Wikipedia a hash function is [...] any algorithm or subroutine that maps large data sets of variable length to smaller data sets of a fixed length. For example, a person's name, ... 1answer 610 views ### How can I prove in zero knowldege that an ElGamal shuffle is correct for a special setting? [closed] In a special ElGamal encryption scheme, every user has an ElGamal encryption key-pair using the same cyclic group G and generator g. The system has a special function :$$ \mathrm{ShuffleEncrypt}... 3answers 2k views ### 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 ... 1answer 1k views ### 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 ... 1answer 104 views ### How do we find the last two correspondences in an otherwise known even permutation? A secret even permutation$P$of the set of non-negative integers less than$n$is chosen. That might be a Feisltel cipher with a random key. We are given in sequence the$P(x)$for$x$from$0$to$...
The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?