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a permutation will rearrange the input producing something of arbitrary length. I'm not sure about this. My understanding of a permutation is that it will always produce an output of the same length as the input. That is, a permutation simply reorders all the parts of the input without adding or removing any elements. A hash function does not have ...

As Henrick notes, permutation is a mathematical term for a function (or map; these two words are essentially synonymous in mathematics) that rearranges the elements of its domain so that exactly one input is mapped to each output. In other words, a function $f$ from a set $S$ to $S$ is a permutation if and only if: no two inputs are mapped to the same ...

In Algebra, a Permutation of a set $X$ is a bijective function $\sigma:X{\rightarrow}X$ that for each element $x \in X$ assigns a unique value $\sigma(x) \in X$. In practice, this could mean a lot of things. For instance, in DES a permutation is used that rearranges the position of the bits of the half block. This is a permutation ...

Measuring the size of the key space in transposition algorithms is not important, because their security is far less than the size of the key space would suggest. Therefore, any measure of effective key length will be misleading and will not give an accurate picture of the true security of the scheme. In general the standard way to compute the effective ...

I don't understand the question (what is public? what is secret? what is the definition of all variables and functions?), but I can give you a pointer to literature that I strongly expect is highly relevant: Take a look at mixnets. There's an enormous amount of research literature on the subject. It solves the following sort of problem (as well as ...

Sticking to monoalphabetic ciphers, Vigenere can be combined with a secret random-like substitution of the plaintext or/and ciphertext alphabet, making it significantly more resistant. If Vigenere encryption is $$x_j\mapsto (x_j+K[j\bmod k])\bmod{26}$$ where array $K$ is the key or length $k$, I'm discussing $$x_j\mapsto (S[x_j]+K[j\bmod k])\bmod{26}$$ ...

For Vigenère specifically, you can make it harder to break by increasing the size of the key and by making the key truly random. If the key is truly random, longer than the plaintext and never reused, then Vigenère becomes equivalent to a One Time Pad. Even without going that far, it is possible to strengthen many, though not all, cyphers by lengthening ...