# Tag Info

29

The initial and final permutation have no influence on security (they are unkeyed and can be undone by anybody). The usual explanation is that they make implementation easier in some contexts, namely a hardware circuit which receives data over a 8-bit bus: it can accumulate the bits into eight shift registers, which is more efficient (in terms of circuit ...

7

Yes, an additional bit permutation of pseudo-random data from a secure Pseudo-Random Number Generator is secure, subject to the condition that this bit permutation is independent of the key material of the PRNG and of any data derived from that (including the pseudo-random data). An argument is that if this permutation is public, the adversary can do/undo ...

6

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 ...

6

The security of a block cipher is, based on what we know, invariant to the permutation cycles of the S-box. This is because the values are always transformed (by a fixed function or a keyed function) before going through the S-box again in the next round. Furthermore, many S-boxes are functions not permutations (i.e., output size is different from input ...

4

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 ...

4

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 ...

3

Something I wrote years ago to describe the IP and Inverse IP. With a copy of the FIPS Pub in hand you can see the correlation between registers and bits. Essentially the data is shifted in serially (for an interface smaller than 64 bits, in this case 8 bits wide) and used in a parallel fashion. In hardware and an 8 bit interface the IP and Inverse IP ...

2

All permutations have a cycle decomposition from which you may immediately read off your $P(n-2)$ and $P(n-1)$. There are trivial algorithms for doing this that run in either $O(n)$ time and $O(n)$ space (invert the permutation), or $O(n^2)$ time and $O(1)$ space (walk backwards by querying everybody repeatedly). You could adapt that invert the permutation ...

2

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 ...

1

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 ...

1

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 $$x_j\mapsto (S[x_j]+K[j\bmod k])\bmod{26}$$ ...

1

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 ...

1

Our Professor, Christof Paar, sat together on lunch a few years ago with one of the main designers of DES. He said that for getting it as specification, they had to build a piece of hardware which encrypts via DES. Shortly before finishing the project, they discovered that their wiring into the box was somewhat intermingled. Building such hardware stuff was ...

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