# Tag Info

8

First of all, we need to review what they mean by "parity of a permutation"; they don't mean whether the input block had a even number of 1's. Instead, they view the $n$ bit cipher (with a specific key) as a permutation on $2^n$ objects; that is, it can be review as a way of rearranging that set of $2^n$ objects onto itself. Now, permutations on a finite ...

6

There is no uniform permutation; there is a permutation uniformly chosen from the set of all possible permutations over $Z_2^{128}$. It is evident that AES is not a uniformly chosen permutation, since its permutation is fixed for any key. One can consider a family $\{AES_K\}$ of AES permutations under all possible keys $K$. Even if the key is chosen ...

4

This is purely a counting problem. We want the number $N(n,m)$ of possible permutations of $n$ things, with the constraint that only $m$ among these things can map to themselves ($0\le m\le n$). The values in the question are $n=11$, $m=5$. It holds that $N(n,n)=n!$ (that's the number of permutations of $n$ elements). It holds that ...

4

The permutations in your question are given in Cauchy's two-line notation, where the upper line gives the input index to the permutation function, and the lower line gives the resulting permuted index. For example, the definition $$\sigma = {1\ 2\ 3 \choose 3\ 1\ 2}$$ means the same as $$\sigma(1) = 3,\quad \sigma(2) = 1,\quad \sigma(3) = 2.$$ Thus, if we ...

4

I thought you were using a block cipher, i.e. a pseudorandom permutation. Instead as per your comment you are only permuting the order of the plaintext bits. This is not secure. For example, you can imagine the bit permutation is an n-by-n square matrix, where each row and column has a single 1 and the rest 0s. The input and output are then vectors of size ...

3

Yes, it is possible to implement the primitive asked, with a 32-bit block cipher that is secure (indistinguishable from a random permutation) no matter how many input-output pairs are known, keyed with a fixed secret randomly-chosen key. That's a standard building block in Format Preserving Encryption. One such block cipher is: Louis Granboulan and Thomas ...

3

How secure is this cipher? At first glance, not very. It would appear to be vulnerable to a ciphertext-only attack, for example, the attacker can recover the plaintext given a ciphertext of about 10k (actually, he probably can deal with less), even assuming that all the attacker initially knows is that the plaintext is "ASCII English", and he has no ...

2

My own answer would be: 2048, 2048, and still 2048 bits. Why ? Because: 2048-bit is the current "standard recommendation"; it has been so for quite some time, and is likely to remain so for quite some time (decades). See this site for pointers. There are plans for removing support for keys shorter than 2048 bits in some widespread software, e.g. Firefox. ...

2

Are there many permutation polynomials in a field? For a field $F$ of order $q$, every function from $F$ to $F$ is expressable (uniquely) as a polynomial of order $q-1$. $q!$ of these will represent permutation polynomials. Is there anyway to pick uniformly at random permutation polynomial in a field of prime order? Given a function from $f$ with $f(x_i) ... 1 AES transformation can be viewed as a sequence of invertible transformations each processing only a small part of the state. All these transformations would be even, and so is the entire AES for any key (see also this question). 1 In general, the key length and number of rounds are the dominant factors in deciding cipher strength. But you need to consider how the rounds are constructed and how the key is used. Substitution and permutation are the bread and butter of DES. That's literally all it is - substitution, permutation, and XOR. Here is a diagram of the DES fiestel function ... 1 I think that you missed a pivotal point in the concept, which is the small blocks that are used to compose a secure PRF (or PRP), i.e. when you permute one bit, you actually change the value of the small block of that bit, i.e. the whole small-block is effected and thus prepared to be confused in the next round, this way you will reach a confusion of the ... 1 Can you use threshold encryption and a mixnet? It might not be the fastest thing in the world but it uses well-understood components. Setup Every player generates an ElGamal keypair and proves knowledge of their secret key. The joint public key is the product of all public keys. (If you're worried about reset attacks, look up "Pedersen threshold key ... 1 There are two possible explanations. The literature you are reading swapped the positions of the plaintext and ciphertext in the second example. If you were to permute TEN, the result is ENT. There is a mistake in either the permutation value or in the resultant ciphertext. If the first example permutation was used, the ciphertext would be correct. ... 1 The first question is already answered here. For the second question, a single key$k \in \left\{0,1\right\}^{168}$can be trivially converted back and forth from three keys$k_1, k_2, k_3 \in \left\{0,1\right\}^{56}\$ – there is no semantic difference between the two. DES itself operates only on 56-bit keys, and triple-DES requires three independent DES ...

1

The closest to my choice is: C. (a) 2048; (b): 4096; (c): I would not use RSA My answer takes in account not only details mentioned in question, but currently widely deployed security practices. I try to point out useful resources to study. Things are not as simple as pick one of A-D. I recommend to study resources I've included and draw your own ...

1

Consider Shor's algorithm, which solves RSA in polynomial time on a quantum computer and the fact that there is publicly available software that could factor a 512 bit modulus on a modern PC in a few days' time.

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