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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

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 ...


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In the substitution step of a typical Substitution-Permutation Network (e.g. in AES SubBytes), the whole state is broken in parts and each part substituted. That's not the case in (the core of) a Feistel cipher, where at each step/round some sizable part of the state is bound to remain unchanged (in order that each step be reversible).


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If you can generate uniform random numbers, you can use a variant of Fisher-Yates. //given an array s with the elements to be permuted for i from n-1 to 1: t = rand(0, i) # inclusive swap(s[i], s[t])


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Assuming that the probability distributions of $\pi_{k_1}$ and $\pi_{k_2}$ are both uniform (that is, each permutation can take on any particular setting with probability $1/n!$), then no, adversary does not have enough information to learn anything about the original positions. This remains true even if we assume the adversary can perform unbounded ...


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 ...


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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) ...


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Hint: you can notice that $n! > 2^n$ (except for very small $n$).


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A while ago, I spent time playing with modern field/pen & paper ciphers, especially with Card-Chameleon. Card-Chameleon needs two separate full alphabet permutations as a key. As it's a field/pen & paper cipher, I tried to find a computer-less, math-less, way to generate these permutations from passwords. My solution is a two steps process. Let's ...


1

What is meant by vectors here? Just the inputs and outputs of the function. The function $f$ takes, as input, a sequence of bits (for example, 1010), and returns a sequence of bits (for example, 1100); the text refers to such a sequence of bits as a vector Can someone explain this? Well, the idea is that every output bit depends on all input ...


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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).


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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 ...


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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 ...


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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 ...



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