# Tag Info

Accepted

### How to check whether the permutation is random or not

There are at most $n \cdot (n - 1)$ permutations of $\mathbb Z/n\mathbb Z$ of the form $x \mapsto ax + b$: if $n$ is prime, there are $n - 1$ choices for $a$ and $n$ choices for $b$ under which this ...
• 46.1k

### Why is the permutation in AES (and other ciphers) not random or key-dependent?

You have clarified the question as asking about whether replacing ShiftRows with a random byte permutation would strengthen AES against differential attacks. It would not. ShiftRows and MixColumns ...
• 4,355
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### Are encryption algorithms with fixed-point free permutations inherently flawed?

Are all encryption algorithms with fixed-point free permutations inherently flawed? Yes - when fixed points, or the lack of them, is knowable and detectable. This is a violation of multiple ...
• 359

### Are encryption algorithms with fixed-point free permutations inherently flawed?

Are all encryption algorithms with fixed-point free permutations inherently flawed? No, they are not inherently flawed. Consider the following cipher: Let $k_0$ be a key for AES-256, and let $k_1$...
• 46.1k

### Why is the permutation in AES (and other ciphers) not random or key-dependent?

I assume that you mean the S-box. The answer is NO! Randomly chosen S-boxes are not good choices for differential and linear cryptanalysis. When Biham and Shamir presented differential attacks on DES, ...
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• 126k
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### Parity attack on block cipher

When dealing with a block cipher of large block size, the text appearing as a quote in the question Most modern block ciphers have a 128-bit block size, but they operate on 32-bit words. They build ...
• 126k
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### When all shares of a secret are given to adversary as a permuted matrix

Let us first consider the problem without involving Shamir secret-sharing at all. Suppose that $n = 140$ and that the secret $\sigma$ is a 140-byte Twitter message. The space is thus restricted ...
• 2,636
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### Periodic One Way Function

Security is clearly broken if there is a polynomial-length period with non-negligible probability (where by this I mean if a random point falls in a cycle with a poly-length period with non-negligible ...
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### Simple proof that shows AES is not a uniform permutation on any n-bit string?

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, ...
• 5,557
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### Relationship between existence of OWFs and OWPs

Short answer: "No". The standard way to establish a statement of the form if a primitive $B$ exists then another primitive $A$ also exists is through a black-box reduction. This involves two steps: ...
• 4,548

### Are encryption algorithms with fixed-point free permutations inherently flawed?

Block ciphers operators from $\{0,1\}^n \to \{0,1\}^n$. Each key selects one permutation among all possible permutations $n!$ and this is very small one if you compare $2^{128}$ to $128^{128}$ For ...
• 44.1k

### Randomness Testing

There is no such thing as randomness of a sequence (or of a permutation, or of a string, etc.). There is only randomness of a process for choosing sequences (permutations, strings, etc.), which is ...
• 46.1k
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### How strong is XooDoo vs AES?

Gimli is an unkeyed permutation, mapping a 384-bit input to a 384-bit output, $\{0,1\}^{384} \rightarrow \{0,1\}^{384}$. It is not a cipher by itself as you can reverse the output if you have it in ...
• 13.8k
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### Are any block ciphers provably free of equivalent keys?

Yes, some block ciphers provably have no equivalent keys. For a start, it's very easy to exhibit such a block cipher, by restricting the key and message spaces to something enumerable. Granted, that ...
• 126k
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### Does there exist a universal one-way permutation?

To the best of my knowledge, this is unknown. That is, Levin's construction is a one-way function but most certainly not a one-way permutation. I don't see any way in which it can be modified to make ...

### Shannon confusion and diffusion concept

I find the terms "confusion" and "diffusion" to be slightly nebulous and can lead to over-simplifications. Confusion For example, saying that "substitution" is responsible for "confusion" is not ...
• 19.3k

### Revealing random bit permutation

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 ...
• 31.4k
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### Can we exchange the permutation of a sponge construction?

The security of the sponge construction rely on two parts: the size of the capacity. and the strength of the permutation used in the construction. This permutation is expected to have at least the ...
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### Can we exchange the permutation of a sponge construction?

The permutation should be as close to a random permutation as possible. This is essentially a block-cipher with a fixed key. A random permutation with given width $b$ is a permutation drawn ...
• 24.3k

### Creating single-cycle permutations

The obvious way to construct such a pseudorandom single-cycle permutation is to take a pseudorandom permutation $P$ (which need not be single-cycle), a simple fixed single-cycle permutation $Inc$ (e.g....
• 134k

### DES: how does Richard Outerbridge's Initial Permutation operate?

By definition, applying the initial Permutation of DES is shuffling bits per ...
• 126k

### modified substitution permutation networks

Your construction is completely insecure: a single known plaintext / ciphertext block pair is sufficient to decrypt all blocks encrypted with the same key. Specifically, let me write your block ...
• 44.6k

### How to check whether the permutation is random or not

This precise issue recently arose in light of suspicious patterns in the S-box of a Russian cipher Kuznyechik. See: Xavier Bonnetain and Léo Perrin and Shizhu Tian: Anomalies and Vector Space ...
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### Why I can't permutate an email and get away with it?

I can understand why a simple substitution cipher can be broken easily due to English letter frequencies can be used and even English diagrams like th can be used, ...
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### What is the importance of $f_k$ in a feistel network being a permutation
I assume that you are referring to the round function. This is false. The whole advantage of a Feistel network is that $f_k$ does not need to be a permutation. Indeed in DES, it is not a permutation. ...