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Questions tagged [diffusion]

Diffusion refers to the property of an encryption primitive that small changes in the plaintext result in big changes in the ciphertext and vice-versa.

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Early propagation of carries in the BLAKE hash function

The BLAKE paper uses round constants derived from $\pi$ to improve diffusion, even if the additions modulo $2^{32}$ are replaced with bitwise XOR when processing a null message and null initial state: ...
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What's the difference between confusion/diffusion and mode of operation?

I understand the concepts of confusion (substitution) and diffusion (permutation). My understanding of what a mode is that it's an algorithm that lets us encrypt arbitrary message size. i.e. AES is ...
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Cryptographic Strength of MDS Matrix

Maximum Distance Separable (MDS) Matrices are used for providing diffusion in a cipher. How to test the strength (with respect to cryptographic properties) of an MDS matrix used in a cipher?
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Understanding the wide trail design strategy

I am trying to understand the wide trail design strategy. I have read the paper which describes it from the point of view of AES. From what I understand, it is a technique to increase diffusion in a ...
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How do we reduce the multiplications in the AES mix column layer using $x^4 +1$

I recently learned AES uses $x^4 +1$ to reduce the multiplications in the MixCol layer. However, I used $p(x) = x^8 + x^4 + x^3 + x + 1$ not knowing it was the wrong polynomial and got the correct ...
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How can I get the binary form of AES's MDS matrix in MixColumns tranformation?

I need to write a procedure for calculating the MixColumns's operation result in the following form: $M*X^T,$ where $M$ is a 128x128 binary matrix, $X$ is a 128-bit vector (the state). My question ...
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Confusion and Diffusion in the AES functions

I am pondering, how each of the four functions that a full AES round does consist of (Add Round Key, Substitute Bytes, Shift Rows and Mix Columns) add to the confusion and diffusion of the full AES. ...
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Why did they choose $x^4+1$ for the MixColumns step in Rijndael/AES?

In The Design of Rijndael page 39, It describe the design criteria for MixColumns step Dimensions. The transformation is a bricklayer transformation operatingon 4-byte columns. Linearity. The ...
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What is an advantage of MDS matrices in block ciphers?

I saw the several articles about MDS matrices. They said that, one goal of MDS matrices is to protect the block ciphers against linear and differential attacks. My question is: For example in the ...
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328 views

Prove the branch of number of Advanced Encryption Standard

In the Advanced Encryption Standard (AES) document: page 27 section 7.3.1, It defines branch number. It said " Let F be a linear transformation acting on byte vectors and let the byte weight ...
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Full diffusion or Partial diffusion between s-box applications?

In regards to maximizing active s-boxes: is it advantageous to apply the non-linear layer after complete diffusion of the state, rather after then partial diffusion? Using AES as an example, with ...
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What does this notation means $\mathbb{F}_{2^{-}}$?

I have seen various papers to use this notation $\mathbb{F}_{2^{-}}$ to describe the diffusion layer. As for example the permutation in AES (MixColumns). So, we have a field with order of 2, what does ...
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How 2 rounds in AES achieve full diffusion?

I have read somewhere that 2 rounds is AES provide full diffusion. So I looked it up to find out what it exactly meant. In The Design of Rijndael page 41, section 3.5 and it states that: Two ...
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Alternatives to sbox's for diffusion?

Are there any other alternatives to Sbox's or SP networks to provide diffusion preferably more basic alternatives which still provide a good degree of security?
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How does AES introduce confusion and diffusion?

I know that in AES the shift-rows and mix-columns operations introduce diffusion, but I don't understand how they create diffusion. Also, I know the add-round-key operation creates confusion, but I ...
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How were the diffusion statistics for norx calculated?

I was reading the norx specification and came across this section, which provides some kind of statistics about the diffusion of the norx round function. However, I don't see how these values were ...
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Does the One Time Pad rely on confusion or diffusion?

From what I could research, XORing a random key adds confusion. But I do not undertand the rationale for that classification. Shannon's confusion is supposed to obscure the relationship between the ...
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Encrypt-Mix-Encrypt: Full Diffusion?

I've read "A Parallelizable Enciphering Mode" by Halevi and Rogaway about the encrypt-mix-encrypt mode for ciphers and was asking myself if this mode provides "full" diffusion. So if an attacker ...
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Block cipher mode with diffusion on ciphertext

As I understand, diffusion property in AES-CBC ensures that one-bit change in plaintext will yield changes in all following blocks in ciphertext upon encryption. I'm looking for algorithm that will ...