# Definition of diffusion matrix

I've been studying this article and since I'm not studying cryptography in English and it is not my native language, I don't understand some of the terminology. More precisely: what are diffusion matrices as mentioned on page 3 right at the beginning of chapter 2? Do they have something to do with diffusion defined in Shannon's theory?

Yes, it is related. Claude Shannon in his famous article A Mathematical Theory of Cryptography defines the Confusion and Diffusion. Wikipedia's Confusion and diffusion page defines diffusion as;

Diffusion means that if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then approximately one half of the plaintext bits should change. Since a bit can have only two states, when they are all re-evaluated and changed from one seemingly random position to another, half of the bits will have changed state.

A diffusion matrix transforms columns and it similar to the MixColumns operation of AES. It is optionally followed by a ShiftRows (like in AES) to provide further mixing where ShiftRows permutes the rows*.

If there is no diffusion matrix applied to AES ( or similar SPN based block cipher, and also no ShiftRows), then only a single bit change in the input will only affect the corresponding byte. Therefore, diffusion is necessary but not sufficient.