Generalized Rijndael, an approach

Following the idea of the first post about a Generalized Rijndael, I have started an implementation with some constants of the standard implementations becomes variables.

An schematic for the Rijndael would be:

This operations uses a state matrix, it's the data structure who receives the transformations during the (de)cipher process. This state matrix, in the AES, contains words of 8 bits in a 4x4.

First of all the input (of 128 bits) is cut in this basic words of 8 bits:

There are two ways to modify the size of the input: change the size of the matrix or change the size of the word. Following the article Small Scale Variants of the AES, the two options to reduce the input size from 128 to 32 bits under a Rijndael model:

• Reduce the state matrix to 2x2 (in the AES is 4x4)
• Reduce the word size to 2 bits (in the AES is 8 bits)

But, what's the best way? And there is another question, how big would be the key?

In the AES there are 3 options: 128, 192, 256 bits:

This matrix will be the input of a keyExpansion() function to have the segments of this key to be used in each part of the rounds. 

Why this sizes? Like many of the times, the choice of this 3 sizes corresponds to standardisation reasons like set a small but enough number of them to choose. The original Rijndael supports much more options: you can set a key of 512 bits and structure it into 16 columns in the key matrix. Even 1024 bits key, with 32 columns, the key expanded will still be 44 elements if the number of rows and the number of rounds are still the same.

Furthermore, with a 128 bits block of plain text and key (matrix 4x4 and word size 8) there would be 40 rounds instead of 10. In this case the key expansion will have 164 elements instead of the 44 of the standard. (the number of elements in the key expansion is #columns*#rounds) 

But how to define this parameters in the good direction? Can be the number of rounds be less with in a safety way? Or can some day be necessary to increase this number?

The Rijndael have a good performance over 32 bit hardware. The word size of 8 bits together with the 4 rows who gives 32 bit operation in the ring: . But in deep, the most powerfull feature of the Rijndael from the computation point of view is that it works in the very basic and that means binary.

I hope I'll write soon answering this questions.