multi-message encryption strategy #1: matrix specialisation for _Hypercomplex_

[AngryMaciek]

Initial check.

• [X] I added a very descriptive title above.
• [X] I searched the documentation and found no similar feature.
• [X] I searched through the issues in this repository to find a similar request, but didn't find any.

Describe briefly the idea behind the improvement.

Provide a method to encrypt multiple messages at once;
successful decryption possible only when all encrypted messages are available;
hypercomplex coefficients will be matrices instead of ring polynomials;

$H = [ [\circ]e_1, ..., [\circ]e_i ]$

$M = [M_1,...,M_i]$

Please specify what would you like to add/change.

We would need another class specialisation for Hypercomplex: Hypercomplex<Matrix<n>, dim>

n - matrix size, for the matrix multiplication to work we will need square matrices here!

Please add other solutions if you considered them.

No response

Feel free to provide additional information or more context for your idea.

• encrypting $k$ messages: would it require $k$ sets of $(F,G,\Phi)$?
• each message is a square matrix then; alternatively we have one message composed of $k$ squared matrices
• How does these other parameters influence $p$ and $q$?
• Find and use a standard container for matrices in Cpp
• There will be no polynomials, therefore no convolution multiplication(!)
• Speed comparison vs. standard approach - much faster? much slower? comparable?
• Most importantly, will the cryptographic scheme even work? encryption/decryption possible?

Code of Conduct

• [X] I agree to follow this project's Code of Conduct

[github-actions[bot]]

Hey @AngryMaciek,

Thanks for taking interest in the project and the effort to help us improve it :+1:
Project lead will probably come around and assign proper labels shortly...

Actually... maybe you would like to work on this issue yourself?
You may start with reading our contributing instructions.

Your help is much appreciated!