multi-message encryption strategy #2: vector coefficients for polynomials

[AngryMaciek]

Initial check.

• I added a very descriptive title above.
• I searched the documentation and found no similar feature.
• 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;
coefficients of ring polynomials will be vectors with modular vector product between them;

hypercomplex coefficients will be matrices instead of ring polynomials;

$H = [ P_1e_1, ..., P_ie_i ]$

$P_i = a_0x^0 + ... a_kx^k$

(!) $a_X = [\alpha, \beta, \gamma, ...]$

(!) $M = [M_1,...,M_{...}]$

Each message component $i$ corresponds to $i$-th element in the vector.

Please specify what would you like to add/change.

Refactor current code to include vector coefficients instead of scalars.
Should this be default? Maybe for calculations speed reasons not? Operations on scalars will be faster then on vectors.
Or maybe this should be default with specialisation for case of vectors size == 1?

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 $(F,G,\Phi)$?
• How does this complexity influence $p$ and $q$?
• Most importantly, will the cryptographic scheme even work? encryption/decryption possible?

Code of Conduct

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

[github-actions]

Hey @AngryMaciek,

Thanks for taking interest in the project and the effort to help us improve it 👍
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!