Introducing the MB09 algorithm

First, we will start with some considerations regarding the algorithm and reintroduce Fermat's Last Theorem. The first time I presented MB09, it was as an encryption algorithm, but effectively it is much more a protocol for digital payments. As I have already mentioned, while blockchain and cryptocurrency were not yet well known, I developed MB09 as an encryption/decryption algorithm to exchange a message between two actors. Many years later, I worked on the algorithm, taking it as the basis for a fully homomorphic encryption system and creating MB23, which was a fully homomorphic algorithm. Eventually, in 2020, it was turned into a new version, called MBXX, to overcome the consensus problem proposed by Satoshi Nakamoto.

Let's examine how the first version of MB09 worked. To do that, we'll recall Fermat's Last Theorem:

a^n + b^n = z^n 

Here, the (n) exponents represent all the sets of positive integers.

This equation,...