Analysis of homomorphic encryption and its implications

Analyzing the partial homomorphic scheme proposed for RSA in the preceding section, we can see an interesting correspondence between the operations on cryptograms (data expressed in clear) and messages (data in blind).

This correspondence is just what we call homomorphism.

Now, the problem is that RSA, just like most of the algorithms explored until now, is partially homomorphic and can only represent some mathematical operations, such as multiplication or addition. The real difficulty is finding an efficient algorithm that represents all the mathematical and Boolean operations together.

Another simple example (case study) of how a form of homomorphism can be represented is performed by addition.

Let's take [A] and [B], two secret values that give [C] as their sum:

A + B ≡ C (mod Z)

Now, let's take two encrypted value correspondents respective to A and B.

For example, the encrypted values...