**Homomorphic encryption**

For the Credits platform, complete homomorphic encryption is used. Complete homomorphic encryption (Fully homomorphic encryption schemes, FHE schemes) is an encryption type that allows all, and not just the key holder, to obtain the encrypted text of any desired function f (π1, ..., πt) for the encrypted text π1 ..., πt, as long as this function can be effectively calculated.

The NTRU scheme (N-th degree Truncated polynomial ring or Number theorists that are U) was chosen - it was designed by Adriana L Opes-Alt, Eran Tromero and Vinod Veikantanasan (LTV). The implementation of the platform uses C ++ and C # programming languages.

## Reasons for using:

The chosen scheme answers the following question:

Is it possible to effectively use the approaches described in other studies (i.e., ideal lattice and ring training with errors-RLWE) effectively, so that the advantages of both approaches can be achieved simultaneously?

Yes, the functional strength of the first (ideal lattice approach) and the simplicity and efficiency of the second (RLWE) allow effectiveness. The authors introduced a new technology switch called the "reliance". If used with switching modules, the circuit can facilitate noise increase and maintain a linear increase in comparison with the levels. It inherits the simplicity and efficiency of ideal gratings. In addition, this scheme has a message security depending on the key (KDM security, also known as circular security), which can safely encrypt the polynomial functions of its secret key. The authors clearly explain the significance of these features in the context of homomorphic encryption. They also showed how to convert the proposed scheme into a complete homomorphic encryption scheme, as follows from the Gentry project for writing and downloading. The proposed scheme also has an additive holomorphic key, and this property is used to protect it against key attacks (Applebaum et al., 2011).