CertSGN

We will briefly describe here the contributions of the article, in which members of the certSign research group introduced a new method for producing the following:

• Starting with an encryption scheme which is homomorphic with respect to one operation (such as multiplication), the recipe of the authors produces another encryption scheme which is now homomorphic with respect to two operations (for example, addition and multiplication).

The authors use this technique to construct examples of encryption schemes that, theoretically can handle any algebraic function on encrypted data.

The homomorphic encryption scheme CSGN, a symmetric homomorphic encryption scheme with plaintext $\mathbb {F} _{2}$ (the field with two elements) was introduced in the same article. The latter plays an essential role the architecture of a privacy-preserving contact tracing application, developed by certSign as part of the TAMEC project.

The content of the article is protected under the law by two patents.

Ring homomorphic encryption schemes from monoidal ones. The blueprint

Given a monoid $M$ and any commutative ring $R$ with unity, one can associate to these an algebra $R[M]$. As an $R$-module, the monoid algebra $R[M]$ is free with a basis consisting of the symbols $[x]$, where $x\in M$.