Fully homomorphic encryption scheme on a nonCommutative ring R

This article is an introduction to a well known problem on the ring $\mathbb{F}_{q}[e]$ where $\pmb{e}^{3}=\pmb{e}^{2}$: Fully homomorphic encryption scheme. In this paper, we introduce a new diagram of encryption based on the conjugate problem on $\mathrm{F}_{q}[\pmb{e}],(\mathbf{ESR}(\mathbb{F}_{q}[\pmb{e}]))$ · This diagram is generally impossible to decipher because it rests on a new problem very difficult to solve called problem of conjugate on a noncommutative reference; $\mathbb{F}_{q}[\pmb{e}]$. This encryption scheme is based on two difficult methodes; discrete logarithm problem and conjugal classical problem.