Homomorphic encryption allows to make specific operations on private data which stays encrypted. While applications such as cloud computing require to have a practical solution, the encryption scheme must be secure. In this article, we detail and analyze in-depth the homomorphic encryption scheme proposed by Zhou and Wornell in~\cite{zhou}. From the analysis of the encryption scheme, we are able to mount three attacks. The first attack enables to recover a secret plaintext message broadcasted to multiple users. The second attack performs a chosen ciphertext key recovery attack and it was implemented and verified. The last attack is a related chosen plaintext decryption attack.