Résumé : At Eurocrypt 2010 van Dijk et al described a fully-homomorphic encryption scheme over the integers. The main appeal of the scheme (compared to Gentry's) was its conceptual simplicity; however with a public key size k^10 for security parameter k the scheme looked completely unpractical. In this talk we show how to reduce the public key size down to k^5, and we describe a practical implementation of the scheme. Interestingly we obtain significantly better efficiency than the recent Gentry-Halevi implementation of Gentry's scheme, despite using very modest hardware. At the ``high'' security level, equivalent to the ``large'' setting of Gentry-Halevi, we obtain encryption in about 3 minutes and a bootstrapping operation in about 5 minutes, while key generation and decryption take negligible time. Public-key size is also moderate: 250 MB at the ``high'' level (almost 10 times smaller than Gentry-Halevi). This shows that practical fully homomorphic encryption can be obtained with a very simple scheme.