Following Gentry’s breakthrough work , there is currently great interest on fully-homomorphic encryption (FHE), which allows to compute arbitrary functions on encrypted data. Though the area has seen much progress recently (such as [10,11,5,2,1,8,6]), it is still unknown if fully-homomorphic encryption will ever become truly practical one day, or if it will remain a theoretical curiosity. In order to find out, several FHE numerical challenges have been proposed by Gentry and Halevi , and by Coron
, which provide concrete parameters whose efficiency and security can be studied. We report on recent attempts [3,4] at breaking FHE challenges, and we discuss the difficulties of assessing precisely the security level of FHE challenges, based on the state-of-the-art. It turns out that security estimates were either missing or too optimistic.