The major application of FHE is cloud computing.

By this way, user can store his/her data in encrypted form in public cloud without letting know the real data. Cloud is having more storage and computing capabilities then user’s system. So the computation can be done in cloud with the help of FHE without the knowledge of secret key to the cloud administrator. More precisely, FHE is having the following property whenever f is a function composed of addition and multiplication operation in the ring:

            Decrypt (f (c₁,……..,c_t)) = f {m₁,………, m_t }                                                                   

On the off chance that the cloud (or an adversary) can proficiently compute f(c₁,……, c_t) from ciphertexts c₁,……,c_t , without realizing any data about the relating plaintexts m₁,…..,m_t , then the framework is proficient and secure. An another prerequisite for FHE is that the ciphertext sizes stay remain bounded, independent of the function f ; this is known as the “compact ciphertexts” prerequisite.