Several public-key encryption schemes used to solve the problem of ciphertext data processing on the fly are discussed.A new targeted fully homomorphic encryption scheme based on the discrete logarithm problem is presented.Public-key encryption cryptosystems are classified to examine homomorphic encryption.Without employing techniques proposed by Gentry such as somewhat homomorphic and bootstrapping techniques,or relinearization technique proposed by Brakerski et al.,a new method called“Double Decryption Algorithm”is employed in our cryptography to satisfy a fully or targeted fully homomorphic property.Inspired by ElGamal and BGN cryptography,we obtain the desired fully homomorphic property by selecting a new group and adding an extra component to the ciphertext.Proof of semantic security is also demonstrated. Several public-key encryption schemes used to solve the problem of ciphertext data processing on the fly are discussed. A new targeted fully homomorphic encryption scheme based on the discrete logarithm problem is presented. Public-key encryption cryptosystems are classified to examine homomorphic encryption. Without Applied methods proposed by Gentry such as somewhat homomorphic and bootstrapping techniques, or relinearization technique proposed by Brakerski et al., a new method called “Double Decryption Algorithm ” is employed in our cryptography to satisfy a fully or targeted fully homomorphic property. Inspired by ElGamal and BGN cryptography, we obtain the desired fully homomorphic property by selecting a new group and adding an extra component to the ciphertext. Proof of semantic security is also demonstrated.