Evaluating AND gates over encrypted data in cloud computing

Encrypting data before storing it in a remote cloud server is highly recommended, but when using traditional symmetric algorithms as AES, 3DES… we lose the ability of manipulating freely our data in the cloud. For example, if we request the cloud computing to do a huge treatment over our encrypted big data it should decrypt it at first, which means revealing the private encryption key to an untrusted part and that constitute a security problem. Processing encrypted data in cloud computing is an efficient solution. Homomorphic encryption schemes are powerful tools that allow performing computations over ciphertexts without any prior decryption. We propose a new efficient homomorphic encryption scheme based on Lucas theorem. Our cryptosystem allows performing several AND gates over encrypted cloud data. The cost of one AND of two ciphertexts is equivalent to the cost of addition on numbers. The proposed scheme uses the {0,1} as cleartext space and one key for encryption and decryption, i.e it is a symmetric encryption scheme.