PUBLIC KEY FULLY HOMOMORPHIC ENCRYPTION

Abstract

The meaning of cloud computing is the Information Technology (IT) model for computing, which is consist of all the IT components (software, hardware, services and, networking ) that are needed to enable delivery and development of cloud services through the private network or the internet. In the cloud computing the client put his data on the cloud, and any computations on his stored data will be implemented in the cloud. Intentionally the cloud service provider can access, change or even delete the stored data of the client. To produce the effective services, some of the cloud service providers share the information with third parties. The third party can access to the client private data and modifies on this data to make it beneficial to him. Moreover, providers, untrusted servers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. For these reasons, the security has become the most important thing in cloud computing. The mechanism that protects the privacy of sensitive information is called the encryption. To protect the data that it’s stored on the cloud we must use an encryption system that can perform computations on the encrypted data. The scheme that allows to executing several computations on the encrypted message without decrypting this message is called homomorphic encryption. This paper provides encryption scheme (PKFHE) that can applied it on a cloud computing .The proposed scheme is based on Euler’s theorem, which proved both addition and multiplication operations at the same time on ciphertext without decryption. we compute the time complexity of the encryption and decryption function for the Elgamal, RSA cryptosystems and our proposed PKFHE scheme which, the order of encryption function of all the schemes is O ((log (n))3) and the order of decryption function of Elgamal, RSA cryptosystems is O (log (n)3), while the order of decryption function of PKFHE scheme is O (log (n)2) that mean the proposed PKFHE scheme is faster in the time complexity. Also compared the execution time among the three schemes with five sizes of the messages and used five lengths of a secret key, where we concluded that the execution time of the proposed scheme was slower than the execution time of Elgamal, RSA cryptosystems except in the case of the key 128-bit which, the execution time of RSA was slower than the two others. Also we noticed that the length of the private key was effect on the execution time of the algorithms in which the execution time increased when the length of the private key was increase and finally the security of the schemes is analyzed. The proposed scheme showed a good security for the stored data on the cloud