Design of Fully Homomorphic Encryption by Prime Modular Operation

Abstract

The meaning of cloud computing is the Information Technology (IT) model for computing, which consists of all the IT components (software, hardware, services and, networking) that are needed to enable the delivery and development of cloud services through a private network or the internet. In cloud computing, the client (user) puts his data in the cloud, and any computations on his stored data will be implemented in the cloud. Security is the main thing in cloud computing because a service provider can access, intentionally change or even delete the stored data. To protect data that is stored in the cloud, it is necessary to use an encryption system that can perform computations on the encrypted data. The scheme that allows executing several computations on the encrypted message without decrypting the message is called homomorphic encryption. The implementation of fully homomorphic encryption over the integer (DGHV scheme) and a Simple Fully Homomorphic Encryption Scheme Available in Cloud Computing (SDC Scheme), are slow in execution time because all of them convert the message to a binary format and then encrypt it. Therefore, we propose another scheme called Fully Homomorphic encryption based on a prime modular operation, this scheme encrypts the message character by character by using a prime secret key without converting that character into a binary format. As a result, we compute the time complexity and compare the execution time among the three schemes and analyse the security of the three schemes