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In this paper we will propose hybrid homomorphic system that will be applied to the banking data to perform operations on encrypted data without decrypting, based on the encrypting, the decryption and the operation treatment time on the ciphertext which were obtained by simulating an addition and multiplication homomorphic cryptosystem and comparing it with DGHV that is somewhat homomorphic; then we will choose our model which is most suitable for banking application.

The use of Cloud Computing in the mobile networks offer more advantages and possibilities to the mobile users such as storing, downloading and making calculation on data on demand and its offer more resources to these users such as the storage resources and calculation power. So, Mobile Cloud Computing allows users to fully utilize mobile technologies to store, to download, share and retrieve their personal data anywhere and anytime. As many recent researches show, the main problem of fully expansion and use of mobile cloud computing is security, and it's because the increasing flows and data circulation through internet that many security problems emerged and sparked the interest of the attackers. To face all this security problems, we propose in this paper an authentication and confidentiality scheme based on homomorphic encryption, and also a recovery mechanism to secure access for mobile users to the remote multi cloud servers. We also provide an implementation of our framework to demonstrate its robustness and efficiently, and a security analysis.

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