DOI: 10.14738/tmlai.54.3225 Publication Date: 15th August, 2017 URL: http://dx.doi.org/10.14738/tmlai.54.3225 VOLUME 5 NO 4, 2017 Computing on Encrypted Data into the Cloud though Fully Homomorphic Encryption Samiha Jlilab, Hassan Satori, Khalid Satori LIIAN, Department of Mathematics and Computer Science, FSDM, USMBA, Fez, Morocco Department of Mathematics and Computer Science, FPN, UMP Nador, Morocco samihajlilab00@gmail.com, hsatori@yahoo.com ABSTRACT Securing Data in the cloud based on Fully Homomorphic Encryption (FHE) is a new and potential form of security that allows computing on encrypted data without decrypted it first. However, a practical FHE solution is not available for implementation today. In this work, we propose a platform based on open source solutions to perform data computations (addition and multiplication) on encrypted form. In addition, taking account of efficiently and the security component, the most popular partially homomorphic encryption algorithms (RSA, Paillier and ElGamal) are studied to analyze the process times of encryption, decryption and computation of each algorithm. Furthermore, to compromise between performance and security, we need to study different key sizes and different data sizes as parameters. Keywords: Cloud Computing, ThirdParty;Data Privacy, Fully Homomorphic Encryption, Partially Homomorphic Encryption, RSA, ElGamal, Paillier, Gentry’s scheme. 1 Introduction Cloud computing holds enormous potentials (cost reduction, shared computingresources, elasticity, good performance, etc.). As a matter of fact, the cloud has few challenges like any other innovative technology. Data security is a key challenge when moving to the cloud[1]. In fact, when you move your data to the cloud, you are losing control. Cloud gives access to data, but you have no way to make sure that someone else does not have access to it as well. In addition, exposing your data in a public cloud environment shared with other companies may put your data at risk and may you lose the confidentiality of your sensitive data.The key solution is tostore and perform computations on ciphertext over a public area. This goal can be achieved using the homomorphic encryption proprieties[2]. Homomorphic encryption is the mathematical process of performing calculations on encrypted data which cannot be read or analyzed by anyone other than the client who retains the encryption and decryption keys. This kind of cryptography is an efficient solution to protect from internal and externals threats (curious cloud administrator, malicious cloud users, attackers). Recently, many researchers are interested in fully homomorphic encryption solutions to improve data privacy and eliminate trusted third parties i.e. performing computational operations on encrypted data without learning anything about it by a third party. Naveed Islam et al[3] have exploited the multiplicative