Towards a fully homomorphic symmetric cipher scheme resistant to plain-text/cipher-text attacks

Users’ privacy becomes nowadays an important need and a big challenge for a lot of enterprises and service providers especially after adopting the cloud migration strategy. Thus, Homomorphic Encryption (HE) came as a novel cryptographic approach that enables users’ privacy at the cloud side by allowing computation over encrypted data. Existing HE schemes are based on either symmetric or asymmetric encryption algorithms. While asymmetric HE schemes provide the high and the required level of security, they suffer from high computational complexity and high storage overhead making a big majority of them not practical for real world applications. On the other hand, symmetric schemes assure the required efficiency, but they are vulnerable to attacks and especially the known plain-text/cipher-text attacks making their usage limited in practical implementation. The main objective of this paper is to design a new symmetric HE variant that provides the desired level of efficiency in implementation and the immunity against data breaches especially the known plain-text/cipher-text attacks. The proposed scheme, named Homomorphic Hybrid Symmetric Encryption Scheme (HHSES), which is based on combining the homomorphic behavior of two well-known symmetric encryption schemes that are the MORE (Matrix Operation for Randomization and Encryption) approach and the Domingo Ferrer (DF) scheme. The performance analysis of HHSES confirms its efficiency for real-world applications in comparison with a big variety of existing and well known symmetric and asymmetric schemes. A main drawback of HHSES is the cipher-text dimension expansion after the homomorphic multiplication since homomorphic operations are restricted to polynomial operations over the matrices. Therefore, to fix this issue, we propose a specific Key Switching (KS) technique after the homomorphic multiplication that reduces the cipher-texts’ dimension without altering its homomorphic behavior and the primitive classified data. Security analysis of the new scheme also verifies its immunity against different types of attacks and especially the known plain-text/cipher-text attacks. Another important contribution in this work is the optimization of the HHSES encryption and decryption procedures by making them parallelized using the Chinese Remainder Theorem (CRT). The implementation results have shown that the proposed optimization technique reduces the execution time of the HHSE encryption and decryption algorithms with a