Can hybrid Homomorphic Encryption schemes be practical?

The ability to perform computations on ciphertexts without knowing any information about the plaintexts makes homomorphic encryption technique useful in a wide variety of confidentiality preserving protocols (e.g., e-voting, e-health, etc.). Unfortunately, the traditional encyption schemes support a limited number of homomorphic operations (usually addition or multiplication). Indeed, in 2009, Gentry proposed a fully homomorphic encryption scheme which supports both multiplicative and additive homomorphic operations. Since then, several fully homomorphic encryption schemes have been proposed. However, the fully homomorphic encryption schemes are still undergoing experimentation and improvement. The hybridization of homomorphic encryption schemes seems to be an effective way to overcome their limitations and to benefit from their resistance against the confidentiality attacks. In this paper, we will study the possibility to hybridize the homomorphic encryption schemes so as to support all homomorphic properties.