On the Weakness of Fully Homomorphic Encryption
This is an incremental critique challenging the practical utility of FHE for general computing applications.
The paper argues that fully homomorphic encryption (FHE) is limited to modular arithmetic in finite fields or rings, making it ineffective for most common computations like arithmetic and relational expressions, and questions its overstated importance in client-server or cloud computing.
Fully homomorphic encryption (FHE) allows anyone to perform computations on encrypted data, despite not having the secret decryption key. Since the Gentry's work in 2009, the primitive has interested many researchers. In this paper, we stress that any computations performed on encrypted data are constrained to the encrypted domain (finite fields or rings). This restriction makes the primitive useless for most computations involving common arithmetic expressions and relational expressions. It is only applicable to the computations related to modular arithmetic. We want to reaffirm that cryptography uses modular arithmetic a lot in order to obscure and dissipate the redundancies in a plaintext message, not to perform any numerical calculations. We think it might be an overstated claim that FHE is of great importance to client-server computing or cloud computing.