Homomorphic encryption comes in various forms, each with different levels of homomorphic properties. The three main types of homomorphic encryption are:
- Partial Homomorphic Encryption (PHE): In PHE schemes, only one type of mathematical operation (either addition or multiplication) can be performed on encrypted data without decryption. For example, if an encryption scheme is additively homomorphic, you can perform additions on ciphertexts without decrypting them, but you cannot perform multiplicative operations. Similarly, if it’s multiplicatively homomorphic, you can perform multiplicative operations without decryption but not additions. PHE is limited in its ability to perform complex computations on encrypted data.
- Somewhat Homomorphic Encryption (SHE): SHE schemes are more versatile than PHE but less powerful than Fully Homomorphic Encryption (FHE). They allow a limited number of both addition and multiplication operations to be performed on encrypted data without decryption. These schemes strike a balance between efficiency and functionality and are suitable for many practical applications where complex computations aren’t required. Examples of SHE schemes include the RSA cryptosystem and the Paillier cryptosystem.
- Fully Homomorphic Encryption (FHE): FHE is the most powerful form of homomorphic encryption. It allows arbitrary computations (both addition and multiplication) to be performed on encrypted data without any knowledge of the plaintext. FHE is highly versatile but computationally intensive, making it less efficient than PHE and SHE. FHE has applications in scenarios where privacy and security are paramount, such as secure cloud computing and privacy-preserving data analysis.
The choice of which type of homomorphic encryption to use depends on the specific use case and the trade-off between computational efficiency and the level of privacy and security required. While PHE and SHE are more efficient, FHE provides the highest level of security and functionality at the cost of increased computational overhead. Researchers continue to work on optimizing and improving the efficiency of FHE schemes to make them more practical for real-world applications.