Homomorphic Encryption

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Homomorphic encryption is a specialized form that allows computations on encrypted data without requiring decryption. The computation result is also encrypted and can be decrypted to reveal the correct output. This enables secure data analysis and manipulation in encrypted form, protecting the data from unauthorized access even during computation.

Types of Homomorphic Encryption

Partially Homomorphic Encryption (PHE). Allows addition or multiplication operations, but not both, to be performed on encrypted data. RSA encryption, for example, is multiplicatively homomorphic.
Somewhat Homomorphic Encryption (SHE). Allows both addition and multiplication, but only to a limited extent, due to issues like noise growth, which limits the number of operations that can be performed.
Fully Homomorphic Encryption (FHE). Allows both addition and multiplication on encrypted data an unlimited number of times. FHE is the most flexible but also the most computationally intensive.

How It Works

Alice encrypts a number $x$ into $\text{Enc}(x)$ and another number into .

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Secure Multi-Party Computation Vertical Federated Learning honest-but-curious Indirect Information Leakage Qiang Yang et al. Federated Machine Learning Concept and Applications Tian Li et al. Federated Learning Challenges, Methods, and Future Directions

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