## Overview **Homomorphic Encryption** is a form of encryption that allows computations to be carried out on ciphertexts, producing an encrypted result. When decrypted, the result matches the result of the operations as if they were performed on the plaintext. ## Key Features - **Privacy-Preserving Computations**: Enables operations on encrypted data without needing to decrypt it first, preserving privacy in cloud computing, secure voting systems, and more. - **Types of Homomorphism**: - **[[Partially Homomorphic Encryption]] (PHE)**: Supports either addition or multiplication, but not both. - **[[Somewhat Homomorphic Encryption]] (SHE)**: Supports both operations but with limitations. - **[[Fully Homomorphic Encryption (FHE)]] ([[Fully Homomorphic Encryption (FHE)|FHE]])**: Supports unlimited additions and multiplications. - **Noise**: As computations occur, noise is added to the encrypted data, which can eventually make decryption impossible. Modern schemes manage and control this noise. ## Applications - **Secure Data Analysis**: Data can remain encrypted while being analyzed or processed in the cloud. - **Privacy-Preserving Medical Research**: Enables researchers to operate on encrypted medical data without exposing sensitive patient information. - **Secure Voting Systems**: Allows for votes to be encrypted but still counted without revealing individual votes. ## Challenges - **Performance Overhead**: Homomorphic encryption introduces computational overhead, making it slower than traditional operations. - **Complexity**: Implementing and managing noise in these systems can be complex. - **Interoperability**: Integrating with existing systems and databases can be challenging due to its unique computational requirements. ## Related Concepts - **[[Asymmetric Encryption]]**: The foundation on which homomorphic encryption is built. - **[[Symmetric Cryptography|Symmetric encryption]]**: Another encryption paradigm, not suitable for operations on encrypted data. - **[[Zero-Knowledge Proofs]]**: A cryptographic method where one party can prove to another party that they know a value without conveying any information apart from the fact they know the value.