Fully Homomorphic Encryption (FHE)

Fully Homomorphic Encryption (FHE) is a powerful cryptographic technique that enables computation on encrypted data without ever needing to decrypt it. This means that FHE allows data to be processed in a secure, encrypted form, ensuring the confidentiality of the data even while it is being actively used or manipulated.

The concept of FHE was first introduced by Rivest, Adleman, and Dertouzos in 1978, but it wasn't until 2009 that the first practical scheme was developed by Craig Gentry. FHE has the potential to revolutionize data privacy and security in various fields, including cloud computing, finance, healthcare, and beyond. With FHE, sensitive data can be analyzed, aggregated, or processed by third parties without exposing the underlying data, thus preserving privacy and security.

Fully Homomorphic Encryption (FHE) offers a powerful way to conduct neural network inference while preserving the privacy of sensitive data. Consider a scenario where N represents a pre-trained neural network, A is a dataset, and (E, D) denotes an asymmetric FHE scheme. The objective is to perform inference on a record a from A without disclosing its sensitive contents to the neural network.

Encryption and Setup: The process begins with the data owner encrypting the record a using the encryption function E and a public key, resulting in the encrypted record a' = E(public_key, a).

Neural Network Processing: The encrypted record a', along with the public key, is sent to the neural network N. It is crucial that N is equipped to handle the FHE scheme, understanding its parameters to accurately perform homomorphic operations on a'. Due to the homomorphic properties of E, any arithmetic operation that N needs to perform can be safely applied to a'.

Handling Non-linearities: A significant challenge in this setup is managing non-linear activation functions commonly used in neural networks, such as sigmoid or ReLU. These functions, which involve non-arithmetic operations, must be approximated by low-degree polynomials. This approximation enables the computation of activation functions directly on the encrypted data a' using homomorphic operations.

Inference and Decryption: After processing through the necessary homomorphic operations and activation approximations, N produces an encrypted inference result. This result, still encrypted, is transmitted back to the data owner.

Result Interpretation: The data owner then uses the private key of the FHE scheme to decrypt the inference outcome with D, yielding the decrypted result that can be interpreted and utilized accordingly.