# What is TFHE-rs?

TFHE-rs is a pure Rust implementation of Fully Homomorphic Encryption over the Torus (TFHE) to perform Boolean and integer arithmetic on encrypted data.

TFHE-rs implements advanced TFHE features, empowering developers and researchers with fine-grained control over TFHE so that they can focus on high-level functionality without delving into low-level implementation.

TFHE-rs includes:

• Rust API: the primary API for working with TFHE-rs in Rust projects.

• C API: for developers who prefer to use C.

• Client-side WASM API: to integrate TFHE-rs functionalities into WebAssembly applications.

## Key cryptographic concepts

TFHE is a Fully Homomorphic Encryption (FHE) scheme based on Learning With Errors (LWE), which is a secure cryptographic primitive against even quantum computers. The TFHE-rs library implements Zama’s variant of TFHE.

#### Homomorphic Encryption Basics

The basic elements of cryptography:

• Message (or Cleartext): raw values before encryption.

• Plaintext: encoded messages.

• Ciphertext: encrypted messages.

FHE allows to compute on ciphertexts without revealing the content of the messages. A scheme is fully homomorphic if it supports at least two of the following operations when evaluating any programs. ($x$ is a plaintext and $E[x]$ is the corresponding ciphertext):

• Homomorphic univariate function evaluation: $f(E[x]) = E[f(x)]$

• Homomorphic addition: $E[x] + E[y] = E[x + y]$

• Homomorphic multiplication: $E[x] * E[y] = E[x * y]$

## Zama's variant of TFHE

Zama's variant of TFHE is a fully homomorphic scheme that takes fixed-precision numbers as messages. It implements all homomorphic operations needed, such as addition and function evaluation via Programmable Bootstrapping.

Refer to the the preliminary whitepaper for more details.

Using TFHE-rs in Rust includes the following steps:

1. Key generation: generate a pair of keys using secure parameters.

• Client key: used for encryption and decryption of data. This key must be kept secret.

• Server key (or Evaluation key): used for performing operations on encrypted data. This key could be public.

2. Encryption: encrypt plaintexts using the client key to produce ciphertexts.

3. Homomorphic operation: perform operations on ciphertexts using the server key.

4. Decryption: decrypt the resulting ciphertexts back to plaintexts using the client key.

To understand more about FHE applications, see the 6-minute introduction to homomorphic encryption.

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