Homomorphic AES-128 Implementation

Overview

This Rust program implements AES-128 encryption and decryption using Fully Homomorphic Encryption (FHE). It enables secure computations on encrypted data without the need for decryption, preserving privacy in sensitive operations.

The implementation is split into two main components:

1. Key Expansion

2. Encryption/Decryption

System design

System Requirements

Rust (nightly version specified in toolchain.txt)

The provided executable is specifically built for x86-64 GNU/Linux systems with the following specifications:

ELF 64-bit LSB pie executable, x86-64, version 1 (SYSV), dynamically linked,
interpreter /lib64/ld-linux-x86-64.so.2, for GNU/Linux 3.2.0,
BuildID[sha1]=b750ce9b0857a830c06429a55f6ce72a59b5647f, not stripped

To compile an executable as per your system specifications, run the following commands:

cargo build --release
./target/release/fhe-aes128 [OPTIONS]

Installation

Clone the repository and navigate to the project directory:

git clone <repo-url>
cd fhe-aes128

Build/test the project:

cargo build --release
cargo test

How to run the provided executable ?

Usage:

./fhe-aes128 [OPTIONS]

./fhe-aes128 [OPTIONS]

Options:
--number-of-outputs <N>     Specify the number of outputs (default: 1).
--iv <IV>                   Initialization vector for AES.
--key <KEY>                 128-bit AES key (32 hexadecimal characters).

From source

./target/release/fhe-aes128 --number-of-outputs <N> --iv <IV> --key <KEY>

Standard example:

cargo run --release -- -n 1 -k 000102030405060708090a0b0c0d0e0f -i 00112233445566778899aabbccddeeff

./target/release/fhe-aes128 --number-of-outputs 10 --iv 00112233445566778899AABBCCDDEEFF --key 000102030405060708090A0B0C0D0E0F

From executable

./fhe-aes128 --number-of-outputs <N> --iv <IV> --key <KEY>

./fhe-aes128 --number-of-outputs 10 --iv 00112233445566778899AABBCCDDEEFF --key 000102030405060708090A0B0C0D0E0F

How to use our FHE implementation ?

The implementation consists of 3 major modules:

1. Key-Expansion

This module implements AES key expansion using Fully Homomorphic Encryption (FHE), defining necessary constants like round constants (RCON) and using encrypted bytes (FheUint8) to securely perform the AES key expansion, applying operations such as cyclic shifting,S-Box substitution, and XOR with round constants while ensuring the privacy of the key throughout the process, and leveraging parallelism via the Rayon library to speed up S-Box substitutions.

To perform FHE AES128 key-expansion as a separate task, execute the following function with correct parameter types, and the expanded_key will store the required output.

pub fn key_expansion_fhe(key: &[FheUint8; 16], expanded_key: &mut [FheUint8; 176])

2. Encryption

This module implements key transformations in AES encryption using Fully Homomorphic Encryption (FHE), including operations like AddRoundKey (XOR), SubBytes (S-Box substitution), ShiftRows (row shifting), and MixColumns (Galois Field multiplication), with each transformation optimized for performance through parallelism using the Rayon library and FHE techniques.

To perform FHE AES128 encryption as a separate task, execute the following function with correct parameter types, and the output will store the required FHE-AES128 encrypted ciphertext.

fn aes_encrypt_block(
    input: &Vec<FheUint8>,
    output: &mut [FheUint8; 16],
    expanded_key: &[FheUint<FheUint8Id>; 176],
)

3. Decryption

This module implements the inverse transformations used in AES decryption utilizing Fully Homomorphic Encryption (FHE). It defines three key operations: inv_sub_bytes (inverse byte substitution using the inverse S-Box), inv_shift_rows (inverse row shifting to restore the original matrix configuration), and inv_mix_columns (inverse mixing of columns with Galois Field multiplication). These functions work in parallel using the Rayon library to optimize performance and leverage FHE to maintain data privacy during the decryption process.

To perform FHE AES128 encryption as a separate task, execute the following function with correct parameter types, and the output will store the required FHE-AES128 decrypted plaintext.

fn aes_decrypt_block(
    input: &Vec<FheUint8>,
    output: &mut [FheUint8; 16],
    expanded_key: &[FheUint<FheUint8Id>; 176],
)

Acknowledgments

• TFHE-rs library for enabling Fully Homomorphic Encryption.
• Rayon for parallelism.
• The AES cryptography research community for their invaluable work in secure encryption standards.