Fully Homomorphic Encryption and Post-Quantum Cryptography

Post-Quantum Cryptography (PQC) has garnered significant attention due to concerns about quantum computers potentially breaking existing cryptographic systems like RSA and ECC, which are crucial for modern security. To address this, the National Institute for Standards and Technology (NIST) has embarked on creating new algorithms resistant to quantum decryption, selecting Kyber for encryption and Dilithium, Falcon, and SPHINCS+ for signatures as part of their formal standardization process in July 2022. These selections predominantly involve lattice-based cryptography, which is believed to withstand quantum computing challenges due to its reliance on complex mathematical problems unsolvable by quantum algorithms like Shor's. Lattice problems involve finding short vectors to generate a lattice, which becomes increasingly difficult with higher dimensions, providing a robust foundation for cryptographic standards. This advancement also benefits homomorphic encryption schemes, such as the TFHE scheme by Zama, which utilize lattice-based cryptography and the Lattice Estimator tool, showcasing a collaborative effort to ensure secure cryptographic solutions in a post-quantum world.