D-1 TFHE Scheme

The TFHE scheme is designed for homomorphic addition and multiplication on integers (especially bit-wise computation, like logic circuits). Unlike BFV, GBV, or CKKS, TFHE is characterized by fast noise bootstrapping; therefore, it is efficient for processing deep multiplication depths. TFHE’s noise bootstrapping technique can be further applied to functional encryption.

In TFHE, each plaintext is encrypted as an LWE ciphertext. Therefore, TFHE’s ciphertext-to-ciphertext addition, ciphertext-to-plaintext addition, and ciphertext-to-plaintext multiplication are implemented based on GLWE’s homomorphic addition and multiplication described in $\mathit{𝑃𝑎𝑟𝑡 𝐼𝐼𝐼}$, with $n=1$ to make GLWE an LWE.

This section will explain TFHE’s novel components: key switching, ciphertext-to-ciphertext multiplication, coefficient extraction, and noise bootstrapping.