TFHE Deep Dive - Part II - Encodings and linear leveled operations

This second blog post of the series shows you how to perform operations on the ciphertexts used in TFHE.

In the previous blog post of the series, we have described the ciphertexts used in TFHE. In this post we will start discovering how to perform operations on these ciphertexts. In particular, we will describe two simple homomorphic operations: homomorphic addition and multiplication by unencrypted constants.

We will mainly focus on GLWE ciphertexts: since GLev and GGSW are composed by GLWE ciphertexts themselves, it will be easier in the end to see how the same operations are performed on them.

Note that most of the homomorphic operations have an impact on the noise. In this series of blog posts we will give intuitions on this noise growth  -- both in the text and in the figures (with little thermometers) -- but we will not enter into the details of noise analysis: for more information about the subject, we refer you to the TFHE and [CLOT21] papers.

We will also try to understand a little bit more about how messages are encoded and what the consequences are of this encoding on the result of homomorphic operations. Encodings are, in fact, an overlayer of the encryption and are extremely useful in FHE.

(…) Continue reading on Zama’s blog here.