Main Page

This community wiki is curated by members of the Research and Development group at certSIGN. We hope that it will grow with time, as various topics concerning homomorphic encryption are discussed in our research seminars. Our primary goal is create a portal with useful theoretical for the researchers in our group. Additionally, any new members of our group or students that are interested in these topics can get up to speed with the activity of our group.

Theoretical aspects

As anticipated in the title, the constantly updating content in the pages listed below has an emphasis on the theoretical part of various encryption schemes. We tried to include intuitive explanations for some of the technical FHE constructions.

Homomorphic encryption Defining and describing homomorphic encryption.

FHE Theory and examples

FHE over the Integers. A presentation of the scheme proposed by Dijk, Gentry, Halevi, Vaikuntanathan

Efficient FHE from (Standard) LWE. A presentation of the scheme BV11. The concept of ``key switching" is first introduced there.

BGV. A presentation of the scheme and of the HElib library.

Fully Homomorphic Encryption without Modulus Switching Presentation of the scheme proposed by Brakerski. The BFV scheme is build on ideas presented here.

BFV. A presentation of the scheme and of the SEAL library.

GSW. Homomorphic Encryption from LWE - a presentation of the scheme proposed by Gentry, Sahai and Waters in 2013.

GSW - Bootstrapping. Ideas from the paper "Faster Bootstrapping with Polynomial Error" by Alperin-Sheriff and Peikert. A different version of GSW with tighter error bounds

certSGN Presentation of our symmetric, bounded FHE scheme

FHE Patent Image Morphology @TODO Articol: Operatii morfologice aplicate pe imagini criptate

certBridge @TODO: Description of the bridge.

Some FHE libraries

Libraries implement the underlying cryptographic operations of a FHE scheme. These usually provide key generation, encryption, decryption, homomorphic addition and multiplication interfaces. The libraries listed below include dozens of additional functionalitites for ciphertext maintenance and manipulation.

HELib - GitHub page https://github.com/homenc/HElib

SEAL - GitHub page https://github.com/microsoft/SEAL

HEAAN - GitHub page https://github.com/snucrypto/HEAAN

Concrete - GitHub page https://github.com/zama-ai/concrete

certFHE - GitHub page https://github.com/certfhe

It is important to understand that while these libraries ease the process of writing FHE-based applications, this writing process requires significant knowledge and understanding of the underlying scheme, as the libraries are relatively low-level.