U.S. flag   An official website of the United States government
Dot gov

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Https

Secure .gov websites use HTTPS
A lock (Dot gov) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Presentation

Linear Homomorphic Encryption from Class Groups of Quadratic Fields

June 16, 2021

Presenters

Guilhem Castagnos - University of Bordeaux

Description

Joint work with Fabien Laguillaumie.

Abstract: More than 30 years ago, Buchmann and Williams proposed using ideal class groups of imaginary quadratic fields in cryptography with a Diffie-Hellman style key exchange protocol. After several twists, there has been in recent years a new interest in this area. This rebirth is mainly due to two features. First, class groups of imaginary quadratic fields allow the design of cryptographic protocols that do not require a trusted setup. This particularity has been used for example to build cryptographic accumulators and verifiable delay functions. Secondly, using these groups, we proposed with Fabien Laguillaumie in 2015 a versatile encryption scheme, linearly homomorphic modulo a prime that has found many applications, for instance in secure two-party computation. In this talk, I will give an overview of cryptography based on class groups of imaginary quadratic fields,  present our encryption scheme and discuss applications.

Related paper: ia.cr/2015/047

Presented at

Presentation via Webex video conference

Related Topics

Security and Privacy: digital signatures, encryption

Created June 16, 2021