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Linear Homomorphic Encryption from Class Groups of Quadratic Fields

June 16, 2021


Guilhem Castagnos - University of Bordeaux


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:

Presented at

Presentation via Webex video conference

Parent Project

See: Crypto Reading Club

Related Topics

Security and Privacy: digital signatures, encryption

Created June 16, 2021, Updated June 17, 2021