Class Groups

A library for working with binary quadratic forms as corresponding to elements of a class group.

Purpose

This library was specifically written to be used with respect to the CL15 framework. It has a strong focus on correctness however, clearly documenting what operations are supported within which contexts, and is usable for working with primitive positive definite binary quadratic forms of negative odd discriminant in general.

Design Goals

This library is intended to be up to the standards required for deployment in a production environment. Functions are documented with their technical specification, allowing clear review and the development of alternative implementations which remain compatible. This library is part of an ongoing effort to submit a standard for the representation of and operations with binary quadratic forms. This includes a complete wire specification for the encoding of (un)compressed binary forms and a specification for sampling binary quadratic forms from the class group.

The included [CryptoBigintElement] is a constant-time backend which is intended to stand up to intense scrutiny (with extensive documentation on each intermediary term to prove their correct calculation within the declared bounds) and also be eligible for use with sensitive data such as private keys (which would be at risk of being leaked via timing analysis if used with a variable-time representation of group elements). The library is modular to the backend however.

This library supports no-std and even no-alloc, allowing deployment in constrained environments with statically-defined (bounded) memory.

Status

This library is actively being worked on to evolve from a research proof of concept to such standards, though much progress has been made. It is not yet ready for production use and has not received any external review at this time.