Deep Dive: CL Cryptosystem & Class Groups References

This document contains a curated list of references used for the Deep Dive into the Castagnos-Laguillaumie (CL) cryptosystem, Class Groups of Imaginary Quadratic Fields, and related cryptographic concepts.

Primary References (Used in Deep Dive)

These resources were directly used to construct the core analysis of the CL cryptosystem and its underlying mathematical structures.

• Group Theory Fundamentals

  • Introduction to Group Theory (UFMG - Chapter 1)
  • Group Theory, Abstraction, and the Monster Group (3Blue1Brown)
  • An Introduction to Group Theory (Cofiber)

• Class Groups & VDFs

  • Class Groups of Imaginary Quadratic Fields (Michael Straka)
  • Class Groups for VDFs (Chia Network)

• CL Cryptosystem & Research Papers

  • Linearly Homomorphic Encryption from DDH (IACR 2015/047)
    • Note: High technical complexity. It is recommended to use AI tools to help navigate and summarize this paper.
  • Cryptographic Research Report (IACR 2019/589)
  • A2L Library Repository (GitHub)

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For Enthusiasts (Further Reading)

Additional resources covering Homomorphic Encryption (HE), foundational schemes (ElGamal, Paillier), and broader applications.

• Conference Papers & Presentations

  • CSCM 2012 Conference Paper (EPJ Web of Conferences)
  • WRACH 2025: Castagnos Presentation Slides
  • LHE from Class Groups of Quadratic Fields (NIST Presentation 2021)
  • Academic Thesis/Paper (UFPB Repository)

• Homomorphic Encryption Concepts

  • Homomorphic Encryption Supplemental Info (CEGA Blog)
  • Understanding the ElGamal Encryption Algorithm (Medium)
  • A Comprehensive Guide to Paillier Homomorphic Encryption (Medium)

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Just for fun Concepts

• Noether's Theorem
  • Noether's Theorem: A Complete Guide (Profound Physics)
  • Noether's Theorem (Wikipedia)
  • The most beautiful idea in physics - Noether's Theorem