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Homomorphic Encryption

2 min read

How to start:

  • Learn about BFV, BGV scheme.
  • implement them in rust
  • Look at some small libraries, and how they implement it.

The Beginner’s Textbook for Fully Homomorphic Encryption [2205.03511v1] Lattices, Homomorphic Encryption, and CKKS [2208.08125] A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption Homomorphic Encryption References FHE A Guide to Fully Homomorphic Encryption Survey on Fully Homomorphic Encryption, Theory, and Applications he-chapter.pdf Chen18.pdf Threshold (Fully) Homomorphic Encryption SoK: New Insights into Fully Homomorphic Encryption Libraries via Standardized Benchmarks

timeline
    title Fully Homomorphic Encryption (FHE) Research Timeline
    section Foundations
        1978 : RSA Cryptosystem : Rivest, Shamir, Adleman
        1978 : First mention of homomorphic encryption concept : Rivest, Adleman, Dertouzos
        2005 : Boneh-Goh-Nissim cryptosystem : First partially homomorphic encryption with one multiplication
    section Breakthrough Era
        2009 : First FHE scheme : Gentry's lattice-based construction
        2010 : Second-generation FHE : Gentry-Halevi implementation
        2011-2012 : BGV scheme : Brakerski-Gentry-Vaikuntanathan
        2012 : LWE-based FHE : Brakerski scheme
        2013 : GSW scheme : Gentry-Sahai-Waters
    section Optimization Era
        2014 : FHEW scheme : Ducas-Micciancio
        2016 : TFHE scheme : Chillotti et al.
        2016 : HElib library released : IBM
        2018 : CKKS scheme : Cheon-Kim-Kim-Song
        2018 : Microsoft SEAL library : Microsoft Research
    section Practical Applications
        2019 : Intel HE-Transformer : Integration with neural networks
        2020 : Google's Fully Homomorphic Encryption Transpiler
        2022 : HEIR project : Homomorphic Encryption for AI
        2023 : AWS & Duality Collaboration : Cloud-based FHE
        2024 : IBM Fully Homomorphic Encryption Toolkit for Linux

Libraries:

  • SEAL
  • HElib
  • tfhe-rs

Start with:

  • intense introdcution to cryptography lec 16-17

Questions:

  • Why is CCA security not possible for FHE?

PHE Definition

Let be a binary function family, where . An homomorphic public-key encryption scheme is CPA secure

BGV

FHE over integers

BFV

FHE over integers

https://github.com/AI-Tech-Research-Lab/Introduction-to-BFV-HE-ML/blob/main/BFV_theory/BFV_theory.ipynb

CKSS

FHE over real numbers

FHEW/TFHE

FHE over boolean circuits

HE-GPU

[2410.05934v1] Chameleon: An Efficient FHE Scheme Switching Acceleration on GPUs

Resources

Graph View

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