he.md

Homomorphic Encryption

tl;dr Homomorphic Encryption allows to perform calculations on encrypted data without decrypting it first.

About

Intros for non-cryptographers

• Introduction to FHE by Pascal Paillier
• Marc Joye’s blog for Zama FHE: Homomorphic Encryption 101
• FHE Community of Interest: FHE.org
  • Monthly meetings on FHE: https://www.meetup.com/fhe-org/
  • Chat space https://discord.fhe.org (wealth of information and discussions on how to use the libraries etc)
• HE Standardization https://homomorphicencryption.org/

Example HE cryptosystems

• RSA cryptosystem (unbounded number of modular multiplications)
• ElGamal cryptosystem (unbounded number of modular multiplications)
• Goldwasser–Micali cryptosystem (unbounded number of exclusive or operations)
• Benaloh cryptosystem (unbounded number of modular additions)
• Paillier cryptosystem (unbounded number of modular additions)

See Wikipedia

Breakthrough Gentry's FHE

Ph.D. thesis by Craig Gentry https://crypto.stanford.edu/craig/craig-thesis.pdf

FHE more practical

• Brakerski-Gentry-Vaikuntanathan (BGV, 2011) scheme, building on techniques of Brakerski-Vaikuntanathan

=> good for masking and integer arithmetic

• The NTRU-based scheme by Lopez-Alt, Tromer, and Vaikuntanathan (LTV, 2012)
• Brakerski/Fan-Vercauteren (BFV, 2012) scheme, building on Brakerski's scale-invariant cryptosystem
• NTRU-based scheme by Bos, Lauter, Loftus, and Naehrig (BLLN, 2013), building on LTV and Brakerski's scale-invariant cryptosystem
• Cheon-Kim-Kim-Song (CKKS, 2016) scheme.
  • Note that there were some issues with CCKS reported recently by Li and Micciancio (eprint report). In response, the HElib team published a list of mitigations.

=> floating point arithmetic => machine learning

Mathematics

• Math behind HElib (BGV explained)
• CKKS explained: Part 1, Vanilla Encoding and Decoding

Libraries

HElib

• Website: https://homenc.github.io/HElib
• Repo: https://github.com/HomEnc/HElib
• Docs: https://homenc.github.io/HElib/
• Bug report: https://github.com/homenc/HElib/issues
• Math behind HElib: HElib-design.pdf
• FHE-toolkit https://github.com/ibm/fhe-toolkit-linux (containerized IDE with precompiled libraries and examples)

SEAL

• Website: https://www.microsoft.com/en-us/research/project/microsoft-seal
• Repo: https://github.com/microsoft/SEAL
• Docs: https://github.com/microsoft/SEAL#introduction
• Bug report: https://github.com/microsoft/SEAL/issues

Concrete

• Website: https://zama.ai/concrete
• Repo: https://github.com/zama-ai/concrete
• Docs: https://docs.zama.ai/concrete/lib
• Bug report: https://github.com/zama-ai/concrete/issues
• Python package: GitHub: https://github.com/zama-ai/concrete-numpy

PALISADE

• Website: https://palisade-crypto.org/
• Repo: https://gitlab.com/palisade/palisade-release
• Docs: https://palisade-crypto.org/documentation
• Bug report: https://gitlab.com/palisade/palisade-release/-/issues

Intel Homomorphic Encryption Acceleration Library (HEXL)

• Intel HEXL
• Repo: https://github.com/intel/hexl

Google C++ compiler

• Repo: https://github.com/google/fully-homomorphic-encryption
• Examples: https://github.com/google/fully-homomorphic-encryption/tree/main/transpiler/examples
• Blog Post: Our latest updates on Fully Homomorphic Encryption

First steps to make FHE practical

In 2020, IBM Research conducted a project with a Brazilian Bank to implement a pilot using Homomorphic Encryption (HE) to a machine learning (ML) pipeline. Specifically they used HE in the ML for both the variable selection of the model generation and the actual prediction computation.

• IBM Research, Hursley, UK and Banco Bradesco SA, Osasco, SP, Brasil (link)
• Masters et al. " Towards a Homomorphic Machine Learning Big Data Pipeline for the Financial Services Sector" (eprint)