Homomorphic Encryption References (archived)

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Last updated Wednesday 24 June 2025

Homomorphic Encryption Standardization Webpage

Daniele Micciancio's Lattice Cryptography Links

Surveys

• Craig Gentry
  

  Computing Arbitrary Functions of Encrypted Data
  

  Communications of the ACM
  

• Vinod Vaikuntanathan
  

  Computing Blindfolded: New Developments in Fully Homomorphic Encryption
  

  FOCS 2011 Tutorial (link to local copy)
  

• Shai Halevi
  

  Homomorphic Encryption
  

  Tutorial on the Foundations of Cryptography, Dedicated to Oded Goldreich (linked from Shai's webpage)
  

Pre-FHE

• Ronald Rivest, Leonard Adleman and Mike Dertouzos
  

  On Data Banks and Privacy Homomorphisms
  

  http://people.csail.mit.edu/rivest/RivestAdlemanDertouzos-OnDataBanksAndPrivacyHomomorphisms.pdf
  

• Shafi Goldwasser and Silvio Micali
  

  Probabilistic Encryption
  

  http://groups.csail.mit.edu/cis/pubs/shafi/1984-jcss.pdf
  

• Taher El Gamal
  

  A Public-key Cryptosystem and a Signature Scheme based on Discrete Logarithms
  

  https://link.springer.com/chapter/10.1007/3-540-39568-7_2
  

• Pascal Paillier
  

  Public-key Cryptosystems based on Composite Degree Residuosity Classes
  

  Springer Link
  

• Ivan Damgard and Mads Jurik
  

  A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System
  

  http://www.brics.dk/RS/00/45/
  

• Dan Boneh, Eu Jin Goh and Kobbi Nissim
  

  Evaluating 2-DNF Formulas on Ciphertexts
  

  http://crypto.stanford.edu/~dabo/abstracts/2dnf.html
  

• Craig Gentry, Shai Halevi and Vinod Vaikuntanathan
  

  A Simple BGN-Type Cryptosystem from LWE
  

  https://eprint.iacr.org/2010/182
  

  Note: This cryptosystem was discovered after Gentry's work on FHE, as a first attempt to base FHE on standard assumptions such as learning with errors (LWE).
  

Gen I

• Craig Gentry
  

  A fully homomorphic encryption scheme
  

  https://crypto.stanford.edu/craig/craig-thesis.pdf
  

• Marten van Dijk, Craig Gentry, Shai Halevi and Vinod Vaikuntanathan
  

  Fully Homomorphic Encryption over the Integers
  

  https://eprint.iacr.org/2009/616
  

• Nigel Smart and Frederik Vercauteren
  

  Fully Homomorphic Encryption with Relatively Small Key and Ciphertext Sizes
  

  https://eprint.iacr.org/2009/571
  

• Craig Gentry
  

  Toward basing fully homomorphic encryption on worst-case hardness
  

  http://www.iacr.org/archive/crypto2010/62230116/62230116.pdf
  

• Shai Halevi and Craig Gentry
  

  Fully Homomorphic Encryption without Squashing Using Depth-3 Arithmetic Circuits
  

  https://eprint.iacr.org/2011/279
  

  Note: I would classify this scheme as "somewhere between" the first and second generations, in the sense that it relies on fewer assumptions than the older schemes, yet it still uses ideal lattices.
  

Gen II

Key Papers:

• Zvika Brakerski and Vinod Vaikuntanathan
  

  Efficient Fully Homomorphic Encryption from (Standard) LWE
  

  https://eprint.iacr.org/2011/344
  

• Zvika Brakerski, Craig Gentry and Vinod Vaikuntanathan
  

  Fully Homomorphic Encryption without Bootstrapping
  

  https://eprint.iacr.org/2011/277
  

• Zvika Brakerski
  

  Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP
  

  https://eprint.iacr.org/2012/078
  

• Craig Gentry, Shai Halevi and Nigel Smart
  

  Fully Homomorphic Encryption with Polylog Overhead
  

  https://eprint.iacr.org/2011/566
  

• Craig Gentry, Shai Halevi and Nigel Smart
  

  Homomorphic Evaluation of the AES Circuit
  

  https://eprint.iacr.org/2012/099
  

Other Works:

• Craig Gentry, Shai Halevi, Chris Peikert and Nigel P. Smart
  

  Field Switching in BGV-Style Homomorphic Encryption
  

  http://eprint.iacr.org/2012/240
  

• Zvika Brakerski, Craig Gentry, and Shai Halevi
  

  Packed Ciphertexts in LWE-Based Homomorphic Encryption
  

  https://eprint.iacr.org/2012/565
  

• Adriana Lopez-Alt, Eran Tromer and Vinod Vaikuntanathan
  

  Multikey Fully Homomorphic Encryption and On-the-Fly Multiparty Computation
  

  https://eprint.iacr.org/2013/094
  

• Junfeng Fan and Frederik Vercauteren
  

  Somewhat Practical Fully Homomorphic Encryption
  

  https://eprint.iacr.org/2012/144
  

• Tancrede Lepoint and Michael Naehrig
  

  A Comparison of the Homomorphic Encryption Schemes FV and YASHE
  

  https://eprint.iacr.org/2014/062
  

Gen III

• Craig Gentry, Amit Sahai and Brent Waters
  

  Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based
  

  https://eprint.iacr.org/2013/340
  

• Zvika Brakerski and Vinod Vaikuntanathan
  

  Lattice-Based FHE as Secure as PKE
  

  https://eprint.iacr.org/2013/541
  

• Jacob Alperin-Sheriff and Chris Peikert
  

  Faster Bootstrapping with Polynomial Error
  

  https://eprint.iacr.org/2014/094
  

• Leo Ducas and Daniele Micciancio
  

  FHEW: Bootstrapping Homomorphic Encryption in less than a second
  

  https://eprint.iacr.org/2014/816
  

• Ryo Hiromasa, Masayuki Abe and Tatsuaki Okamoto
  

  Packing Messages and Optimizing Bootstrapping in GSW-FHE
  

  Talk Slides and Springer Link
  

• Ilaria Chillotti and Nicolas Gama and Mariya Georgieva and Malika Izabachène
  

  Faster Fully Homomorphic Encryption: Bootstrapping in less than 0.1 Seconds
  

  https://eprint.iacr.org/2016/870
  

Open Source Implementations

• Shai Halevi and Victor Shoup
  

  HELib: An Implementation of Homomorphic Encryption
  

  https://github.com/shaih/HElib
  

*Algorithms in HELib*<br>

[https://eprint.iacr.org/2014/106](https://eprint.iacr.org/2014/106)<br>

*Bootstrapping for HELib*<br>

[https://eprint.iacr.org/2014/873](https://eprint.iacr.org/2014/873)<br>

• Hao Chen, Kim Laine and Rachel Player (Microsoft Research)
  

  SEAL: Simple Encrypted Arithmetic Library
  

  https://www.microsoft.com/en-us/research/project/homomorphic-encryption/
  

• Yuriy Polyakov, Kurt Rohloff
  

  PALISADE
  

  https://palisade-crypto.org/
  

• Tancrede Lepoint
  

  NFLLib
  

  https://github.com/quarkslab/NFLlib
  

• Leo Ducas and Daniele Micciancio
  

  FHEW
  

  https://github.com/lducas/FHEW
  

• Wei Dai, Yarkin Doroz and Berk Sunar
  

  cuHE: CUDA Homomorphic Encryption Library
  

  https://github.com/vernamlab/cuHE
  

• Daniele Micciancio (based on this paper)
  

  SWIFFT
  

  https://github.com/micciancio/SWIFFT
  

  Note: SWIFFT is a lattice cryptography library that implements (for a specific dimension) power-of-2 cyclotomic using NTT and SSE/AVX parallelism optimizations.
  

Applications

• Kristin Lauter, Michael Naehrig and Vinod Vaikuntanathan
  

  Can Homomorphic Encryption be Practical?
  

  https://eprint.iacr.org/2011/405
  

• Raphael Bost, Shafi Goldwasser, Raluca Ada Popa and Stephen Tu
  

  Machine Learning Classification on Encrypted Data
  

  https://eprint.iacr.org/2014/331
  

• David Wu and Jacob Haven
  

  Using Homomorphic Encryption for Large-Scale Statistical Analysis
  

  https://crypto.stanford.edu/people/dwu4/papers/FHE-SI_Report.pdf
  

Multi-Key FHE

• Adriana Lopez-Alt, Eran Tromer and Vinod Vaikuntanathan
  

  Multikey Fully Homomorphic Encryption and On-the-Fly Multiparty Computation
  

  https://eprint.iacr.org/2013/094
  

• Michael Clear and Ciarán McGoldrick
  

  Multi-Identity and Multi-Key Leveled FHE from Learning with Errors
  

  https://eprint.iacr.org/2014/798
  

• Pratyay Mukherjee and Daniel Wichs
  

  Two Round Multiparty Computation via Multi-Key FHE
  

  https://eprint.iacr.org/2015/345
  

• Zvika Brakerski and Renen Perlman
  

  Lattice-Based Fully Dynamic Multi-Key FHE with Short Ciphertexts
  

  https://eprint.iacr.org/2016/339
  

• Chris Peikert and Sina Shiehian
  

  Multi-Key FHE from LWE, Revisited
  

  https://eprint.iacr.org/2016/196
  

• Yevgeniy Dodis, Shai Halevi, Ron Rothblum and Daniel Wichs
  

  Spooky Encryption and Its Applications
  

  https://eprint.iacr.org/2010/182
  

Miscellaneous

• Craig Gentry, Shai Halevi and Vinod Vaikuntanathan
  

  i-Hop Homomorphic Encryption and Rerandomizable Yao Circuits
  

  https://eprint.iacr.org/2010/145
  

• Rafail Ostrovsky, Anat Paskin-Cherniavsky and Beni Paskin-Cherniavsky
  

  Maliciously Circuit-Private FHE
  

  https://eprint.iacr.org/2013/307
  

• Leo Ducas and Damien Stehle
  

  Sanitization of FHE Ciphertexts
  

  https://eprint.iacr.org/2016/164
  

• Florian Bourse, Rafael Del Pino, Michele Minelli and Hoeteck Wee
  

  FHE Circuit Privacy Almost for Free
  

  https://eprint.iacr.org/2016/381
  

• Ron Rothblum
  

  Homomorphic Encryption: From Private Key to Public Key
  

  https://eccc.weizmann.ac.il/report/2010/146/
  

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