Homomorphic Encryption References (archived)
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/HElibAlgorithms in HELib
https://eprint.iacr.org/2014/106Bootstrapping for HELib
https://eprint.iacr.org/2014/873 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/NFLlibLeo Ducas and Daniele Micciancio
FHEW
https://github.com/lducas/FHEWWei Dai, Yarkin Doroz and Berk Sunar
cuHE: CUDA Homomorphic Encryption Library
https://github.com/vernamlab/cuHEDaniele 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/
Local graph
Linked from
- FHE History — [[Homomorphic Encryption References (archived)]]
- Fully Homomorphic Encryption and the Dawn of a Truly Private Internet (v0) — - [[Homomorphic Encryption References (archived)]]]
- Fully Homomorphic Encryption and the Dawn of a Truly Private Internet (v1) — - [[Homomorphic Encryption References (archived)]]]
- The Coming Wave of Encrypted Computation (v2) — - [[Homomorphic Encryption References (archived)]]]
External links
- Homomorphic Encryption Standardization Webpage
- Daniele Micciancio's Lattice Cryptography Links
- Communications of the ACM
- FOCS 2011 Tutorial (link to local copy)
- Tutorial on the Foundations of Cryptography, Dedicated to Oded Goldreich (linked from Shai's webpage)
- http://people.csail.mit.edu/rivest/RivestAdlemanDertouzos-OnDataBanksAndPrivacyHomomorphisms.pdf
- http://groups.csail.mit.edu/cis/pubs/shafi/1984-jcss.pdf
- https://link.springer.com/chapter/10.1007/3-540-39568-7_2
- Springer Link
- http://www.brics.dk/RS/00/45/
- http://crypto.stanford.edu/~dabo/abstracts/2dnf.html
- https://eprint.iacr.org/2010/182
- https://crypto.stanford.edu/craig/craig-thesis.pdf
- https://eprint.iacr.org/2009/616
- https://eprint.iacr.org/2009/571
- http://www.iacr.org/archive/crypto2010/62230116/62230116.pdf
- https://eprint.iacr.org/2011/279
- https://eprint.iacr.org/2011/344
- https://eprint.iacr.org/2011/277
- https://eprint.iacr.org/2012/078
- https://eprint.iacr.org/2011/566
- https://eprint.iacr.org/2012/099
- http://eprint.iacr.org/2012/240
- https://eprint.iacr.org/2012/565
- https://eprint.iacr.org/2013/094
- https://eprint.iacr.org/2012/144
- https://eprint.iacr.org/2014/062
- https://eprint.iacr.org/2013/340
- https://eprint.iacr.org/2013/541
- https://eprint.iacr.org/2014/094
- https://eprint.iacr.org/2014/816
- Talk Slides
- Springer Link
- https://eprint.iacr.org/2016/870
- https://github.com/shaih/HElib
- https://eprint.iacr.org/2014/106
- https://eprint.iacr.org/2014/873
- https://www.microsoft.com/en-us/research/project/homomorphic-encryption/
- https://palisade-crypto.org/
- https://github.com/quarkslab/NFLlib
- https://github.com/lducas/FHEW
- https://github.com/vernamlab/cuHE
- this paper
- https://github.com/micciancio/SWIFFT
- https://eprint.iacr.org/2011/405
- https://eprint.iacr.org/2014/331
- https://crypto.stanford.edu/people/dwu4/papers/FHE-SI_Report.pdf
- https://eprint.iacr.org/2014/798
- https://eprint.iacr.org/2015/345
- https://eprint.iacr.org/2016/339
- https://eprint.iacr.org/2016/196
- https://eprint.iacr.org/2010/145
- https://eprint.iacr.org/2013/307
- https://eprint.iacr.org/2016/164
- https://eprint.iacr.org/2016/381
- https://eccc.weizmann.ac.il/report/2010/146/
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