Homomorphic Encryption References

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)

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).

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.

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

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

Shai Halevi and Victor Shoup
HELib: An Implementation of Homomorphic Encryption
https://github.com/shaih/HElib

Algorithms in HELib
https://eprint.iacr.org/2014/106

Bootstrapping 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/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.

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

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

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/