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Homomorphic Encryption (HE)

HE, especially FHE(Fully Homomorphic Encryption), does matter and are keys for now and future.

Survey

  • Computing Blindfolded,New Developments in Fully Homomorphic Encryption V. Vinod FOCS 2011, paper, Vin11

  • Practical homomorphic encryption: A survey C. Moore, M. O’Neill, E. O’Sullivan, Y. Doroz, and B. Sunar ISCAS 2014, paper, MOO+14

  • A Guide to Fully Homomorphic Encryption F. Armknecht, C. Boyd, C. Carr, A. Jaschke, and C. A. Reuter 2016, paper, ACC+16

  • Homomorphic Encryption H. Shai 2017, paper, Shai17

  • A Survey on Fully Homomorphic Encryption: An Engineering Perspective P. Martins, L. Sousa, and A. Mariano ACM Comput. Surv. 2018, paper, MSM18

  • Fundamentals of Fully Homomorphic Encryption – A survey Z. Brakerski paper, Bra18

  • A Decade (or So) of Fully Homomorphic Encryption C. Gentry presented at the Eurocrypt2021 invited talk, paper

Partial HE(PHE)

  • ⭐️⭐️⭐️ A method for obtaining digital signatures and public-key cryptosystems R. L. Rivest, A. Shamir, and L. Adleman Communications of the ACM, paper, RSA78

  • Probabilistic encryption & how to play mental poker keeping secret all partial information S. Goldwasser and S. Micali STOC 82, paper, GM82

  • A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms T. ElGamal CRYPTO 1984, paper, ElGamal84

  • ⭐️⭐️⭐️ A new public-key cryptosystem as secure as factoring,” in Advances in Cryptology T. Okamoto and S. Uchiyama EUROCRYPT 1998, paper, OU98

  • A new public key cryptosystem based on higher residues D. Naccache and J. Stern CCS 98, paper, NS98

  • ⭐️⭐️⭐️ Public-Key Cryptosystems Based on Composite Degree Residuosity Classes P. Paillier EUROCRYPT 1999, paper, Paillier99

  • ⭐️⭐️ Why Textbook ElGamal and RSA Encryption Are Insecure? D. Boneh, A. Joux, and P. Q. Nguyen ASIACRYPT 2000, paper, BJN00

  • Chosen-Ciphertext Security for Any One-Way Cryptosystem D. Pointcheval PKC 2000, paper, Poi00

  • A Generalisation, a Simplification and Some Applications of Paillier's Probabilistic Public-Key System Ivan Damgård and Mads Jurik PKC 2001, paper, DJ01

  • Elliptic Curve Paillier Schemes S. D. Galbraith J. Cryptology 2002, paper, Gal02

  • Multi-bit Cryptosystems Based on Lattice Problems A. Kawachi, K. Tanaka, and K. Xagawa PKC 2007, paper,KTX07

  • Optimized Paillier’s Cryptosystem with Fast Encryption and Decryption H. Ma, S. Han, and H. Lei ACSAC 21, paper, MHL21

FHE

Classical(or Milestones)

  • A fully homomorphic encryption scheme Gentry, Craig Stanford university 2009, paper, Gentry09

  • Fully Homomorphic Encryption Using Ideal Lattices Gentry, Craig STOC 2009, paper, Gentry09

  • A simple BGN-type cryptosystem from LWE Gentry, Craig, Shai Halevi, and Vinod Vaikuntanathan EUROCRYPT 2010, paper, GSV10

  • Fully homomorphic encryption from ring-LWE and security for key dependent messages Zvika Brakerski, Vinod Vaikuntanathan CRYPTO 2011, paper, BV11

  • (Leveled) fully homomorphic encryption without bootstrapping *Zvika Brakerski, Craig Gentry, Vinod Vaikuntanathan ITCS 2012, paper, BGV12

  • Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP Zvika Brakerski CRYPTO 2012, paper, Brakerski12

  • Somewhat Practical Fully Homomorphic Encryption Junfeng Fan, Frederik Vercauteren eprint 2012, paper, FV12

  • Packed Ciphertexts in LWE-based Homomorphic Encryption Zvika Brakerski, Craig Gentry, Shai Halevi PKC 2013, paper, BGH13

  • Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based Craig Gentry, Amit Sahai, Brent Waters CRYPTO 2013, paper, GSW13

  • Efficient Fully Homomorphic Encryption from (Standard) LWE Zvika Brakerski, Vinod Vaikuntanathan SIAM Journal on computing 2014, paper, BV14

  • FHEW: Bootstrapping Homomorphic Encryption in less than a second Léo Ducas, Daniele Micciancio EUROCRYPT 2015, paper, DM15

  • Faster Fully Homomorphic Encryption: Bootstrapping in less than 0.1 Seconds Ilaria Chillotti, Nicolas Gama, Mariya Georgieva, and Malika Izabachène ASIACRYPT 2016, paper, CGG+16

  • Homomorphic Encryption for Arithmetic of Approximate Numbers Jung Hee Cheon, Andrey Kim, Miran Kim, Yongsoo Song ASIACRYPT 2017, paper , CKKS17

  • Threshold Cryptosystems from Threshold Fully Homomorphic Encryption Dan Boneh, Rosario Gennaro, Steven Goldfeder, Aayush Jain, Sam Kim, Peter M. R. Rasmussen, Amit Sahai CRYPTO 2018, paper, BGG+18

  • TFHE: Fast Fully Homomorphic Encryption Over the Torus Ilaria Chillotti, Nicolas Gama, Mariya Georgieva, Malika Izabachène Journal of Cryptology 2019, paper, BGG+2019

  • Bootstrapping fully homomorphic encryption over the integers in less than one second Hilder Vitor Lima Pereira PKC 2021, paper, Pereira21

  • Improved Programmable Bootstrapping with Larger Precision and Efficient Arithmetic Circuits for TFHE Ilaria Chillotti, Damien Ligier, Jean-Baptiste Orfila, Samuel Tap ASIACRYPT 2021, paper, CLO+21

  • Efficient FHEW Bootstrapping with Small Evaluation Keys, and Applications to Threshold Homomorphic Encryption Yongwoo Lee, Daniele Micciancio, Andrey Kim, Rakyong Choi, Maxim Deryabin, Jieun Eom, Donghoon Yoo EUROCRYPT 2023, paper, LMK+23

Multi-key FHE

  • On-the-Fly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption Adriana Lopez-Alt, Eran Tromer, Vinod Vaikuntanathan STOC 2012, paper, LTV12

  • Multi-Identity and Multi-Key Leveled FHE from Learning with Errors Michael Clear, Ciarán McGoldrick CRYPTO 2015, paper, CM15

  • Lattice-Based Fully Dynamic Multi-key FHE with Short Ciphertexts Zvika Brakerski, Renen Perlman CRYPTO 2016, paper, BP16

  • Multi-Key FHE from LWE, Revisited Chris Peikert, Sina Shiehian TCC 2016, paper, PS16

  • Two Round Multiparty Computation via Multi-Key FHE Pratyay Mukherjee, Daniel Wichs EUROCRYPT 2016, paper, MW16

  • Efficient Multi-Key Homomorphic Encryption with Packed Ciphertexts with Application to Oblivious Neural Network Inference Hao Chen, Wei Dai, Miran Kim, Yongsoo Song CCS 2019, paper, CDKS19

  • Multi-Key Homomophic Encryption from TFHE Hao Chen, Ilaria Chillotti, Yongsoo Song ASIACRYPT 2019, paper, CCS19

Impl. Efforts

  • Can homomorphic encryption be practical? M. Naehrig, K. Lauter, and V. Vaikuntanathan the 3rd ACM workshop on Cloud computing security workshop 2011, paper, NLV11
  • A Comparison of the Homomorphic Encryption Schemes FV and YASHE T. Lepoint and M. Naehrig AFRICACRYPT 2014, paper, LN14
  • Building an Efficient Lattice Gadget Toolkit: Subgaussian Sampling and More N. Genise, D. Micciancio, and Y. Polyakov EUROCRYPT 2019, paper, GMP19
  • Simple Encrypted Arithmetic Library - SEAL v2.1 Hao Chen, Kim Laine, Rachel Player FC 2017,paper, version 2.3 by Kim Laine, CLP17
  • Faster Homomorphic Linear Transformations in HElib S. Halevi and V. Shoup CRYPTO 2018, paper, HS18
  • OpenFHE: Open-Source Fully Homomorphic Encryption Library A. A. Badawi et al. WAHC 2022, paper, BBB+22

Hardware-based Acceleration

  • Intel HEXL: Accelerating Homomorphic Encryption with Intel AVX512-IFMA52
    Fabian Boemer, Sejun Kim, Gelila Seifu, Fillipe D. M. de Souza, Vinodh Gopal
    Proceedings of the 9th on Workshop on Encrypted Computing & Applied Homomorphic Cryptography 2021, paper, BKS+21

Open-sourced libs

Name Description Scheme Language
Secretflow/HEU A high-performance homomorphic encryption algorithm library Paillier, OU, ElGamal, FHE(in developing) C++, python
OpenFHE OpenFHE is an open-source FHE library that includes efficient implementations of all common FHE schemes - BFV, BGV, CKKS, DM, CGGI,
- Threshold FHE & Proxy Re-Encryption for BFV, BGV, CKKS		 C++
microsoft/SEAL an easy-to-use open-source homomorphic encryption library BFV, BGV, CKKS C++, C#

See more, https://github.com/jonaschn/awesome-he#libraries

Applications

Here just list several inspirational and instructive applicaitons.

Standard Efforts

  • PSEC-3: Provably Secure Elliptic Curve Encryption Scheme T. Okamoto and D. Pointcheval Submission to IEEE P1363a, 2000, paper, OP00; a note by Rachel Shipsey,

  • Homomorphic Encryption Security Standard v1.1
    Martin Albrecht and Melissa Chase and Hao Chen and Jintai Ding and Shafi Goldwasser and Sergey Gorbunov and Shai Halevi and Jeffrey Hoffstein and Kim Laine and Kristin Lauter and Satya Lokam and Daniele Micciancio and Dustin Moody and Travis Morrison and Amit Sahai and Vinod Vaikuntanathan
    HomomorphicEncryption.org, paper, homepage, ACC+18

    Other Resources

  • Homomorphic Encryption References