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Vinod Vaikuntanathan's talk Lattices and Cryptography: A Match Made in Heaven covers Lattices, Learning with Errors, and Fully Homomorphic Encryption at a high level. It shows the big picture where FHE fits in. In particular, FHE is but one application of a new lattice-enabled cryptographic primitive called Homomorphic Trapdoor Function (HTDF) [GVW14] (the other application being Fully Homomorphic Signatures). Applications of lattices, including FHE, starts around 14:33. The main part of the talk is about HTDF.

A good, but older overview of FHE is given by IBM Shai Halevi's August 2013 lecture on Homomorphic Encryption at the UCI Workshop on Lattices with Symmetry. Slides.

This tutorial was an updated talk of a previous version at the CRYPTO 2011: video1, video2, slides.

A better 2015 overview by Shai Halevi on SWHE and FHE is available in the Somewhat Homomorphic Encryption (SWHE), and Fully Homomorphic Encryption (FHE) crypto bites.


  • [G09] Craig Gentry: A Fully Homomorphic Encryption Scheme. PhD Thesis. Stanford University, 2009. (full pdf)
  • [G10] Craig Gentry: Computing Arbitrary Functions of Encrypted Data. In: Communications of the ACM, Volume 53 Issue 3, March 2010, pages 97-105. (acm.org paywalled, full pdf)
  • [DGHV09] Marten van Dijk, Craig Gentry, Shai Halevi, Vinod Vaikuntanathan: Fully Homomorphic Encryption over the Integers. In: LNCS 6110, Advances in Cryptology, EUROCRYPT 2010 (iacr.org 2009/616 revised full pdf, original pdf via link.springer.com)
  • [CMNT11] Jean-Sebastien Coron, Avradip Mandal, David Naccache, Mehdi Tibouchi: Fully Homomorphic Encryption over the Integers with Shorter Public Keys. (iacr.org 2011/441 full pdf)
  • [J13] Aayush Jain: On FHE Without Bootstrapping (Informal) (iacr.org 2013/060 full pdf)
  • [S13] Alice Silverberg: Fully Homomorphic Encryption for Mathematicians (iacr.org 2013/250 full pdf)
  • [R05] Oded Regev: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: STOC'05, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, May 22 - 24, 2005, pages 84-93 (acm.org paywalled, full pdf)
  • [R10] Oded Regev: The Learning with Errors Problem. (full pdf)
  • [P16] Chris Peikert: A Decade of Lattice Cryptography. February 17, 2016. (full pdf)
  • [GVW14] Sergey Gorbunov, Vinod Vaikuntanathan, Daniel Wichs: Leveled Fully Homomorphic Signatures from Standard Lattices. In: STOC'15, Proceedings of the forty-seventh annual ACM symposium on Theory of computing. Portland, Oregon, June 14 - 17, 2015. Pages 469-477. (acm.org paywalled, full pdf an mit.edu, full pdf at iacr.org 2014/897)
  • [V17] Vinod Vaikuntanathan: Computing Blindfolded, New Developments in Fully Homomorphic Encryption. (ieee.org paywalled, full pdf)