### Zvika Brakerski

Dept. of Computer Science and Applied Mathematics

Weizmann Institute

Rehovot

Israel

## Fully homomorphic encryption

#### Abstract

The problem of constructing fully homomorphic encryption (FHE) is
one of the oldest and most fascinating in cryptography. An FHE scheme
allows one to perform arbitrary computations *f* on encrypted
data *Enc(x)*, so as to obtain the encryption *Enc(f(x))*,
using only public information and without learning anything about the
value of *x*. This enables outsourcing computations on private
data to a third party, while maintaining the data's privacy (for
example "oblivious web search") - a core task for secure cloud
computing.

The problem has been presented back in 1978, but the first candidate was only introduced in 2009 in Gentry's breakthrough work. Since then, there have been rapid and exciting developments. In this course I will define fully homomorphic encryption, survey the literature, and present state of the art constructions.

#### Course materials

- Z. Brakerski. Fully homomorphic encryption. Slides from the EWSCS 2015 course. [pdf]
- Z. Brakerski. Fully homomorphic encryption. Exercises to accompany the EWSCS 2015 course. [pdf]
- An additional problem. [txt]
- Videos from the lectures.
- R. L. Rivest, L. Adleman, M. L. Dertouzos. On data banks and
privacy homomorphisms. In R. A. DeMillo, D. P. Dobkin, A. K. Jones,
R. J. Lipton, eds.,
*Foundations of Secure Computation*, pp. 169-179. Academic Press, 1978. - O. Regev. On lattices, learning with errors, random linear codes,
and cryptography.
*J. of ACM*, v. 56, n. 6, article 34, 2009. [doi link] - C. Gentry. A fully homomorphic encryption scheme. PhD thesis. Stanford University, 2009. [copy on author's webpage]
- Z. Brakerski, V. Vaikuntanathan. Efficient fully homomorphic
encryption from (standard) LWE. In
*Proc. of 52nd Ann. IEEE Symp. on Foundations of Computer Science, FOCS '11*, pp. 97-106. IEEE, 2011. [doi link] - C. Gentry, A. Sahai, B. Waters. Homomorphic encryption from
learning with errors: conceptually-simpler, asymptotically-faster,
attribute-based. In R. Canetti, J. A. Garay, eds.,
*Proc. of 33rd Ann. Cryptology Conf., CRYPTO 2013, Part I*, v. 8042 of*Lect. Notes in Comput. Sci.*, pp. 75-92. Springer, 2013. [doi link] - Z. Brakerski, V. Vaikuntanathan. Lattice-based FHE as secure as
PKE. In
*Proc. of 5th Conf. on Innovations in Theoretical Computer Science, ITCS '14*, pp. 1-12. ACM Press, 2014. [doi link]

Last changed **
April 17, 2016 21:56 Europe/Helsinki (GMT +03:00)**
by
local organizers, ewscs15(at)cs.ioc.ee

EWSCS'15 page:
http://cs.ioc.ee/ewscs/2015/