Modern technologies like cloud computing have begun to raise fundamentally new questions that require us to rethink this simplistic view of encryption. In a cloud computing system, users outsource computations on their sensitive data to the cloud, while expecting that their data is kept private. As the number of private cloud service providers increases, the privacy of individual data is increasingly at the risk of being exposed to prying eyes. This raises the following intriguing possibility: can we keep the users' data encrypted and allow the server to compute on encrypted data without decrypting it and without knowledge of the secret key? In other words, is it possible to compute on data while blindfolded?
This poses a seemingly contradictory set of requirements  privacy on the one hand and the ability to work meaningfully with encrypted data on the other. Fortunately, there is a solution to this conundrum which lies in the recently discovered notion of fully homomorphic encryption (FHE). FHE allows us to perform any computation, however complex, on encrypted data without ever decrypting it.
Expository Writing:
 Computing Blindfolded: New Developments in Homomorphic Encryption
Paper accompanying a FOCS 2011 Invited Tutorial. [pdf]
Talks:

An Expository talk at the Microsoft Research Techfest,
March 2011 (together with Josh Benaloh) [.ppsx].
 Talk at the University of Toronto Mississauga MCSS Seminar, November 2012 [.pptx].
Papers:
 OntheFly Multiparty Computation on the Cloud via Multikey Fully Homomorphic Encryption
A. LopezAlt, E. Tromer and V. Vaikuntanathan
To appear in STOC 2012
 Multiparty Computation with Low Communication, Computation and Interaction via Threshold FHE
G. Asharov, A. Jain, A. LopezAlt, E. Tromer, V. Vaikuntanathan and D. Wichs
To appear in Eurocrypt 2012
[ a Merge of this and this ]
 Fully Homomorphic Encryption without Bootstrapping
Z. Brakerski, C. Gentry and V. Vaikuntanathan
Innovations in Theoretical Computer Science 2012 [pdf]
 Efficient Fully Homomorphic Encryption from (Standard) LWE
Z. Brakerski and V. Vaikuntanathan
FOCS 2011 [pdf]
 Can Homomorphic Encryption be Practical?
K. Lauter, M. Naehrig and V. Vaikuntanathan [working draft]
ACM Cloud Computing Security Workshop (CCSW) 2011.
 Fully Homomorphic Encryption from Ring LWE and Security for Key Dependent Messages
Z. Brakerski and V. Vaikuntanathan
CRYPTO 2011.
 ihop Homomorphic Encryption Schemes
C. Gentry, S. Halevi and V. Vaikuntanathan
CRYPTO 2010.
Cryptology Eprint Archive.
 Fully Homomorphic Encryption from Integers
M. van Dijk, C. Gentry, S. Halevi and V. Vaikuntanathan
Eurocrypt 2010, Invited to the Journal of Cryptology.
Cryptology Eprint Archive.
 A Simple BGNstyle Encryption Scheme from LWE
C. Gentry, S. Halevi and V. Vaikuntanathan
Eurocrypt 2010. [pdf]
Cryptology Eprint Archive.