SPEAKER: Stephen Finigan NYU TITLE: Latest on Fully Homomorphic Encryption from LWE ABSTRACT: The idea behind homomorphic encryption is simple: we want to be able to perform calculations on encrypted data. In practice, this is much more difficult than it sounds; after decades as an open question, it was first proved to be possible only in 2009. Fully homomorphic encryption (FHE) schemes allow us to both add and multiply encrypted bits, and from those two basic operations, it is possible to build arbitrary functions. With FHE, we can easily achieve secure systems for cloud computing, private information recall from an encrypted database, and many other important cryptographic constructions. Current FHE schemes come from lattice-based cryptography, and they are complex and inefficient. Nevertheless, we can construct a relatively straightforward example using vector addition and tensor product as our homomorphic operations, following the recent work of Craig Gentry, Oded Regev, Zvika Brakerski, and others. Full homomorphism is achieved with the help of mechanisms for reducing the ciphertext in size (key switching) and in noise (homomorphic decryption or 'bootstrapping').