Stephen Finigan

Latest on Fully Homomorphic Encryption from LWE

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').