Biblio

In 2009, Craig Gentry introduced the first "fully" homomorphic encryption scheme allowing arbitrary circuits to be evaluated on encrypted data. Homomorphic encryption is a very powerful cryptographic primitive, though it has often been viewed by practitioners as too inefficient for practical applications. However, the performance of these encryption schemes has come a long way from that of Gentry's original work: there are now several well-maintained libraries implementing homomorphic encryption schemes and protocols demonstrating impressive performance results, alongside an ongoing standardization effort by the community. In this tutorial we survey the existing homomorphic encryption landscape, providing both a general overview of the state of the art, as well as a deeper dive into several of the existing libraries. We aim to provide a thorough introduction to homomorphic encryption accessible by the broader computer security community. Several of the presenters are core developers of well-known publicly available homomorphic encryption libraries, and organizers of the homomorphic encryption standardization effort \textbackslashtextbackslashhrefhttp://homomorphicencryption.org/. This tutorial is targeted at application developers, security researchers, privacy engineers, graduate students, and anyone else interested in learning the basics of modern homomorphic encryption.The tutorial is divided into two parts: Part I is accessible by everyone comfortable with basic college-level math; Part II will cover more advanced topics, including descriptions of some of the different homomorphic encryption schemes and libraries, concrete example applications and code samples, and a deeper discussion on implementation challenges. Part II requires the audience to be familiar with modern C++.

We report on our implementation of a new Gaussian sampling algorithm for lattice trapdoors. Lattice trapdoors are used in a wide array of lattice-based cryptographic schemes including digital signatures, attributed-based encryption, program obfuscation and others. Our implementation provides Gaussian sampling for trapdoor lattices with prime moduli, and supports both single- and multi-threaded execution. We experimentally evaluate our implementation through its use in the GPV hash-and-sign digital signature scheme as a benchmark. We compare our design and implementation with prior work reported in the literature. The evaluation shows that our implementation 1) has smaller space requirements and faster runtime, 2) does not require multi-precision floating-point arithmetic, and 3) can be used for a broader range of cryptographic primitives than previous implementations.