Joël Alwen

Trapdoors for Hard Lattices and New Cryptographic Constructions - Part II (IBE & LWE)

Craig gentry, Chris Peikert, Vino Vaikuntanathan (Proc. of STOC 2008)

An important line of work presented in GPV08 concerns how to use the Learning With Errors (LWE) problem
as an intermediate hardness assumption for lattice based cryptography. In particular a dual encryption
scheme to that of Reg05 is given which has a very simple an elegant proof of CPA security reducing to the
LWE problem. Next the dual cryptosystem is used as a building block to construct a lattice based IBE scheme
in the RO model which enjoys both a clean proof of security as well as relative asymptotic efficiency 
(when compared with other existing IBE schemes). Finally the authors demonstrate new trapdoor methods for
LWE via a public key encryption system secure under the LWE assumption.

In this talk we will discuss these techniques, constructions and their proofs of security.