CWI Cryptology Group

Abstract: (Slides: [PDF] [PPTX]) In the first part of the talk, I will cover the Ring-LWE problem, its hardness, the equivalence of its search and decision versions, and explain what little is known about the hardness of problems in ideal lattices.

Abstract: In the second part, I will present two (similar) constructions of cpa-secure encryption schemes based on Ring-LWE. Then I will present the NTRU cryptosystem and sketch how it can be easily modified to become a "somewhat-homomorphic" encryption scheme that supports several additions and multiplications, and then finally present the "bootstrapping" technique that converts "somewhat-homomorphic" schemes that meet certain requirements into fully-homomorphic ones. (NB: the NTRU-based scheme that I will present does not meet these requirements, but can be modified to meet them using recent techniques.)

Abstract: In a recent pre-print, Brakerski introduced what he called a "scale invariant" homomorphic scheme. The name comes from the fact that, contrary to other schemes, its homomorphic properties depend only on the modulus-to-noise ratio. Furthermore, while in previous works noise would grow quadratically with each multiplication, here it grows linearly. The aim of the talk is to describe this scheme in detail.

Abstract: The talk will include an overview of some lattice-based Fully Homomorphic Encryption schemes such as those proposed by Smart-Vercauteren and Gentry-Halevi. We will also discuss balancing cryptographic security with ease of decryption, for lattice-based FHE schemes.