For over a decade, a major open question in the theory of lattice-based cryptography has been to construct non-interactive zero-knowledge proofs from standard assumptions, i.e. Learning With Errors. Indeed, about 5 years ago, this problem was inscribed on the wall at the Simons Institute for the Theory of Computation in Berkeley, CA with a $100 bounty. (Big money!)
In this talk, I will survey the detailed work over the past year or so, by Canetti et al (1-- https://eprint.iacr.org/2018/
The main result will be the existence of quantum-secure NIZKs from standard cryptographic hardness assumptions.
Pre-requisites: A basic understanding on LWE will be assumed (e.g. https://cims.nyu.edu/~