A Decade Of Lattice Cryptography Chris Peikert by Chris Peikert instant download after payment.

Lattice-based cryptographyis the use of conjectured hard problems on
point lattices inRnas the foundation for secure cryptographic systems.
Attractive features of lattice cryptography include apparent resistance to
quantumattacks (in contrast with most number-theoretic cryptography),
high asymptotic efficiency and parallelism, security underworst-case
intractability assumptions, and solutions to long-standing open problems
in cryptography.

This work surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational
short integer solution(SIS) andlearning with errors(LWE) problems

(and their more efficient ring-based variants), their provable hardness
assuming the worst-case intractability of standard lattice problems, and
their many cryptographic applications.