Paper 2015/939 Original: eprint.iacr.org/2015/939 ↗

A Decade of Lattice Cryptography

Abstract

\emph{Lattice-based cryptography} is the use of conjectured hard problems on point lattices in~$\R^{n}$ as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to \emph{quantum} attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under \emph{worst-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 \emph{short integer solution}~(SIS) and \emph{learning 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.