International Association
for Cryptologic Research

Lattice-based cryptography is the use of conjectured hard

problems on point lattices in $\\R^{n}$ as the foundation for secure

cryptographic constructions. Attractive features of lattice

cryptography include: apparent resistance to quantum attacks

(in contrast with most number-theoretic cryptography), high asymptotic

efficiency and parallelism, security under 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 short integer solution (SIS) and 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.