A Decade of Lattice Cryptography

Chris Peikert
2016 Foundations and Trends® in Theoretical Computer Science  
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 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
more » ... n 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.
doi:10.1561/0400000074 fatcat:5orjj3lrufdalfufl7ju6rnz3e