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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 developmentsdoi:10.1561/0400000074 fatcat:5orjj3lrufdalfufl7ju6rnz3e