Editing Lattice (group) (section)

==Computational lattice problems==
{{Main|Lattice problem}}
[[lattice problems|Computational lattice problems]] have many applications in computer science. For example, the [[Lenstra–Lenstra–Lovász lattice basis reduction algorithm]] (LLL) has been used in the [[cryptanalysis]] of many [[Public-key cryptography|public-key encryption]] schemes,<ref>{{Cite book|last1=Nguyen|first1=Phong|last2=Stern|first2=Jacques|title=Cryptography and Lattices |chapter=The Two Faces of Lattices in Cryptology |date=2001|volume=2146|pages=146–180|doi=10.1007/3-540-44670-2_12|series=Lecture Notes in Computer Science|isbn=978-3-540-42488-8}}</ref> and many [[Lattice-based cryptography|lattice-based cryptographic schemes]] are known to be secure under the assumption that certain lattice problems are [[Computational hardness assumption|computationally difficult]].<ref>{{Cite book|last=Regev|first=Oded|title=Proceedings of the thirty-seventh annual ACM symposium on Theory of computing |chapter=On lattices, learning with errors, random linear codes, and cryptography |date=2005-01-01|series=STOC '05|location=New York, NY, USA|publisher=ACM|pages=84–93|doi=10.1145/1060590.1060603|isbn=978-1581139600|citeseerx=10.1.1.110.4776|s2cid=53223958}}</ref>