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{{Short description|Optimization problem in computer science}}
In [[computer science]], '''lattice problems''' are a class of [[Mathematical optimization|optimization]] problems related to mathematical objects called ''[[Lattice (group)|lattices]]''. The conjectured [[Intractable problem|intractability]] of such problems is central to the construction of secure [[Lattice-based cryptography|lattice-based cryptosystems]]: Lattice problems are an example of [[NP-hardness|NP-hard]] problems which have been shown to be [[Computational hardness assumption|average-case hard]], providing a test case for the security of cryptographic algorithms. In addition, some lattice problems which are worst-case hard can be used as a basis for extremely secure cryptographic schemes. The use of worst-case hardness in such schemes makes them among the very few schemes that are very likely secure even against [[quantum computers]]. For applications in such [[cryptosystems]], lattices over [[vector space]] (often <math>\mathbb{Q}^n</math>) or [[free module]]s (often <math>\mathbb{Z}^n</math>) are generally considered.
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