> For the complete documentation index, see [llms.txt](https://cryptohack.gitbook.io/cryptobook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems.md).

# Cryptographic lattice problems

- [Short integer solutions (SIS)](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/short-integer-solutions-sis.md)
- [Learning with errors (LWE)](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/learning-with-errors-lwe.md)
- [Ring-LWE](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/ring-lwe.md)
- [NTRU](https://cryptohack.gitbook.io/cryptobook/lattices/cryptographic-lattice-problems/ntru.md)