One-way functions, functions that are easy to compute, but hard to invert on average, are the most basic cryptographic application of lattices. Lattice-based one-way functions have some useful homomorphic properties that immediately yield useful cryptographic applications, like collision resistant hash functions, and commitment schemes.

**Collision-Free Hashing from Lattice Problems**

(*Goldreich, Goldwasser & Halevi* - Studies in Complexity and Cryptography 2011 / ECCC 1996)

**More Efficient Commitments from Structured Lattice Assumptions**

(*Baum, Damgard, Lyubashevsky, Oechsner & Peikert* - SCN 2018)