Security Issues
Lattice-based cryptographic constructions hold a great promise for post-quantum cryptography. Many of them are quite efficient, and some even compete with the best known alternatives; they are typically quite simple to implement; and are all believed to be secure against attacks using conventional or quantum computers.
In terms of security, lattice-based cryptographic constructions can be divided into two types. The first includes practical proposals, which are typically very efficient, but often lack a supporting proof of security. The second type admits strong provable security guarantees based on the worst-case hardness of lattice problems, but only a few of them are sufficiently efficient to be used in practice.
Read more about this topic: Lattice-based Cryptography
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