With post-quantum cryptography (also known as quantum-resistant cryptography), researchers want to create cryptographic systems that are secured against both quantum and classical computers while also being able to interoperate with current communication protocols and network infrastructures. It remains an important research question to find practical and quantum-secure alternatives to current systems based on the hardness of classical security assumptions such as factoring and computing discrete logarithms. One of the popular quantum secure cryptographic constructions is based on lattices since they benefit from extremely strong secure arguments based on worst-case problems, fast implementations, and a high degree of simplicity. Recently, many of new hard-problems based on lattices were proposed such as learning-with-errors (LWE), learning-with-rounding (LWR), short integer solution (SIS), NTRU, and their ring, module, polynomial extensions, see a recent survey https://dl.acm.org/doi/pdf/10.1145/3292548. On the other hand, design of such lattice based alternatives to many of the cryptosystems such as signatures (group, threshold, multi, ring, accountable, delegatable, hierarchical, blind, attribute-based), secret sharing (verifiable, malicious), zero-knowledge (partial, non-interactive), commitment schemes (verifiable, anonymous) and others is a trending research topic. This project aims at studying, constructing and security analysis of these kinds of lattice based cryptographic schemes.
