  Why study Lattice-based Cryptography? There are a few ways to answer this
question. 1. It is useful to have cryptosystems that are based on a variety of
hard computational problems so the different cryptosystems are not all
vulnerable in the same way. 2. The computational aspects of lattice-based
cryptosystem are usually simple to understand and fairly easy to implement in
practice. 3. Lattice-based cryptosystems have lower encryption/decryption
computational complexities compared to popular cryptosystems that are based on
the integer factorisation or the discrete logarithm problems. 4. Lattice-based
cryptosystems enjoy strong worst-case hardness security proofs based on
approximate versions of known NP-hard lattice problems. 5. Lattice-based
cryptosystems are believed to be good candidates for post-quantum cryptography,
since there are currently no known quantum algorithms for solving lattice
problems that perform significantly better than the best-known classical
(non-quantum) algorithms, unlike for integer factorisation and (elliptic curve)
discrete logarithm problems. 6. Last but not least, interesting structures in
lattice problems have led to significant advances in Homomorphic Encryption, a
new research area with wide-ranging applications.
