Abstract: A digital signature is possibly the most important public-key primitive after encryption scheme. One of the most natural ways to construct a digital signature scheme is to transform a three-round identification scheme (ID) into a digital signature. This is essentially done by the well-known Fiat-Shamir transformation. In this talk, I will first give a brief introduction to the average-case lattice assumptions. Then I will focus on the construction of ID scheme from the discrete log assumption (as in the Schnorr protocol) and try to achieve a similar protocol from lattice assumptions. We will see why the same analogy (that of the Schnorr protocol) doesn’t work in the lattice settings and how we can manage to achieve an ID scheme (and thus a digital signature) from lattice assumptions. Then I will discuss some open problems in this direction.