Ngoc Khanh Nguyen:
Zero-knowledge proofs allow a party to convey that a given statement is true without leaking any secret information. These proofs form the foundations of many complex privacy-oriented protocols, such as electronic voting, verifiable computation, and blockchain. In this talk, we will discuss how the theory of cyclotomic fields helps with designing efficient zero-knowledge proofs from lattice-based assumptions.

Eamonn Postlethwaite:
In this talk I will briefly introduce the lattice isomorphism problem – LIP – and structured variants. I will describe approaches to solving generic LIP instances, and some recent progress in solving particular structured variants. For some brief cryptographic context, LIP has recently been used to build signature schemes. These are asymmetric cryptographic primitives that allow one party to authenticate data by appending a "signature", which takes the form of a short bitstring. Only an entity in possession of the secret key should be able to create valid signatures, but the validity of signatures can be checked publicly using the public key. Key recovery in recent proposals of such schemes from LIP – that is, computing the secret key from the public key – is exactly a LIP instance sampled from some distribution.