CAREER: Geometric Methods in Cryptography

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As more and more people use computer networks to exchange confidential data and perform business transactions, public key cryptography is rapidly becoming one of the most critical tools in today's electronic world. Using cryptography it is possible to perform many important tasks ranging from electronic voting, to digital contract signing, secure virtual conferences on public networks and many more. All these applications ultimately rely on the security of the underlying cryptographic primitives (i.e. the fundamental building blocks using which all other more complex cryptographic applications are built). This research involves the study of computational problems from an area of mathematics called geometry of numbers that can be used both to design new cryptographic primitives, and to test old ones and assess their security.The investigators study the complexity of point lattices. These are geometric objects that can be described as the set of intersection points of a regular n-dimensional grid. This research involves both the identification of hard lattice problems, and the search for better algorithms to solve lattice problems that admit efficient solution. Hard lattice problems are subsequently used to design new cryptographic functions, while new lattice algorithms are used to design new cryptanalytic attacks against existing cryptographic primitives.