Cryptography and Information Security Group Research Project: Lattice-Based Cryptography

Identifying hard computational problems which are amenable for cryptographic use is a very important task. Although hard computational problems seem to be all around us, only very few of those problems were found to be useful for cryptography. In fact, after two decades of research in cryptography, the vast majority of the public-key cryptosystems still depend on either the hardness of integer factorization or the hardness of extracting discrete logarithms. Moreover, often it has been the case that algorithmic advance in one of these problems was then applied to the other one as well.

To avoid "putting all the cryptographic eggs in one basket", it is important to find ways to use other hard computational problems in cryptographic schemes. A current research direction of ours is centered around the design of cryptosystems which are based on geometric problems (in particular, problems in the Geometry of Numbers). Along this line, we have the following results:

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