Since its beginnings, modern cryptography has been one of the main fields of applications of abstract mathematics and specifically number theory. At first, the mathematical problems underlying cryptographic protocols have been basic questions about congruences. Since the start of the post-quantum era, where many classical protocols cannot be considered secure in a long-term view, new foundational problems have arisen that build up the basics for constructions in cryptography. These new problems are again inherently mathematical, though, much more elaborate than the classical ones. In our research on mathematical foundations of cryptography we analyze the fundamental problems of modern cryptography in various aspects, such as the hardness of the computational problems. On the other hand, the construction of advanced primitives in cryptography requires new mathematical tools, which we develop as part of our research on mathematical foundations of cryptography.
Our most recent publications in the area Mathematical Foundations are:
