Multiple modern cryptographic protocols rely on classical mathematical problems: For example, the security of the RSA cryptosystem is founded on the difficulty of factorizing integers, whereas the various instances of the Diffie-Hellman key exchange are closely related to the discrete logarithm problem of their respective group. In view of the rapid development of quantum computers, the methods discovered by Peter Shor in 1994 therefore pose a future security threat to many of these systems, thus forcing cryptographers to search various mathematical fields for new problems to base secure protocols on. Among the more promising of these fields is the rich theory of isogenies, which are maps between elliptic curves that are well-behaved with respect to both the geometric and the algebraic structure of the curves.
TopMath Talks
As part of the TopMath talks, TopMath students and doctoral students present parts of their research. They provide an understandable insight into their current area of interest, enabling students and staff from different research fields to broaden their mathematical background knowledge. The talks are open to the public and last about an hour, followed by discussion. You are cordially invited!