The security of cryptographic protocols is based on the conjectured intractability of some mathematical problem, typically a single problem. However, in some cases, novel constructions emerge out of the surprising interplay of seemingly disparate mathematical structures and conjectured hard problems on these. Though unusual, this cooperation between assumptions, when it happens, can lead to progress on important open problems. This sometimes paves the way for subsequent improvements, which may even eliminate the multiplicity and reduce security to a single assumption. In this talk, we will examine some interesting examples of the above phenomenon.
When the whole is more than the sum of parts: interplay of diverse mathematical structures in cryptography*
Shweta Agrawal, IIT Madras
2022 AWM Research Symposium
Mathematical Aspects of Cryptography