In this talk, I will describe a significant open problem in post-quantum cryptography: specifically the quantum security of the sponge construction with invertible permutations (which, among other things, underlies the international hash standard SHA-3). I will motivate the query model in which this problem is usually stated, and give intuition for why it is hard. Then we'll explore some recent progress on this question based on applying the theory of Young subgroups, explained in a beginner-friendly way.
This is a Quantum Information Math RIT Seminar which is part of the larger MathQuantum RTG program at UMD.
https://mathquantum.umd.edu/rit/
(Please note that this talk starts at 4:05 pm).
