- AES and Expansion Properties
- Project Year:
2020
- REU Student (s):
Eli Goldin | Columbia University in the City of New York NY
- Student 1 Institution:
Columbia University in the City of New York
- Project Mentor:
Periklis Papakonstantinou
- Project Mentor Area:
Management Science and Information Systems
- Project Abstract:
AES is one of the best known and most widely used block ciphers to date. However, the primary argument towards the security of AES is simply the fact that it has not been broken in practice. We present a new way of theoretically analyzing the security of AES and related block ciphers by looking at the expansion of a related Cayley graph. More specifically, we provide a generalization of a single round of AES, which we consider as a generating set for the symmetric group. This then gives a Cayley graph for which one could theoretically explicitly calculate the spectral gap. We explicitly perform this calculation for small security parameters, and we compare these results to related expansion results for the ideal cipher. We hope that this analysis, when continued, will either give some indication of the security of AES or will lead to an explicit attack.
