The critical group from a cryptographic perspective. (English) Zbl 1126.05054
Summary: The critical group of a graph is an abelian group that arises in several contexts, and there are some similarities with the groups that are used in cryptography. We construct a family of graphs with critical groups that are cyclic, and discuss the associated computational problems using algorithms based on the theory of ‘chip-firing’.
MSC:
05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
05E99 | Algebraic combinatorics |
94A60 | Cryptography |