Representation Gap of the Motzkin Monoid

Abstract: The linear decomposition attack reveals a vulnerability in encryption algorithms operating within groups or monoids with excessively small representations. The representation gap, defined as the size of the smallest non-trivial representation, therefore serves as a metric to assess the security of these algorithms. This paper will demonstrate that the diagrammatic Motzkin monoids exhibit a large representation gap, positioning them as promising candidates for robust encryption algorithms.