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arXiv · 2510.06707

Representation Gap of the Motzkin Monoid

Katharina Arms
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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.

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Katharina Arms. 2025-10-08. Representation Gap of the Motzkin Monoid. https://arxiv.org/abs/2510.06707

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