Learning the Word Problem: Geodesic Lengths and Cryptographic Applications

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arXiv:2607.26241v1 Announce Type: new Abstract: The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC). While generally undecidable, several families of infinite non-abelian groups exhibit solvable or algorithmically fast word problems, making them attractive platforms for cryptographic design. This paper in