A Practical Key-Recovery Attack on GRAFHEN

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We give a structural cryptanalysis of GRAFHEN, a group-based fully homomorphic encryption scheme whose public rewriting rules hide a group representation used for decryption. Under the designers' isomorphism hypothesis, the compatible representations form one free $\mathrm{Aut}(G)$-orbit. Each maps the presented zero subgroup to an automorphic image and induces the same zero predicate. The published key-class expression is not a lower bound on reconstruction work: for a fixed publication, the sa