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This work presents a certificate-based approach for formally verifying the computation of the vertices of a polyhedron with a new completeness criterion based on an abstract simplicial complex that generalizes a triangulation of the normal fan of the polyhedron.
The notes provided in the original description by Pornin are expanded into a complete formal proof, which eventually relies on the collaboration of deductive program verification and interactive theorem proving through the use of the tools Rocq and Why3.
This work suggests a path toward accelerating cryptographic research: as agents automate the proof-engineering burden, cryptographers can iterate more quickly on new constructions, obtain machine-checked assurance earlier, and bring trustworthy protocols from design to deployment faster.
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