Unified Transfers: Restricted Classification and an Ordinary Ring-Class Realization

Can elliptic-curve discrete logarithms be transferred to an easier group by a mechanism fundamentally different from anomalous-curve and pairing attacks? Today, I’m releasing P1.5, an agent-assisted research project developed in collaboration with AI research agents as part of the math.st ECC Research Program. Unified Transfers: Restricted Classification and an Ordinary Ring-Class Realization We introduce a unified framework for ECDLP transfers, prove restricted impossibility and rigidity results, and construct an explicit ordinary ring-class realization of the known pairing transfer. The honest conclusion is important: this construction is a new representation, not a new attack. The unrestricted classification remains open, but the work substantially narrows where a fundamentally new transfer mechanism could still exist. The paper is accompanied by its code, computational experiments, research log, and reproducibility materials.