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Waters signatures (Eurocrypt 2005) can be shown existentially unforgeable under chosen-message attacks under the assumption that the computational Diffie-Hellman problem in the underlying (pairing-friendly) group is hard. Waters signatures form a simple and efficient digital signature scheme in pairing-friendly groups. The existential unforgeability of the scheme can be proved under the Computational Diffie-Hellman (CDH) assumption. From the proof, it is not immediately clear whether this comparatively large security gap is inherent or an artifact of the used proof technique.
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