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Verifiable Random Functions (VRF) and Selectively-Convertible Undeniable Signature (SCUS) schemes were proposed independently in the literature. In this paper, the authors observe that they are tightly related. This directly yields several deterministic SCUS schemes based on existing VRF constructions. In addition, they create a new probabilistic SCUS scheme, which is very compact. The confirmation and disavowal protocols of these SCUS are efficient, and can be run either sequentially, concurrently, or arbitrarily. These protocols are based on what they call zero-knowledge protocols for generalized DDH and non-DDH, which are of independent interest.
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