Abstract
Ω-protocols, introduced by Garay, Mackenzie and Yang, is a variant of S-protocols with online extractor which is a useful tool to overcome the nest effect in concurrent scenario. In this work, we construct an Ω-protocol for Hamiltonian cycle problem, and therefore, it allows us to present Ω-protocol for any NP relation. For most general NP relations, our construction of Ω-protocols is much more efficient than the informal one described by Garay et al. and we believe that the method for our construction may be of independent interest.
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