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Crisp commitment scheme based on noisy channels

In a crisp commitment schemes, a commitment must be opened using a unique opening key. However in such schemes, there could be many instances where the transmission medium or channel is corrupted by some kind of communication (transmission) noise. In this paper, we proposed a new scheme that enables the injection of fuzziness property to current ordinary crisp commitment scheme. In this way, the uncertainty occurring due to the noise presence is mitigated. It is a known fact that this kind of uncertainty naturally leads to the introduction of a fuzziness dimension to the commitment problem at hand. The security characteristic of our scheme relies on any cryptographic assumption unlike the fuzzy commitment scheme in the literature, which is based on hash function and should be strongly collision-free for the scheme to be secure.