On the Complexity of UC Commitments

Motivated by applications to secure multiparty computation, we study the complexity of realizing universally composable (UC) commitments. Several recent works obtain practical UC commitment protocols in the common reference string (CRS) model under the DDH assumption. These protocols have two main disadvantages. First, even when applied to long messages, they can only achieve a small constant rate (namely, the communication complexity is larger than the length of the message by a large constant factor). Second, they require computationally expensive public-key operations for each block of each message being committed.

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