Universally Composable Commitments Using Random Oracles

In the setting of universal composability [Can01], commitments cannot be implemented without additional assumptions such as that of a publicly available common reference string [CF01]. Here, as an alternative to the commitments in the common reference string model, the use of random oracles to achieve universal composability of commitment protocols is motivated. Special emphasis is put on the security in the situation when the additional “helper functionality” is replaced by a realizable primitive. This contribution gives two constructions which allow to turn a given non-interactive commitment scheme into a noninteractive universally composable commitment scheme in the random oracle model. For both constructions the binding and the hiding property remain valid when collision-free hash functions are used instead of random oracles. Moreover the second construction in this case even preserves the property of perfect binding.