Input-Aware Equivocable Commitments and UC-secure Commitments with Atomic Exchanges

We define a new primitive, input-aware equivocable commitment, baring similar hardness assumptions as plaintext-aware encryption and featuring equivocability. We construct an actual input-aware equivocable commitment protocol, based on a flavor of Diffie-Hellman assumptions allowing adversarially chosen domain parameters. On a parallel front, and since our commitment is extractable and equivocable in a straight-line way, we show that our commitment enjoys UC-security, when atomic exchanges are available as a UC setup. We further compare our protocol and our UC setup with similar, existing ones (i.e., in terms of efficiency, assumptions needed, etc.). Finally, we show that cryptography becomes UC-realizable in a natural way when participants are able to have “close encounters” or when atomic exchanges can be enforced onto the communication.