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Efficient long-term secure universally composable commitments

Oana Ciobotaru

Long-term security ensures a protocol is secure during its execution while interacting with a computationally bounded adversary, as well as after its completion, when an attacker, trying to uncover the secrets used in the protocol, could become computationally unbounded. Universal composability guarantees the security of a cryptographic protocol even when it is arbitrarily composed with other protocols as well as instances of itself. The security notion which ensures preservation of long-term security under the strong universal composition property is called long-term universal composability. While this notion has been thoroughly defined and analyzed, the results so far can only prove the existence of long-term secure universally composable commitments, while completely overlooking the efficiency of such protocols for everyday use. In this thesis, we present a novel long-term universally composable secure commitment protocol that is both very efficient and plausible to use in practice. The efficiency of our scheme is due to the fact that we are able to modify, fine tune and combine three existing and efficient cryptographic primitives: a digital signature scheme by [Camenisch-Lysyanskaya-SCN-2002], the zero-knowledge proofs of knowledge by [Camenisch-Lysyanskaya-SCN-2002] and the commitment protocol by [Damgard-Fujisaki-ASIACRYPT-2002], while improving the overall efficiency of the system. An additional challenge comes from the fact that our protocol needs to use a hardware device called a signature card, and for efficiency purposes, it should invoke the card as seldom as possible. We are able to reduce the number of necessary calls to the signature card to only one call.