Three-round Protocol Research Articles

From Key Encapsulation to Authenticated Group Key Establishment—A Compiler for Post-Quantum Primitives †

Assuming the availability of an existentially unforgeable signature scheme and an (IND- CCA secure) key encapsulation mechanism, we present a generic construction for group key establishment. The construction is designed with existing proposals for post-quantum cryptography in mind. Applied with such existing proposals and assuming their security, we obtain a quantum-safe three-round protocol for authenticated group key establishment that requires only one signature per protocol participant.

Complexity of Causal Order Structure in Distributed Quantum Information Processing: More Rounds of Classical Communication Reduce Entanglement Cost

We prove a trade-off relation between the entanglement cost and classical communication round complexity of a protocol in implementing a class of two-qubit unitary gates by two distant parties, a key subroutine in distributed quantum information processing. The task is analyzed in an information theoretic scenario of asymptotically many input pairs with a small error that is required to vanish sufficiently quickly. The trade-off relation is shown by (i)one ebit of entanglement per pair is necessary for implementing the unitary by any two-round protocol, and (ii)the entanglement cost by a three-round protocol is strictly smaller than one ebit per pair. We also provide an example of bipartite unitary gates for which there is no such trade-off.

On the Power of Hybrid Networks in Multi-Party Computation

Perfectly-secure verifiable secret sharing (VSS) and multi-party computation (MPC) protocols in asynchronous network tolerate only at most one-fourth of corruption, while their counterparts in synchronous network sustain against at most one-third corruption. Moreover property-wise, synchronous protocols provide much stronger guarantees than the asynchronous counterparts. Taking note of the fact that asynchronous network is more realistic on one hand and on the other, synchrony of a network has positive impact on several aspects of distributed protocols including properties and fault-tolerance, we explore the power of hybrid networks that combines best of both the worlds by supporting a few synchronous rounds at the onset of a protocol execution, before turning to asynchronous mode. In hybrid networks, we investigate various feasibility questions pertaining to protocols giving guarantees attainable in synchronous and asynchronous networks. For the asynchronous protocols in hybrid networks, we hope to leverage the initial synchronous rounds to bridge the gap in the fault-tolerance with the synchronous protocols under minimal synchrony assumption. We ask the following fundamental question of both theoretical and practical importance: What is the minimum number of initial synchronous rounds necessary and sufficient in a hybrid network to construct asynchronous perfectly-secure VSS and MPC protocols with the fault-tolerance of synchronous protocols? On the positive note, we show that the answer is one for VSS which is clearly optimal. Notably no broadcast oracle is invoked in the synchronous round of our proposed VSS protocol. On the negative side, we prove that one synchronous round is not enough for MPC, putting MPC on a higher pedestal than VSS in terms of difficulty. For synchronous protocols in hybrid networks, we hope to save on the synchronous rounds leveraging conveniently the available asynchronous phase. We settle the question for VSS in the negative showing that three rounds that are known to be necessary (and sufficient) for VSS in synchronous networks, are also required in hybrid networks. VSS being a special case of MPC, the lower bound holds true for MPC. We match the lower bound with a three-round protocol. Notably, synchronous MPC with cryptographic security is known to be achievable in hybrid networks with one synchronous round.

Scalable Protocols for Authenticated Group Key Exchange

We consider the problem of authenticated group key exchange among n parties communicating over an insecure public network. A number of solutions to this problem have been proposed; however, all prior provably-secure solutions do not scale well and, in particular, require O (n) rounds. Our main contribution is the first scalable protocol for this problem along with a rigorous proof of security in the standard model under the DDH assumption; our protocol uses a constant number of rounds and requires only O (1) \full modular exponentiations per user. Toward this goal (and adapting work of Bellare, Canetti, and Krawczyk), we first present an efficient compiler that transforms any ngroup key-exchange protocol secure against a passive eavesdropper to an authenticated protocol which is secure against an active adversary who controls all communication in the network. This compiler adds only one round and O (1) communication (per user) to the original scheme. We then prove secure | against a passive adversary | a variant of the two-round group key-exchange protocol of Burmester and Desmedt. Applying our compiler to this protocol results in a provably-secure three-round protocol for authenticated group key exchange which also achieves forward secrecy.

Scalable Protocols for Authenticated Group Key Exchange

We consider the problem of authenticated group key exchange among n parties communicating over an insecure public network. A number of solutions to this problem have been proposed; however, all prior provably secure solutions do not scale well and, in particular, require O(n) rounds. Our main contribution is the first scalable protocol for this problem along with a rigorous proof of security in the standard model under the DDH assumption; our protocol uses a constant number of rounds and requires only O(1) full modular exponentiations per user. Toward this goal (and adapting work of Bellare, Canetti, and Krawczyk), we first present an efficient compiler that transforms any group key-exchange protocol secure against a passive eavesdropper to an authenticated protocol which is secure against an active adversary who controls all communication in the network. This compiler adds only one round and O(1) communication (per user) to the original scheme. We then prove secure—against a passive adversary—a variant of the two-round group key-exchange protocol of Burmester and Desmedt. Applying our compiler to this protocol results in a provably secure three-round protocol for authenticated group key exchange which also achieves forward secrecy.