In this work, we initiate the study of network-agnostic perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries, where the corruption capacity of the adversary is specified through an adversary structure, which is a set of potentially corrupt subsets of parties. Known MPC protocols are designed either assuming a synchronous network where every sent message is guaranteed to be delivered within some known time or assuming an asynchronous network where no timing assumptions are made and every sent message is eventually delivered. Perfectly-secure MPC protocols in the synchronous network can be designed as long as the underlying adversary structure satisfies the$ {{\mathcal {Q}}}^{(3)} $condition, meaning that the union of no three subsets from the adversary structure covers the entire set of parties. On the other hand, perfectly-secure MPC protocols in the asynchronous network can be designed only against$ {{\mathcal {Q}}}^{(4)} $adversary structures, meaning that the union of no four subsets from the adversary structure covers the entire set of parties. A natural question is whether a single MPC protocol exists, which remains secure even if the parties are unaware of the network conditions at execution time. That is, if the synchrony is satisfied throughout the protocol execution then the protocol should be secure against any$ {{\mathcal {Q}}}^{(3)} $adversary structure. However, even if any synchrony assumption is violated during the execution, the protocol should still be secure against any$ {{\mathcal {Q}}}^{(4)} $adversary structure. We answer the above question affirmatively. Fix any adversary structure$ {\mathcal {Z}}_{s} $and$ {\mathcal {Z}}_{a} $satisfying$ {{\mathcal {Q}}}^{(3)} $and$ {{\mathcal {Q}}}^{(4)} $conditions respectively, such that$ {\mathcal {Z}}_{a} \subset {\mathcal {Z}} _{s} $. We show the existence of a network-agnostic perfectly-secure MPC protocol tolerating$ {\mathcal {Z}}_{s} $and$ {\mathcal {Z}}_{a} $in synchronous and asynchronous networks respectively as long as the$ {{\mathcal {Q}}}^{(3, 1)} $condition is satisfied, meaning that the union of no three subsets from$ {\mathcal {Z}}_{s} $and one subset from$ {\mathcal {Z}}_{a}$covers the entire set of parties. Our result generalizes the result of Appan, Chandramouli and Choudhury (IEEE Transactions on IT, 2023), which presents the only known perfectly-secure network-agnostic MPC protocol against threshold adversaries.In this work, we initiate the study of network-agnostic perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries, where the corruption capacity of the adversary is specified through an adversary structure, which is a set of potentially corrupt subsets of parties. Known MPC protocols are designed either assuming a synchronous network where every sent message is guaranteed to be delivered within some known time or assuming an asynchronous network where no timing assumptions are made and every sent message is eventually delivered. Perfectly-secure MPC protocols in the synchronous network can be designed as long as the underlying adversary structure satisfies the$ {{\mathcal {Q}}}^{(3)}$condition, meaning that the union of no three subsets from the adversary structure covers the entire set of parties. On the other hand, perfectly-secure MPC protocols in the asynchronous network can be designed only against$ {{\mathcal {Q}}}^{(4)}$adversary structures, meaning that the union of no four subsets from the adversary structure covers the entire set of parties. A natural question is whether a single MPC protocol exists, which remains secure even if the parties are unaware of the network conditions at execution time. That is, if the synchrony is satisfied throughout the protocol execution then the protocol should be secure against any$ {{\mathcal {Q}}}^{(3)}$adversary structure. However, even if any synchrony assumption is violated during the execution, the protocol should still be secure against any$ {{\mathcal {Q}}}^{(4)}$adversary structure. We answer the above question affirmatively. Fix any adversary structure${\mathcal {Z}}_{s}$and${\mathcal {Z}}_{a}$satisfying$ {{\mathcal {Q}}}^{(3)}$and$ {{\mathcal {Q}}}^{(4)}$conditions respectively, such that${\mathcal {Z}}_{a} \subset {\mathcal {Z}} _{s}$. We show the existence of a network-agnostic perfectly-secure MPC protocol tolerating${\mathcal {Z}}_{s}$and${\mathcal {Z}}_{a}$in synchronous and asynchronous networks respectively as long as the$ {{\mathcal {Q}}}^{(3, 1)}$condition is satisfied, meaning that the union of no three subsets from${\mathcal {Z}}_{s}$and one subset from${\mathcal {Z}}_{a}$covers the entire set of parties. Our result generalizes the result of Appan, Chandramouli and Choudhury (IEEE Transactions on IT, 2023), which presents the only known perfectly-secure network-agnostic MPC protocol against threshold adversaries.

IEEE Transactions on Information TheorySep 30, 20241 citation

condition, meaning that the union of no three subsets from the adversary structure covers the entire set of parties. On the other hand, perfectly-secure MPC protocols in the asynchronous network can be designed only against

{{\mathcal {Q}}}^{(4)}

adversary structures, meaning that the union of no four subsets from the adversary structure covers the entire set of parties. A natural question is whether a single MPC protocol exists, which remains secure even if the parties are unaware of the network conditions at execution time. That is, if the synchrony is satisfied throughout the protocol execution then the protocol should be secure against any

{{\mathcal {Q}}}^{(3)}

adversary structure. However, even if any synchrony assumption is violated during the execution, the protocol should still be secure against any

{{\mathcal {Q}}}^{(4)}

adversary structure. We answer the above question affirmatively. Fix any adversary structure

{\mathcal {Z}}_{s}

and

{\mathcal {Z}}_{a}

satisfying

{{\mathcal {Q}}}^{(3)}

and

{{\mathcal {Q}}}^{(4)}

conditions respectively, such that

{\mathcal {Z}}_{a} \subset {\mathcal {Z}} _{s}

. We show the existence of a network-agnostic perfectly-secure MPC protocol tolerating

{\mathcal {Z}}_{s}

and

{\mathcal {Z}}_{a}

in synchronous and asynchronous networks respectively as long as the

{{\mathcal {Q}}}^{(3, 1)}

condition is satisfied, meaning that the union of no three subsets from

{\mathcal {Z}}_{s}

and one subset from

{\mathcal {Z}}_{a}$covers the entire set of parties. Our result generalizes the result of Appan, Chandramouli and Choudhury (IEEE Transactions on IT, 2023), which presents the only known perfectly-secure network-agnostic MPC protocol against threshold adversaries.