  Asset custody is a core financial service in which the custodian holds
in-safekeeping assets on behalf of the client. Although traditional custody
service is typically endorsed by centralized authorities, decentralized custody
scheme has become technically feasible since the emergence of digital assets,
and furthermore, it is greatly needed by new applications such as blockchain
and DeFi (Decentralized Finance).
  In this work, we propose a framework of decentralized asset custody scheme
that is able to support a large number of custodians and safely hold customer
assets of multiple times the value of the total security deposit. The proposed
custody scheme distributes custodians and assets into many custodian groups via
combinatorial designs, where each group fully controls the assigned assets.
Since every custodian group is small, the overhead cost is significantly
reduced. The liveness is also improved because even a single alive group would
be able to process transactions.
  The security of this custody scheme is guaranteed under the rational
adversary model, such that any adversary corrupting a bounded fraction of
custodians cannot move assets more than the security deposit paid. We further
analyze the security and performance of our constructions from both theoretical
and experimental sides and give explicit examples with concrete numbers and
figures for a better understanding of our results.
