Abstract
We introduce the Byzantine Approximate Agreement Cross-chain Task in the smart contract model, a recently proposed framework for capturing computation in blockchain-based systems. In this model, a set of m parties, of which up to a minority may be Byzantine, interact via n trusted smart contracts deployed on multiple independent ledgers (blockchains).
We present two protocols that solve the Byzantine Approximate Agreement Cross-chain Task and prove their correctness. Both protocols are optimal with respect to Byzantine resilience - tolerating a minority of Byzantine parties - and time complexity, completing in two rounds in synchronous executions. We further analyze their bit complexity within the smart contract model. The first protocol requires O(k) 𝓞(k) bits of local memory per party, where k denotes the number of bits needed to encode the proposed values, and achieves a total message bit complexity of O(n·m·k) 𝓞(n⋅ m⋅ k) . The second protocol reduces the local memory usage at each party to O(1) 𝓞(1) bits, at the cost of increasing the total message bit complexity to O(n2·m·k) 𝓞(n²⋅ m⋅ k) .