Divide and Scale: Formalization and Roadmap to Robust Sharding

TL;DR

This paper introduces a formal framework and roadmap for robust sharding in blockchain systems, defining key properties, limitations, and components necessary for secure and scalable distributed ledgers.

Contribution

It provides the first formal model for sharding, analyzes its limitations under adversarial conditions, and proposes a protocol abstraction called Divide & Scale.

Findings

Sharded ledgers cannot scale under fully adaptive adversaries.

Scalability is achievable up to m shards with epoch-adaptive adversaries, given succinct proofs.

Existing sharded blockchains often fail to meet the desired security and scalability properties.

Abstract

Sharding distributed ledgers is a promising on-chain solution for scaling blockchains but lacks formal grounds, nurturing skepticism on whether such complex systems can scale blockchains securely. We fill this gap by introducing the first formal framework as well as a roadmap to robust sharding. In particular, we first define the properties sharded distributed ledgers should fulfill. We build upon and extend the Bitcoin backbone protocol by defining consistency and scalability. Consistency encompasses the need for atomic execution of cross-shard transactions to preserve safety, whereas scalability encapsulates the speedup a sharded system can gain in comparison to a non-sharded system. Using our model, we explore the limitations of sharding. We show that a sharded ledger with $n$ participants cannot scale under a fully adaptive adversary, but it can scale up to $m$ shards where $n=c'm\log m$, under an epoch-adaptive adversary; the constant $c'$ encompasses the trade-off between security and scalability. This is possible only if the sharded ledgers create succinct proofs of the valid state updates at every epoch. We leverage our results to identify the sufficient components for robust sharding, which we incorporate in a protocol abstraction termed Divide & Scale. To demonstrate the power of our framework, we analyze the most prominent sharded blockchains (Elastico, Monoxide, OmniLedger, RapidChain) and pinpoint where they fail to meet the desired properties.