## Cryptology ePrint Archive: Report 2020/675

Ledger Combiners for Fast Settlement

Matthias Fitzi and Peter Gazi and Aggelos Kiayias and Alexander Russell

Abstract: Blockchain protocols based on variations of the longest-chain rule--whether following the proof-of-work paradigm or one of its alternatives--suffer from a fundamental latency barrier. This arises from the need to collect a sufficient number of blocks on top of a transaction-bearing block to guarantee the transaction's stability while limiting the rate at which blocks can be created in order to prevent security-threatening forks.

Our main result is a black-box security-amplifying combiner based on parallel composition of $m$ blockchains that achieves $\Theta(m)$-fold security amplification or, equivalently, $\Theta(m)$-fold reduction in latency. Our construction breaks the latency barrier to achieve, for the first time, a worst-case constant-time-settlement ledger based purely on Nakamoto longest-chain consensus: Transaction settlement can be accelerated to a constant multiple of block propagation time with negligible error.

Operationally, our construction shows how to view any family of blockchains as a unified, virtual ledger without requiring any coordination among the chains or any new protocol metadata. Users of the system have the option to inject a transaction into a single constituent blockchain or--if they desire accelerated settlement--all of the constituent blockchains. Our presentation and proofs introduce a new formalism for reasoning about blockchains, the dynamic ledger, and articulate our constructions as transformations of dynamic ledgers that amplify security. We additionally illustrate the versatility of this formalism by presenting a class of robust-combiner constructions for blockchains that can protect against complete adversarial control of a minority of a family of blockchains.

Category / Keywords: cryptographic protocols / blockchain, amplification, combiner, ledger, proof-of-work, proof-of-stake