Leveraging Weight Functions for Optimistic Responsiveness in Blockchains

ManuscriptRefereed Workshop
Simon Holmgaard Kamp and Bernardo Magri and Christian Matt and Jesper Buus Nielsen and Søren Eller Thomsen and Daniel Tschudi
Publication year: 2020

Abstract: Existing Nakamoto-style blockchains (NSBs) rely on some sort of synchrony assumption to offer any type of safety guarantees. A basic requirement is that when a party produces a new block, then all previously produced blocks should be known to that party, as otherwise the new block might not append the current head of the chain, creating a fork. In practice, however, the network delay for parties to receive messages is not a known constant, but rather varies over time. The consequence is that the parameters of the blockchain need to be set such that the time between the generation of two blocks is typically larger than the network delay (e.g., 1010 minutes in Bitcoin) to guarantee security even under bad network conditions. This results in lost efficiency for two reasons: (1) Since blocks are produced less often, there is low throughput. Furthermore, (2) blocks can only be considered final, and thus the transactions inside confirmed, once they are extended by sufficiently many other blocks, which incurs a waiting time that is a multiple of 10 minutes. This is true even if the actual network delay is only 11 second, meaning that NSBs are slow even under good network conditions. We show how the Bitcoin protocol can be adjusted such that we preserve Bitcoin’s security guarantees in the worst case, and in addition, our protocol can produce blocks arbitrarily fast and achieve optimistic responsiveness. The latter means that in periods without corruption, the confirmation time only depends on the (unknown) actual network delay instead of the known upper bound. Technically, we propose an approach where blocks are treated differently in the “longest chain rule”. The crucial parameter of our protocol is a weight function assigning different weight to blocks according to their hash value. We present a framework for analyzing different weight functions, in which we prove all statements at the appropriate level of abstraction. This allows us to quickly derive protocol guarantees for different weight functions. We exemplify the usefulness of our framework by capturing the classical Bitcoin protocol as well as exponentially growing functions as special cases, where the latter provide the above mentioned guarantees, including optimistic responsivene

Refresh When You Wake Up: Proactive Threshold Wallets with Offline Devices

ManuscriptRefereed Workshop
Yashvanth Kondi, Bernardo Magri, Claudio Orlandi and Omer Shlomovits
Publication year: 2019

Abstract: Proactive security is the notion of defending a distributed system against an attacker who compromises different devices through its lifetime, but no more than a threshold number of them at any given time. The emergence of threshold wallets for more secure cryptocurrency custody warrants an efficient proactivization protocol tailored to this setting. While many proactivization protocols have been devised and studied in the literature, none of them have communication patterns ideal for threshold wallets. In particular a (t,n) threshold wallet is designed to have t parties jointly sign a transaction (of which only one may be honest) whereas even the best current proactivization protocols require at least an additional thonest parties to come online simultaneously to refresh the system.

In this work we formulate the notion of refresh with offline devices, where any tparties (no honest majority) may proactivize the system at any time and the remaining nt offline parties can non-interactively “catch up” at their leisure. However due to the inherent unfairness of dishonest majority MPC, many subtle issues arise in realizing this pattern. We discuss these challenges, yet give a highly efficient protocol to upgrade a number of standard (2,n) threshold signature schemes to proactive security with offline refresh. Our approach involves a threshold signature internal to the system itself, carefully interleaved with the larger threshold signing. We design our protocols so that they can augment existing implementations of threshold wallets for immediate use– we show that proactivization does not have to interfere with their native mode of operation.

Our proactivization technique is compatible with Schnorr, EdDSA, and even sophisticated ECDSA protocols, while requiring no extra assumptions. By implementation we show that proactivizing two different recent (2,n) ECDSA protocols incurs only 14% and 24% computational overhead respectively, less than 200 bytes, and no extra round of communication.

Category / Keywords: cryptographic protocols / threshold cryptography; key management; digital signatures; oblivious transfer

Afgjort: A Partially Synchronous Finality Layer for Blockchains

ManuscriptRefereed Workshop
Bernardo Magri, Christian Matt, Jesper Buus Nielsen and Daniel Tschudi
Publication year: 2019

Abstract: Most existing blockchains either rely on a Nakamoto-style of consensus, where the chain can fork and produce rollbacks, or on a committee-based Byzantine fault tolerant (CBFT) consensus, where no rollbacks are possible. While the latter ones offer better consistency, the former can be more efficient, tolerate more corruptions, and offer better availability during bad network conditions. To achieve the best of both worlds, we initiate the formal study of finality layers. Such a finality layer can be combined with a Nakamoto-style blockchain and periodically declare blocks as final, preventing rollbacks beyond final blocks.

As conceptual contributions, we identify the following properties to be crucial for a finality layer: finalized blocks form a chain (chain-forming), all parties agree on the finalized blocks (agreement), the last finalized block does not fall too far behind the last block in the underlying blockchain (updated), and all finalized blocks at some point have been on the chain adopted by at least k honest parties (k-support).

As technical contributions, we propose two variants of a finality layer protocol. The first variant satisfies all of the aforementioned requirements (with k=1) when combined with an arbitrary blockchain that satisfies the usual common-prefix, chain-growth, and chain-quality properties. The second one needs an additional, mild assumption on the underlying blockchain, but is more efficient and satisfies k=n/3-support. We prove both of them secure in the setting with t<n/3 Byzantine parties and a partially synchronous network. We finally show that t<n/3 is optimal for partially synchronous finality layers.

Category / Keywords: cryptographic protocols / blockchain, finality, Byzantine agreement

Paper presented at the PENCIL workshop co-located with EuroCrypt 2019