Handel: Practical multi-signature aggregation for large byzantine committees

Nicolas Gailly

# Introduction

Handle is a aggregation protocol for large scale byzantine committees. This is work with my colleagues in addition to myself.

# Why aggregate?

Distributed systems often require gathering statements about large subsets of nodes. However, processing (filtering, aggregating...) measurements can be a bottleneck. We want to apply some processing while collecting the measurements.

# Why byzantine?

A byzantine node is a node that can be arbitrary. It can be offline and it can be anything it wants and it doesn't need to respect the protocol specification. In proof-of-stake consensus protocols, you have designated leaders and validators attest the validity of a new block by issuing a signature which gets aggregated into one small signature.

Security is impacted by the number of signatures aggregated ("the bigger, the better"). Scalability is impacted by the aggregation protocol completion time with respect to the number of nodes.

# Aggregation methods

Direct retrieval: A central server contacts all other nodes to get their statements. This is O(n) and it's inefficient.

Tree nodes could send aggregate from children nodes to parent nodes. This is O(log(n)) but failure is costly, causing restructuring of trees.

Another method is "complete graph" where each node contacts all other nodes to gather their statements. It's robust but this requires O(n^{2}) time and communication.

Another method is "gossipping" where each node gossips their statements on a gossipping relay network. You contact k neighbors randomly, updates, and repeat. This is robust but it's bandwidth-inefficient with large numbers of nodes to aggregate. See Makhloufi et al. 2009.

# Handel: problem statement

We want to aggregate thousands of statements in seconds. We want time complexity of O(log(n)) on average. We want a system where there's a delay but nobody knows the delay. We want fairness, where the ratio of honest contributions over honest nodes converges towards 1. We want efficiency- resource consumption of CPU bandwidth and memory should also be in O(log(n)) in average. Handel does not guarantee uniformity of the results from honest nodes.

# Aggregation function

We are looking at aggregation functions which satisfy commutativity and associativity. A valid statement is a statement verified by function V such that V(statement, public information) = 1. This is a perfect fit for multi-signature schemes like BLS multi-signatures from Boneh et al. 2003.

# Binomial swap forest

Before we talk about how it works, I want to review some techniques called binomial swap forests which was introduced by Cappos 10 years ago or San Fermin. This makes an aggregation framework in time O(n). With a binomial swap forest, each node constructs its own tree. We start by contacting the immediate next node. Then we take those groups and repeat the same protocol with these pairwise groups as the new nodes in the next round. The last one of them will swap half of the contribution at the last phase.

San Fermin is defined in the fail-stop model where a crash is detected via a timeout. Upon timeout, a node sends request to next node in a target group. The timeout serves to detect crashes. The key parameter (timeouts) could be too short- nodes may be evicted too early, or the key parameter might be too long- which increases completion time linearly.

Now I will talk about a byzantine actor in the binomial swap forest. Also, there needs to be byzantine ffault tolerance.

There's concurrent levels and a few other methods.