[Paper Review] Homomorphic Sortition -- Secret Leader Election for PoS Blockchains

Luciano Freitas de Souza, Andrei Tonkikh+5 more|arXiv (Cornell University)|Jun 23, 2022

Distributed systems and fault tolerance5 citations

TL;DR

This paper introduces Homomorphic Sortition, the first asynchronous Single Secret Leader Election (SSLE) protocol with non-expiring registration, enabling secure and efficient leader selection in partially-synchronous proof-of-stake (PoS) blockchains. It leverages Threshold Fully Homomorphic Encryption (ThFHE) to allow parallel, stateless elections without re-registration, supporting arbitrary stake distributions and enabling deterministic termination with strong security guarantees.

ABSTRACT

In a single secret leader election protocol (SSLE), one of the system participants is chosen and, unless it decides to reveal itself, no other participant can identify it. SSLE has a great potential in protecting blockchain consensus protocols against denial of service (DoS) attacks. However, all existing solutions either make strong synchrony assumptions or have expiring registration, meaning that they require elected processes to re-register themselves before they can be re-elected again. This, in turn, prohibits the use of these SSLE protocols to elect leaders in partially-synchronous consensus protocols as there may be long periods of network instability when no new blocks are decided and, thus, no new registrations (or re-registrations) are possible. In this paper, we propose Homomorphic Sortition -- the first asynchronous SSLE protocol with non-expiring registration, making it the first solution compatible with partially-synchronous leader-based consensus protocols. Homomorphic Sortition relies on Threshold Fully Homomorphic Encryption (ThFHE) and is tailored to proof-of-stake (PoS) blockchains, with several important optimizations with respect to prior proposals. In particular, unlike most existing SSLE protocols, it works with arbitrary stake distributions and does not require a user with multiple coins to be registered multiple times. Our protocol is highly parallelizable and can be run completely off-chain after setup. Some blockchains require a sequence of rounds to have non-repeating leaders. We define a generalization of SSLE, called Secret Leader Permutation (SLP) in which the application can choose how many non-repeating leaders should be output in a sequence of rounds and we show how Homomorphic Sortition also solves this problem.

Motivation & Objective

• To address the limitations of existing SSLE protocols that require expiring registration or rely on synchrony assumptions.
• To design an SSLE protocol compatible with partially-synchronous consensus protocols, where long network delays can prevent re-registration.
• To support arbitrary stake distributions without requiring multi-entry registration for users with multiple coins.
• To enable efficient, off-chain execution of leader elections with high parallelism.
• To generalize SSLE to Secret Leader Permutation (SLP), supporting sequences of non-repeating leaders.

Proposed method

• The protocol uses Threshold Fully Homomorphic Encryption (ThFHE) to enable homomorphic evaluation of leader election logic over encrypted stakes.
• Each participant encrypts their stake using a shared public key, and the election is computed homomorphically without revealing individual stakes.
• The leader is selected via a deterministic, verifiable function applied to the encrypted stake vector, with output decrypted only after the election completes.
• The protocol supports non-expiring registration: elected participants do not need to re-register, enabling long-term participation across rounds.
• The system is designed to be highly parallelizable and can be executed entirely off-chain after an initial setup phase.
• A generalization to Secret Leader Permutation (SLP) is achieved by composing multiple independent elections with constraints on leader repetition.

Experimental results

Research questions

• RQ1 Can a secret leader election protocol be designed to work in asynchronous systems without requiring re-registration after election?
• RQ2 Is it possible to support arbitrary stake distributions in SSLE without requiring multiple registrations per user?
• RQ3 Can ThFHE be efficiently applied to build a scalable, off-chain SSLE protocol for PoS blockchains?
• RQ4 How can SSLE be extended to support sequences of non-repeating leaders (SLP) in a secure and efficient manner?
• RQ5 What are the performance and security trade-offs of using ThFHE in a practical blockchain setting?

Key findings

• Homomorphic Sortition is the first asynchronous SSLE protocol with non-expiring registration, making it compatible with partially-synchronous consensus protocols.
• The protocol supports arbitrary stake distributions without requiring users with multiple coins to register multiple times.
• It enables fully off-chain execution of elections, with high parallelism and no state maintenance by elected leaders.
• The protocol achieves deterministic termination and provides strong security guarantees under the assumption of bounded adversarial stake.
• The authors demonstrate that their approach generalizes naturally to Secret Leader Permutation (SLP), supporting sequences of non-repeating leaders.
• Performance evaluation is ongoing, but the design is optimized for use with state-of-the-art ThFHE protocols and SIMD-friendly arithmetic circuits.