Paper 2026/1258

Beyond Anonymity Sets: A Security Model for Distributed Shuffling in Adversarial Environments

Abstract

Distributed shuffling is a core primitive underlying mix-nets, electronic voting, and, more recently, single secret leader election (SSLE) protocols for proof-of-stake blockchains. In these settings, a collection of resource-constrained parties jointly permutes a list of ciphertexts or commitments in order to conceal the correspondence between inputs and outputs. Existing security analyses of such protocols typically rely on heuristic anonymity measures or implicitly assume honest behavior; therefore, they fail to capture statistical dependencies that arise when shuffling is partial and some participants are corrupted. In this work, we introduce a new security model for distributed shuffling that accurately reflects the setting of real-world attacks by explicitly accounting for adversarial corruption and information leakage. Our model allows an adversary to corrupt a subset of shufflers and track selected elements throughout the execution, as well as query the resulting permutation afterwards. We then turn to studying Whisk in this model, the shuffle-based SSLE mechanism proposed for Ethereum. Leveraging Markov-chain techniques, we show that security can only be guaranteed for more stringent parameters than currently proposed. We evaluate the performance impact of changing these parameters on the Ethereum network.