LightBEAT: Scalable Epochless Batched Threshold Encryption via Hierarchical Identity-Based Puncturing

Threshold-encrypted mempools protect users from maximal extractable value (MEV) by keeping transactions private until block inclusion. Batched threshold encryption (BTE) enables succinct decryption of a block-sized batch, but the state-of-the-art epochless protocol BEAT-MEV suffers a prohibitiveO(N2) setup and storage overhead from its pairwise-key construction, whereNdenotes the identity universe. In sparse operating regimes with large identity universes and comparatively small active batches (B≪N), this quadratic bottleneck pushes deployments toward bucketing strategies that reintroduce succinctness pressure. In this work, we propose LightBEAT, an epochless BTE protocol that replaces the flat pairwise puncturable layer with HIDP (Hierarchical ID-based Puncturing), a hierarchical construction derived from hierarchical identity-based encryption (HIBE) delegation. This change reduces the setup complexity toO(Nlog2N) and supports large sparse identity spaces without the same flat pairwise storage wall. Our analysis and evaluation show that LightBEAT preserves constant-size per-user ciphertext objects and constant-size per-member decryption shares, while leaving validator-side combine costs and deployment integration as explicit system-level concerns.