Welcome to the resource topic for 2025/2018
Title:
Batched and Packed (Publicly) Verifiable Secret Sharing: A Unified Framework and Applications
Authors: Shahla Atapoor, Karim Baghery, Georgio Nicolas, Robi Pedersen, Jannik Spiessens
Abstract:Verifiable Secret Sharing (VSS) allows a dealer to distribute a secret among n parties so that each can verify their share’s validity, and any qualified subset can reconstruct the secret. Publicly Verifiable Secret Sharing (PVSS) extends VSS by enabling anyone to verify the correctness of distributed shares. Both VSS and PVSS schemes are core building blocks in many cryptographic applications. We introduce a k-batched and l-packed extension of \pie, a unified framework from PKC 2025 for Shamir-based computational VSS in the synchronous setting with optimal resilience. Our framework enables the sharing and verification of l\times k secrets in a single protocol execution, offering a tunable trade-off between efficiency and robustness: the k-batched, non-packed variant (l=1) improves performance while maintaining optimal resilience, whereas the k-batched, l-packed variant achieves even greater efficiency at the cost of slightly reduced fault tolerance. Using this framework, we construct several Batched and Packed (BP) VSS and PVSS schemes that significantly reduce both computational and communication costs for the dealer and parties. When sharing many secrets, two of our VSS schemes and our PVSS scheme perform almost as efficiently as plain Shamir sharing. For example, when sharing more than 100 secrets, the overhead of our hash-based BP-VSS is below 3%, for our BP-VSS with information-theoretic privacy it remains around 8%, and for our BP-PVSS it is under 2%. These results show that verifiability in Shamir secret sharing can be achieved in post-quantum and large-scale settings with negligible overhead for the dealer. Our proposed BP-PVSS scheme is the first that can achieve these properties and outperforms existing state-of-the-art protocols. As an application, we show that our BP-PVSS yields substantial performance improvements for the ALBATROSS randomness generation protocol from ASIACRYPT 2020.
ePrint: https://eprint.iacr.org/2025/2018
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