Paper 2022/266 Original: eprint.iacr.org/2022/266 ↗

Verifiably Distributed Multi-User Secret Sharing schemes

Abstract

Distributed secret sharing techniques, where a specific secret is encoded into its shares which are conveyed to the IoT device or its user via storage nodes, are considered. A verifiably distributed secret sharing (VDSS) provides a way for a legitimate user to verify the secret he reconstructs through the downloaded shares while the secrecy condition is satisfied in a weak or a perfect sense. This article examines the impact of minimizing verification information in a VDSS on the communication complexity and storage overhead, and achieves the verifiability in resource-limited IoTs by aggregating the verification information of different devices/users. Then, two secure VDSS are proposed. The first VDSS attains the lower bound on the communication complexity while providing the fault tolerance. The second VDSS simultaneously achieves the lower bounds of both communication complexity and storage overhead while providing the balanced storage load, thus showing the scheme that is optimal in terms of both parameters.