A scalable post-quantum hash-based group signature

Abstract

We present a construction for hash-based one-time group signature schemes, and develop a traceable post-quantum multi-time group signature upon it. A group signature scheme allows group members to anonymously sign a message on behalf of the entire group. The signatures are unforgeable, and the scheme enables authorized openers to trace the signature back to the original signer when needed. Our construction utilizes three nested layers to build the group signature scheme. The first layer performs the key-management task; it deploys a transversal design to assign keys to the group members and the openers, establishing anonymity and providing the construction with traceability. The second layer utilizes sets of hash values, hash pools, to build the group public verification key and to connect group members together. The final layer uses a post-quantum hash-based signature scheme, that adds unforgeability to our construction. We extend our scheme to multi-time signatures using Merkle trees and show that this process maintains the scalability property of Merkle-based signatures, while it supports the group members signing any number of messages.