Post-Quantum Verifiable Random Function from Symmetric Primitives in PoS Blockchain

Maxime Buser, Rafael Dowsley, Muhammed F. Esgin, Shabnam Kasra Kermanshahi, Veronika Kuchta, Joseph K. Liu, Raphaël C.-W. Phan, Zhenfei Zhang

Abstract: Verifiable Random Functions (VRFs) play a key role in Proof-of-Stake blockchains such as Algorand to achieve highly scalable consensus, but currently deployed VRFs lack post-quantum security, which is crucial for future-readiness of blockchain systems. This work presents the first quantum-safe VRF scheme based on symmetric primitives. Our main proposal is a practical many-time quantum-safe VRF construction, \(\mathsf {X\hbox {-}VRF}\), based on the \(\textsf{XMSS}\) signature scheme. An innovation of our work is to use the state of the blockchain to counter the undesired stateful nature of \(\textsf{XMSS}\) by constructing a blockchain-empowered VRF. While increasing the usability of \(\textsf{XMSS}\), our technique also enforces honest behavior when creating an \(\mathsf {X\hbox {-}VRF}\) output so as to satisfy the fundamental uniqueness property of VRFs. We show how \(\mathsf {X\hbox {-}VRF}\) can be used in the Algorand setting to extend it to a quantum-safe blockchain and provide four instances of \(\mathsf {X\hbox {-}VRF}\) with different key life-time. Our extensive performance evaluation, analysis and implementation indicate the effectiveness of our proposed constructions in practice. Particularly, we demonstrate that \(\mathsf {X\hbox {-}VRF}\) is the most efficient quantum-safe VRF with a maximum proof size of 3 KB and a possible TPS of 449 for a network of thousand nodes.