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

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.