NTRU-VRF: A Verifiable Random Function from NTRU Lattices with Applications to Post-Quantum Leader Election in Proof-of-Stake Blockchains

Abstract

We introduce NTRU-VRF, the first verifiable random function (VRF) constructed directly from the NTRU lattice hardness assumption, and instantiated concretely using the NIST-standardized Falcon-512 (FN-DSA) signature scheme. A VRF is a pseudorandom function that produces a publicly verifiable proof of correctness for each output. All currently deployed VRFs (IETF RFC 9381, Algorand, Ethereum) rely on elliptic-curve assumptions broken by Shor's algorithm. Prior post-quantum VRF constructions either require only a few-time security guarantee (Esgin et al., ePrint 2020/1222), rely on symmetric primitives that lack a worst-case lattice hardness reduction (Buser et al., ePrint 2021/302), or are based on Module-LWE/Module-SIS rather than NTRU. No prior work constructs a many-time, lattice-based VRF from NTRU hardness with a formal security proof. Our construction exploits a fundamental and previously unformalized property of Falcon's deterministic signing mode: for any fixed public key and input, there exists exactly one valid short-norm signature. This unique-signature property is the key structural feature that transforms a lattice signature into a VRF. We prove three theorems: Uniqueness: For any input, the NTRU-VRF output is unique. This follows directly from the unique-short-coset-vector property of the NTRU lattice. Pseudorandomness: If the Short Integer Solution (SIS) problem on NTRU lattices is hard and the hash function is modelled as a random oracle, then the VRF output is computationally indistinguishable from a uniformly random value. Provability: The Falcon signature is an efficient, publicly verifiable proof, checkable by any party holding the public key. As a concrete application, we define PQ-Sortition, a post-quantum proof-of-stake leader-election protocol that replaces ECVRF-based sortition with our NTRU-VRF construction. We provide the entropy-chain design, stake-weighted win condition, adaptive liveness mechanism, equivocation slashing, and a formal security analysis of the resulting consensus protocol. Instantiated with Falcon-512, NTRU-VRF achieves a VRF output of 32 bytes, a proof size of <= 666 bytes, evaluation time of ~0.8 ms, and verification time of ~0.1 ms on standard hardware—significantly outperforming all existing post-quantum VRF constructions and making it the first many-time, compact, lattice-based VRF suitable for high-throughput blockchain consensus.