  We present a secure and private blockchain-based Verifiable Random Function
(VRF) scheme addressing some limitations of classical VRF constructions. Given
the imminent quantum computing adversarial scenario, conventional cryptographic
methods face vulnerabilities. To enhance our VRF's secure randomness, we adopt
post-quantum Ring-LWE encryption for synthesizing pseudo-random sequences.
Considering computational costs and resultant on-chain gas costs, we suggest a
bifurcated architecture for VRF design, optimizing interactions between
on-chain and off-chain. Our approach employs a secure ring signature supported
by NIZK proof and a delegated key generation method, inspired by the
Chaum-Pedersen equality proof and the Fiat-Shamir Heuristic. Our VRF scheme
integrates multi-party computation (MPC) with blockchain-based decentralized
identifiers (DID), ensuring both security and randomness. We elucidate the
security and privacy aspects of our VRF scheme, analyzing temporal and spatial
complexities. We also approximate the entropy of the VRF scheme and detail its
implementation in a Solidity contract. Also, we delineate a method for
validating the VRF's proof, matching for the contexts requiring both randomness
and verification. Conclusively, using the NIST SP800-22 of the statistical
randomness test suite, our results exhibit a 98.86% pass rate over 11 test
cases, with an average p-value of 0.5459 from 176 total tests.
