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.

翻译：我们提出了一种安全且私密的基于区块链的可验证随机函数方案，旨在解决经典可验证随机函数构造的局限性。鉴于量子计算攻击场景的临近，传统密码学方法面临脆弱性。为增强可验证随机函数的安全随机性，我们采用后量子Ring-LWE加密来合成伪随机序列。考虑到计算成本及由此产生的链上燃料消耗，我们建议采用一种分叉架构设计可验证随机函数，优化链上与链下的交互。我们的方法采用基于NIZK证明的安全环签名和受Chaum-Pedersen等式证明及Fiat-Shamir启发式启发的委托密钥生成方法。该可验证随机函数方案将多方安全计算与基于区块链的去中心化标识相结合，确保安全性与随机性。我们阐明了可验证随机函数方案的安全与隐私方面特性，分析了时间与空间复杂度，并近似计算了方案熵值，详细描述了其在Solidity合约中的实现。同时，我们阐述了一种验证可验证随机函数证明的方法，适用于需要随机性与验证性的场景。最终，使用NIST SP800-22统计随机性测试套件，我们的结果在11个测试案例中达到98.86%的通过率，176次总测试的平均p值为0.5459。