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私密的基于区块链的可验证随机函数（VRF）方案，解决了经典VRF构造的若干局限性。鉴于量子计算攻击场景的现实威胁，传统密码学方法面临安全漏洞。为增强VRF的随机安全性，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Gas费用，我们提出了VRF设计的双分支架构，优化了链上-链下交互。该方法采用由NIZK证明支持的安全环签名和委托密钥生成技术，其设计灵感源于Chaum-Pedersen等式证明和Fiat-Shamir启发式方法。我们提出的VRF方案将多方计算（MPC）与基于区块链的去中心化标识符（DID）相结合，同时确保安全性与随机性。我们阐释了VRF方案的安全与隐私特性，分析了其时间与空间复杂度，估算了VRF方案的熵值，并详细说明了其在Solidity智能合约中的实现。此外，我们提出了一种验证VRF证明的方法，适用于同时需要随机性和可验证性的场景。最终，采用NIST SP800-22统计随机性测试套件，本方案在11个测试案例中通过率达98.86%，总计176次测试的平均p值为0.5459。