In this study, we present a secure smart contract-based Verifiable Random Function (VRF) model, addressing the shortcomings of existing systems. As quantum computing emerges, conventional public key cryptography faces potential vulnerabilities. To enhance our VRF's robustness, we employ post-quantum Ring-LWE encryption for generating pseudo-random sequences. Given the computational intensity of this approach and associated on-chain gas costs, we propose a hybrid architecture of VRF system where on-chain and off-chain can communicate in a scalable and secure way. To ensure the validity and integrity of the off-chain computations (e.g., Ring-LWE encryption), we employ a quantum-secure linkable ring signature scheme on NTRU lattice and also delegated key generation (DKG) with a secure key encapsulation mechanism (KEM). Our decentralized VRF employs multi-party computation (MPC) with blockchain-based decentralized identifiers (DID), ensuring the collective efforts of enhanced randomness and security. We show the security and privacy advantages of our proposed VRF model with the approximated estimation of overall temporal and spatial complexities. We also evaluate our VRF MPC model's entropy and outline its Solidity smart contract integration. This research also provides a method to produce and verify the VRF output's proof, optimal for scenarios necessitating randomness and validation. Lastly, using NIST SP800-22 test suite for randomness, we demonstrate the commendable result with a 97.73% overall pass rate on 11 standard tests and 0.5459 of average p-value for the total 176 tests.

翻译：本研究提出一种基于安全智能合约的可验证随机函数（VRF）模型，以解决现有系统的缺陷。随着量子计算时代的到来，传统公钥密码学面临潜在安全隐患。为增强VRF的鲁棒性，我们采用后量子Ring-LWE加密算法生成伪随机序列。鉴于该方法的计算密集性及链上Gas成本问题，我们提出一种链上链下可扩展安全通信的VRF混合架构。为确保链下计算（如Ring-LWE加密）的有效性与完整性，我们采用基于NTRU格的量子安全可链接环签名方案，并结合安全密钥封装机制（KEM）实现委托密钥生成（DKG）。该去中心化VRF通过多方计算（MPC）与基于区块链的去中心化标识（DID），实现增强随机性与安全性的集体协作。通过时空复杂度的近似估计，我们展示了所提VRF模型的安全与隐私优势，并评估了VRF-MPC模型的熵值，概述其与Solidity智能合约的集成方案。本研究还提供VRF输出证明的生成与验证方法，特别适用于需随机性与验证的场景。最后，通过NIST SP800-22随机性测试套件验证，11项标准测试整体通过率达97.73%，176项测试平均p值为0.5459，表现优异。