A Quantum-resistant Threshold Signature Scheme for Database Audit Logs
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摘要: 随着量子计算的迅猛发展，数据库审计日志中常用的RSA, ECDSA等经典数字签名机制因依赖大整数分解与离散对数等难题而在Shor算法下面临失效风险，同时Grover算法对哈希函数及对称密码的攻击复杂度降低也进一步削弱了现有审计机制的长期安全性。为提升审计日志在云计算与大数据环境中的完整性与可追溯能力，有必要构建能够抵御量子攻击的审计签名体系。为此，该文采用抗量子密码学原理，以FORS少次签名与XMSS-T树型结构为基础构建量子安全签名层，结合Shamir门限秘密共享机制实现私钥的安全分发与分布式管理，并利用链式哈希结构确保日志在存储与传输过程中的不可篡改性。安全性分析表明，该机制在量子随机预言机模型下满足不可伪造性与机密性要求，并具备抵御量子攻击的能力。实验结果进一步验证了体系在高并发日志场景下保持较低签名延迟与稳定吞吐率，且在不同日志规模与消息大小下表现出良好的扩展性，适用于大规模分布式数据库审计环境。Abstract:
Objective Database audit logs are a core basis for ensuring data integrity, accountability, and traceability in distributed systems. However, current audit-log protection mechanisms still rely on classical public-key signature algorithms such as RSA and ECDSA, which are vulnerable to quantum attacks. Shor’s algorithm can break integer-factorization- and discrete-logarithm-based cryptography in polynomial time, while Grover’s algorithm reduces the brute-force security of hash-based and symmetric primitives. These threats weaken the long-term reliability of existing database audit-log protection mechanisms in cloud and data-intensive environments. To address this issue, a quantum-resistant framework for database audit logs is proposed to satisfy practical requirements for efficiency, real-time verification, scalable deployment, and distributed trust management. The goal is to provide a robust cryptographic foundation for next-generation database audit-log systems with unforgeability and tamper resistance under quantum threats. Methods A hybrid hash-based signature layer is constructed by combining Few-Time Signature (FORS) and eXtended Merkle Signature Scheme-Tree (XMSS-T). FORS supports efficient signing for high-frequency log events, whereas XMSS-T organizes authentication paths in a Merkle-tree hierarchy for scalable state management. This combination yields a multi-level quantum-resistant signing structure. A Shamir (r,n) threshold secret-sharing mechanism is then adopted to split the signing key into multiple shares managed by independent audit agents. This design avoids a single point of failure, supports collaborative attestation, and ensures that no single party holds complete signing authority. In addition, a chained-hash structure is used to bind consecutive log entries through one-way linkage, thereby ensuring tamper evidence and chronological integrity. The framework further defines a complete set of system algorithms, including setup, key distribution, partial-signature generation, signature aggregation, log-chain update, and verification, all of which operate efficiently in a distributed setting. For formal security analysis, the scheme is modeled in the Quantum Random Oracle Model (QROM), and adversarial capabilities are characterized through UF-CMA, IND-CCA2, and IND-CKA2 games to capture forgery, decryption misuse, and index-indistinguishability attacks. A prototype implementation is developed and evaluated under realistic multi-node settings across different log scales, message sizes, interval configurations, and threshold ratios. Results and Discussions Experimental results show that the proposed scheme achieves a good balance between quantum-resistant security and system performance. For large-scale logs, the average signing latency increases linearly with log volume, which supports the efficiency of the chained-hash structure ( Table 2 ). Compared with representative quantum-resistant signatures such as Dilithium and SPHINCS+, the threshold-signing design reduces the peak computational burden on individual nodes while preserving strong security guarantees. The system also maintains a stable throughput of about 2 000 operations per second. The message-size analysis shows that latency increases with message size but remains manageable even when the message exceeds 4 kB (Fig. 2(b) ). Additionally, variation in the threshold ratio (r/n) has a measurable but moderate effect on system latency. A higher threshold improves resistance to collusion, but slightly increases delay (Fig. 2(e) ). The interval-based chained-signing strategy further reduces the signing frequency and improves throughput without weakening log-integrity guarantees. These results indicate that the proposed scheme is well suited to cloud-based and distributed database environments that require real-time auditing and high-volume log processing.Conclusions A quantum-resistant mechanism for database audit logs is presented by integrating hash-based signatures, threshold secret sharing, and chained log-integrity protection. The scheme provides strong quantum-resistant security guarantees, including provable unforgeability, confidentiality, and tamper resistance, supported by formal proofs in the QROM. Experimental results show that the mechanism maintains high signing and verification efficiency under large-scale deployment, with good scalability across different log volumes, message sizes, and threshold settings. Owing to its distributed trust model and quantum-resistant cryptographic basis, the proposed scheme offers a practical and secure solution for next-generation database audit systems in cloud computing, big-data processing, and compliance-critical environments. -
表 1 系统符号表
符号 含义 $ {1}^{\lambda } $ 安全参数(后量子安全) $ p,q $ 大质数 (Shamir域和哈希/输出长度控制) $ {Z}_{p} $ Shamir多项式运算的有限域 $ G $ 基于椭圆曲线的循环群,阶为$ q $ $ P $ 循环群生成元 msk 密钥管理中心(KMC)主私钥 mpk KMC主公钥$ \text{mpk}=\alpha P $ $ \mathrm{s}{\mathrm{k}}_{{{\mathrm{share}},i}} $ 签名参与方第$ i $个私钥分片 $ \mathrm{p}{\mathrm{k}}_{\text{global}} $ 系统全局公钥, 由XMSS-T签名FORS公钥生成 $ \text{LogChai}{\text{n}}_{i} $ 日志链节点，包括${d}_{i} $, ${h}_{i-1} $, $ {t}_{i} $ $ {d}_{i} $ 日志具体审计数据 $ {h}_{i} $ 日志链哈希值 $ {t}_{i} $ 日志时间戳 $ {\sigma }_{i} $ 节点签名，由FORS+XMSS-T生成 $ {K}_{\text{enc}}{,K}_{\text{hash}} $ 对称加密和索引哈希密钥 $ {H}_{1},{H}_{2},{H}_{3} $ 抗碰撞哈希函数, 用于身份验证、加密、签名验证 PRF 伪随机函数，用于生成FORS叶节点私钥 
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表 2 不同日志规模下的签名性能数据(消息大小:1 kB，签名对所有日志)
日志数 方案 签名数 平均延迟 (ms) 吞吐 (ops/s) 最大/最小延迟 (ms) 总耗时 (s) 标准差(ms) 10 000 ECDSA 10000 0.314 3 226 1.22/0.22 3.11 0.03 10 000 Dilithium 10000 0.392 2 564 1.10/0.30 3.90 0.05 10 000 SPHINCS+ 10000 0.655 1 538 1.19/0.50 6.52 0.11 10 000 Our Scheme 10000 0.453 2 222 2.92/0.10 4.50 0.25 50 000 ECDSA 50000 0.310 3 226 1.55/0.24 15.56 0.04 50 000 Dilithium 50000 0.419 2 413 1.21/0.31 20.72 0.06 50 000 SPHINCS+ 50000 0.706 1 429 6.04/0.51 35.23 0.12 50 000 Our Scheme 50000 0.484 2 083 3.20/0.11 24.16 0.30 100 000 ECDSA 100000 0.322 3 125 1.88/0.25 32.04 0.05 100 000 Dilithium 100000 0.431 2 326 12.10/0.31 43.80 0.08 100 000 SPHINCS+ 100000 0.783 1 282 11.40/0.51 78.37 0.15 100 000 Our Scheme 100000 0.551 1 818 5.31/0.38 55.72 0.78 500 000 ECDSA 500000 0.339 2 941 5.33/0.25 170.82 0.13 500 000 Dilithium 500000 0.485 2 083 10.71/0.31 240.16 0.22 500 000 SPHINCS+ 500000 0.848 1 176 15.81/0.52 425.19 0.41 500 000 Our Scheme 500000 0.756 1 333 30.09/0.10 375.19 2.49 1 000 000 ECDSA 1000000 0.361 2 777 12.11/0.26 360.26 0.16 1 000 000 Dilithium 1000000 0.520 1 923 16.32/0.31 520.75 0.28 1 000 000 SPHINCS+ 1000000 0.857 1 176 20.78/0.51 850.02 0.62 1 000 000 Our Scheme 1000000 0.952 1 053 52.45/0.10 950.42 4.98
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表 3 本方案在不同消息大小下的性能对比(日志数量=100 000条)
消息大小(kB) 平均延迟 (ms) 吞吐率(ops/s) 总时间 (s) 最大/最小延迟 (ms) 标准差 (ms) 0.5 0.522 1 923 52.13 3.40/0.35 0.83 1.0 0.551 1 818 55.72 5.31/0.38 0.78 2.0 0.619 1 667 60.98 10.47/0.43 0.91 4.0 0.750 1 333 75.43 12.61/0.55 2.54 8.0 0.824 1 220 82.41 15.48/0.60 3.17 16.0 0.956 1 053 95.56 20.06/0.75 5.42
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