标题： 六边形形态哈希 HMH- 用于数据完整性验证中的安全高效密码操作同态哈希 显示英文标题

标题： HexaMorphHash HMH- Homomorphic Hashing for Secure and Efficient Cryptographic Operations in Data Integrity Verification

摘要： 在大数据和云计算领域，分布式系统被赋予了在众多节点上高效管理、存储和验证大规模数据集的任务，同时保持强大的数据完整性。 传统的哈希方法虽然简单，但由于在节点发生变化时需要全面重新哈希，在动态环境中会遇到显著的困难。 一致性哈希通过减少数据重新分布来缓解一些这些问题；然而，在密集更新条件下，它在负载均衡和可扩展性方面仍存在局限。 本文介绍了一种创新方法，使用基于格的同态哈希函数HexaMorphHash，该方法能够在保持恒定摘要大小的同时实现常数时间的增量更新。 通过利用短整数解（SIS）问题的复杂性，我们的方法提供了强大的保护措施，即使在量子威胁下也是如此。 我们进一步将我们的方法与现有的方法进行了比较，例如每次更新的直接签名、全面数据库签名、基于Merkle树的技术、AdHash、MuHash、ECMH和同态签名方案，突出了计算效率、内存使用和可扩展性方面的显著进步。 我们的贡献提供了一个可行的解决方案，用于在大型分布式系统中频繁更新的分发，同时保护数据完整性和系统性能。 显示英文摘要

摘要： In the realm of big data and cloud computing, distributed systems are tasked with proficiently managing, storing, and validating extensive datasets across numerous nodes, all while maintaining robust data integrity. Conventional hashing methods, though straightforward, encounter substan tial difficulties in dynamic settings due to the necessity for thorough rehashing when nodes are altered. Consistent hashing mitigates some of these challenges by reducing data redistribution; however, it still contends with limitations in load balancing and scalability under intensive update conditions. This paper introduces an innovative approach using a lattice based homomorphic hash function HexaMorphHash that facilitates constant time, incremental updates while preserving a constant digest size. By utilizing the complexity of the Short Integer Solutions SIS problem, our method secures strong protective measures, even against quantum threats. We further com pare our method with existing ones such as direct signatures for each update, comprehensive database signing, Merkle tree based techniques, AdHash, MuHash, ECMH, and homomorphic sig nature schemes highlighting notable advancements in computational efficiency, memory usage, and scalability. Our contributions present a viable solution for frequent update dissemination in expansive distributed systems, safeguarding both data integrity and system performance.