中文摘要：

基于交叉检验思想的细粒度数据完整性检验方法在实现完整性检验的同时可以对少数错误进行准确和高效的隔离,从而避免因偶然错误或个别篡改造成整体数据失效的灾难性后果.针对需要隔离多个错误时现有方案效率不高的问题,提出了多维结构下基于有限域均匀划分的完整性交叉检验方法,相应地构造了高效的多错完整性指示编码.该方法将完整性检验Hash数据分为若干组,任一组Hash可在某一中间粒度独立指示所有数据对象的完整性,多组Hash结合起来则在更小的基本粒度指示数据的完整性.该方法实现了模块化的Hash结构,对于GF（q）上的d维向量空间,每增加（d-1）组共（d-1）q个Hash即可多指示一个错.分析了该编码在不同参数下的性能,分析结论和实验结果表明该编码效率高,具有灵活的参数选择,可满足各种应用的不同需要.

英文摘要：

Fine-grained data integrity checking methods by crossing hashing could isolate a portion of corrupted data segments and assure the integrity of other data at the same time,so as to mitigate the disaster effect on the data by some random errors or intentional forging modification.To improve the efficient of current available method for multi-error cases,a new crossing-hash integrity checking method is proposed based on Galois field uniform partition of multi-dimension structure,herein an efficient integrity indication code for multi-errors case is constructed accordingly.The method has a modular hash check structure.All hashes are divided into several groups,where each group with q rows d-1 columns hashes can indicate the integrity of all data independently in a moderate grain and combined hashes of several groups can indicate the integrity of data in a finer grain.At the same time,in a d dimension vector space over GF（q）,one more error can be indicated by adding q rows d-1 columns hashes every time.Performances with various parameters of the code are analyzed.The performances analysis and experiments results show that this code can indicate multiple errors accurately and efficiently.The code provides a scalable scheme for different applications with several parameters.