With the advent of cloud-based parallel processing techniques, services such as MapReduce have been considered by many businesses and researchers for different applications of big data computation including matrix multiplication, which has drawn much attention in recent years. However, securing the computation result integrity in such systems is an important challenge, since public clouds can be vulnerable against the misbehavior of their owners (especially for economic purposes) and external attackers. In this paper, we propose an efficient approach using Merkle tree structure to verify the computation results of matrix multiplication in MapReduce systems while enduring an acceptable overhead, which makes it suitable in terms of scalability. Using the Merkle tree structure, we record fine-grained computation results in the tree nodes to make strong commitments for workers; they submit a commitment value to the verifier which is then used to challenge their computation results’ integrity using elected input data as verification samples. Evaluation outcomes show significant improvements comparing with the state-of-the-art technique; in case of 300*300 matrices, 73% reduction in generated proof size, 61% reduction in the proof construction time, and 95% reduction in the verification time.

随着基于云的并行处理技术的出现，诸如MapReduce之类的服务已被许多企业和研究人员考虑用于大数据计算的不同应用，包括矩阵乘法，这在近年来引起了很多关注。但是，在这样的系统中确保计算结果的完整性是一项重要的挑战，因为公共云可能容易受到其所有者（尤其是出于经济目的）和外部攻击者的不当行为的影响。在本文中，我们提出一种使用Merkle树结构的有效方法来验证MapReduce系统中矩阵乘法的计算结果，同时又要承受可接受的开销，这使其在可伸缩性方面很合适。使用Merkle树结构，我们在树节点中记录细粒度的计算结果，以对工作人员做出强有力的承诺；他们向验证者提交承诺值，然后使用选定的输入数据作为验证样本来挑战其计算结果的完整性。与最新技术相比，评估结果显示出显着改进；如果是300 * 300矩阵，则生成的证明尺寸减少73％，证明构建时间减少61％，验证时间减少95％。