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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.

Efficient verification of parallel matrix multiplication in public cloud: the MapReduce case