Publicly Verifiable Delegation of Matrix Operation

Given the emergence of verifiable computation, it has made an approach to deal with the security bottlenecks in cloud computing. In this paper, we present two public verifiable delegation schemes for polynomials and matrix multiplication. Since cloud providers may not be trusted, a weak client will outsource a function f and encoded input sigma(x). After evaluating, the server returns related result along with signature w guarantying the correctness of computation. Roughly speaking, our constructions are mainly based on decision Diffie-Hellman assumption and bilinear group. Comparing with previous solutions, ours could preserve the input privacy and achieve publicly efficient verification for univariate polynomial evaluation and then extend to matrix multiplication.