矩阵乘积的高效可验证安全外包计算

Efficient,Verifiable and Secure Outsourcing of Matrix Multiplication

云外包作为近年来各科研团队热点研究课题,各类复杂的科学计算问题与云外包课题的结合也备受关注.基于各类科学计算,矩阵的高效外包计算是云计算和大数据背景下的一个非常有意义的研究方向.通过分析得知,目前的矩阵外包计算协议还不能高效的实现所有矩阵之间的计算,尤其是任意非方阵之间的乘积运算.如何在不泄露用户信息的情况下,设计出高效可验证安全的矩阵乘积外包协议是一个有意义的研究问题.为此,首先利用几何学中的填补法和分割法将矩阵进行分块处理,并结合置换函数和可逆矩阵相乘的处理操作,设计出一个高效可验证且安全的矩阵乘积外包协议.其次,对提出新的矩阵乘积外包协议给出正确性、合理性、隐私性、可验证性、高效性分析及证明.并重点分析和证明本文所提出的新的高效验证方式.最后,与近几年相关矩阵运算的外包协议进行对比,我们协议不需要任何的密码学假设,合理利用盲化技术实现矩阵外包计算,且满足任意矩阵之间的乘积外包计算.

Cloud outsourcing has been a hot spot in recent years and researchers pay much attention to complex problems in scientific computing via cloud outsourcing. In the field of scientific computing, efficient outsourcing of matrix computation is a very significant direction of research under the background of cloud computing and big data. It is known that the outsourcing of matrix computation cannot achieve all computing of matrices, especially for the computation of non-square matrices.Without leakage of user's information, how to design a high efficient verifiably outsourcing protocol of matrix computation is an important research problem. In this paper, we first divide bigger matrices by the method of compensation and segmentation in geometry and combining permutation function and a blind technique of the invertible matrix multiplication to design an efficient outsourcing computing protocol of matrix multiplication verifiably and safely. Then, we give analysis and proof of the correctness, rationality, privacy, verifiability and efficiency of the new protocol of matrix multiplication,especially analyze and prove the new verifiable way about our protocol. Finally, we compare with protocols of matrix multiplication in recent years. We use the rational blind technology to design our protocol of matrix outsourcing. In addition, our protocol does not need any cryptographic assumption,and satisfies outsourcing computing of arbitrary matrix multiplication.