Efficient Verifiable Security Outsourcing Calculations For Matrix Products

Outsourced cloud as a hot topic uses the cloud with unlimited computing and storage to carry out the expensive and bulky calculation.But there is opaque in cloud server caused by dishonest behavior.Therefore,privacy and content security are an issue to be resolved desperately.Matrix operation in various scientific computation is not only an important part in the field of numerical analyses,but also included in many cryptographic schemes and multi-dimensional processed images.The incapable users in cloud are difficult to deal with the expensive matrix operation.We propose hence three matrix multiplication’s schemes possessing efficiency,verification and security.There are currently many researches used blind technologies and cryptographic primitives(such as,fully homomorphic encryption,additive homomorphic encryption,multiplicative homomorphic encryption and so on).We study the multi-dimensional matrix based on those two technologies and the main innovations are as follows.The first scheme preprocesses original matrix used by segmentations and fills in geometry in order to achieve verifiable and efficiency outsourced matrix.In the preprocessing stage,we divide the original matrix into four branches based on the dimensions of the matrix and blind further the preprocessing matrix to form the new sequence of matrix which uses technologies of replacement and reversibility.Then we outsource the new sequence of matrix to the cloud server and verify the response.We finish the procedure of outsourced matrix when the returned data passes the verification.Meanwhile we prove the correctness,rationality,privacy and verifiability of scheme.Finally,we compare with the other similar outsourced matrix used blind technology in recent years.Secondly,combined with technology of identity based encryption we propose outsourced matrix to an optimized calculation of verification for the realization of verifiable and secure outsourced matrix.We encrypt the matrix to form a new ciphertext sequence which is outsourced to the cloud servers.The cloud server needs two kinds of operations when it accepts the sended datas.The first operation of multiplication is to obtain the final goal of matrix multiplication and the second pairing operations is to simplify the calculation of verification.At the same time,we use the theory of provable security to prove the security of scheme under decisional bilinear Diffie-Hellman problem.Finally,we make a comparison with other similar outsourced scheme structured by cryptographic primitives.Thirdly,we put forward the chosen ciphertext attacking outsourced matrix of the shorter length of ciphertext in order to reduce the ciphertext length structured by cryptographic primitives.We encrypt the matrix based the advanced injective function to form the sequence of matrix and outsource to the cloud servers.The cloud server only need an operation of multiplication when it receive the sended datas and return the entire treated datas.At the same time,we also analyse the security of scheme base on the theory of provable security under bilinear Diffie-Hellman problem.Finally,we make a comparison of analysis.Above all,the shape of outsourced matrix is not only square,but also non-square.At the same time,we can apply the schemes to image procedure、scientific computation and other fileds when we deal with the related expensive matrix’s datas.