Computing the high power of huge-dimension square matrix is a hard job for those entities (clients) with limited compute capability. To resolve this problem, a secure and verifiable cloud computation outsourcing protocol of square matrix power was designed using the cloud computing platform. In the protocol, the client firstly constructed a random permutation and generated a secret key which included a non-singular square matrix and its inverse matrix by combining the permutation with the Kronecker function. Secondly, the original square matrix was encrypted with the secret key by the client, and then the encrypted matrix was sent to the cloud along with the original exponent. After completing the calculation of the encrypted square matrix power, the cloud returned the result to the client. The client decrypted the returned result with its own secret key and correspondingly compared the elements which were randomly chosen by the client with the correct values to verify the correctness of the result. Theoretical analysis shows that the protocol meets the requirements of outsourcing protocol well, including correctness, security, verifiability and high efficiency. Based on this protocol model, the simulation experiments were conducted in two aspects: dimension fixed exponent changing and exponent fixed dimension changing. Finally the experiment result indicates that, compared with completing the original job by client himself, the outsourcing computation can substantially reduce the time consumption of the client in both cases and get a desirable outsourcing performance which becomes better with the increase of dimension and exponent.

To solve the low speed of synchronization, a new learning rule was proposed by employing Tree Parity Machine (TPM). By setting queues to record the results of each communication in the synchronization process, this rule estimated the degree of synchronization of the two TPMs communicating with each other in real time. According to the results of estimation, the rule selected appropriate values to modify the weights, appropriately increased weight modifications in the lower degree of synchronization and reduced weight modifications in the higher degree of synchronization. Finally, the simulation results show that synchronization efficiency is improved more than 80% by applying new learning rule. Meanwhile, it is also indicated that the rule is computationally inexpensive and it improves the security of communication compared to the classic learning rules.

In this paper, a new image encryption algorithm was presented by employing Cellular Neural Network (CNN). The main objective was to solve the problem of traditional stream ciphers insensitivity to the change of plain text. By using a hyper chaotic system of 6-D CNN as the key source, selecting the secret key based on the results of logical operations of pixel values in the plain image, and introducing simultaneously both position permutation and value transformation, the new algorithm was presented. It is shown that both NPCR value and the sensitivity to key (>0.996) can meet the security requirements of image encryption. The simulation process also indicates that the algorithm is relatively easy to realize with low computation complexity, and ensures, accordingly, the secure transmission of digital images.