Research On Safe Outsourcing Calculation Of Bilinear Pairing

Cloud computing has the characteristics of low cost and easy expansion,and is widely used in many fields.Through cloud computing,users can outsource computing tasks to cloud servers,thereby improving local efficiency.However,cloud computing also brings some security issues.First,cloud servers are not completely trusted,so private information in user computing tasks needs to be protected.In addition,the cloud server may directly return a random result for the purpose of cost savings.The random result and the real result might be computational indistinguishable to the user,so the user needs to be able to verify the correctness of the result.In addition,the cost for users to execute outsourcing scheme must much smaller than the cost for users to compute tasks locally,otherwise outsourced computing will lose its meaning.Therefore,designing a secure,efficient,and verifiable outsourcing scheme is worth studying.Bilinear pairing is widely used in the field of cryptography,and it is also one of the most time-consuming operations in cryptographic algorithms.For devices with limited computing resources,outsourcing bilinear pairing to a cloud server is a viable option.This article proposed three bilinear pairing outsourcing schemes based on two servers,single server,and blockchain:(1)Resource-constrained devices rely on encryption algorithms for secure communications,and bilinear pairing is the basic operation of many encryption algorithms.Encryption algorithms based on bilinear pairings are difficult to directly use on resource-constrained device because bilinear pairing is time-consuming.Most of the existing bilinear pairing outsourcing schemes are based on pre-computation,however,resource-constrained devices don't have sufficient storage space to store pre-computation results.We proposed an outsourcing scheme based on two servers,which does not require precomputation,and its verifiable probability is close to 1.(2)The security outsourcing computing scheme based on the two servers requires two servers to participate in the outsourced computing,and it is assumed that the two servers cannot conspire.Such strong security assumptions are difficult to meet in practical application.To solve this problem,we proposed an outsourcing scheme based on single server.The user in this scheme can verify the result with 100% probability.This scheme also has the advantages of not requiring any pre-computation and high efficiency.(3)None of the existing bilinear pairing outsourcing schemes can achieve fair payment.The blockchain technology with decentralization as its main feature can solve this problem.By authorizing the blockchain,a bilinear pairing outsourcing scheme based on blockchain technology is designed to achieve fair payment.And this scheme is proved practical through experiment.