Research On The Secure Outsourcing Calculation Protocol Of Modular Index Based On Single Server

With the widespread use of cloud computing,more and more enterprises and individuals are beginning to use the services provided by cloud computing,outsourcing computing also came into being.Outsourcing computing enables users with limited resources to apply the computing resources provided by the cloud server by means of paid purchases.While outsourcing computing brings convenience to users,it inevitably brings some new problems and challenges.Outsourcing computing tasks usually contain sensitive information that should not be exposed directly to the cloud server and require the encryption or blind way to achieve data privacy protection.In addition,the cloud server is semi-trusted and may return the wrong calculation results.Therefore,how to realize the data privacy protection and the verifiability of calculation results in outsourcing computing are the key issues that need to be urgently addressed in secure outsourcing computing.This paper focuses on the exponent computing in outsourcing computing.The specific work is as follows:(1)Most of the existing modular exponentiations schemes are developed around prime modular exponentiations.However,due to the difficulties of a large number decomposition,those exponentiations modular a prime outsourcing algorithms can hardly be used for composites scene.We first proposed a secure and efficient scheme for secure outsourcing of composite modular exponentiation with single untrusted server named CExp,which can effectively avoid the collusion attack in the dual server model.CExp can guarantee the privacy of the input/output data while detecting the wrong result returned by the cloud server with 100%probability,and ensures that the user can fully verify the result of outsourcing calculation.In order to efficiently handle the outsourcing calculation multiple modular exponentiations,we proposed an efficient outsource-secure algorithm called MCExp for composite multiple modular exponentiations.MCExp solves the problem of large time overhead when using the CExp to achieve outsourcing multiple modular exponentiations.Safety analysis and simulation experiments show that the proposed schemes CExp and MCExp are safe and efficient.(2)The current power exponent outsourcing schemes are mostly concerned with outsourcing power exponent in a number field,and pay less attention to outsourcing power exponent in a group field.In order to solve this problem,we propose a new scheme for outsourcing power exponent in a group field based on single untrusted server,called GEXP.GEXP realizes the privacy protection of the original data and has greatly improved the verifiable probability of the outsourcing calculation result,Which achieves a complete verification of outsourcing computing results.Using GEXP to achieve outsourcing multiple power exponents is expensive,we also propose an outsourcing computing scheme called MGEXP for multiple power exponents in a group field.Safety analysis and simulation experiments show that the proposed schemes GEXP and MGEXP are safe and efficient.(3)Many digital signatures and cloud storage schemes require exponentiation calculation frequently,but the computations are often expensive.For that reason,we implement the secure outsourcing of Shamir's identity-based signature scheme and identity-based multi-signatures scheme using the proposed composite modular exponentiation outsourcing algorithms.Meanwhile,we realize the outsourcing of proxy re-signature HAPS in the Panda scheme and cloud storage scheme EPDP based on power exponent outsourcing algorithms in a group field.The experimental results show that the time cost of the outsourcing solution using our algorithm is far less than original schemes.This paper proposes a single(multiple)composite exponential outsourcing computing scheme and a single(multiple)power exponent outsourcing computing scheme in a group field based on a single untrusted server model.We implement the secure outsourcing of identity-based signature scheme and cloud storage scheme using the proposed schemes.The experimental results show that the outsourcing scheme using our algorithm is more efficient than original schemes,so the outsourcing scheme will further broaden the scope of original schemes.