Research On Verifiable Outsourcing Computation Schemes Of Modular Exponentiations And Bilinear Pairings

With the rapid development of information technology and the explosive growth of data volume,more and more Internet users tend to use cloud services and the development of cloud computing has reached an unprecedented depth.Enterprises and individuals are unable to store and calculate the data in in local due to limited resources,so that outsourcing computation arise at the right moment.By adopting outsourcing computation technology user can delegate complex storage tasks or computing workloads to cloud servers which have stronger storage and computing power.Of course,outsourcing computation brings more convenience for people,while accompanied by a number of new security challenges and problems.Modular exponentiation and bilinear pairings are widely used in cryptography,and are often used to construct cryptographic algorithms.For security reasons,we usually choose a larger number for operations when we design cryptography algorithms.Although the research of outsourcing of modular exponentiation and bilinear pairings has made some achievements,but most of them require two cloud servers to compute.Moreover,it is very difficult to implement in practical application under the condition that one of the two cloud servers must be honest.This thesis focuses on the study of secure outsourcing computation for modular exponentiation,and the main work of this thesis includes:1.Firstly,this thesis makes research on the existing security model and sums up their limitations.Then this thesis proposes the improved scheme that is based on verifiable computation.Two kinds of secure and efficient outsourcing schemes for modular exponentiations are also proposed to support single untrusted cloud server.One is secure outsourcing scheme of fixed base-variable exponent modular expontiations—Exp and the other is secure outsourcing scheme of simultanenous modular exponentiations—Sexp.Before starting the outsource task,the user’s input data and output result should be made logic split and blind to ensure their privacy.Then cloud server will not get anything about the information of input and output.The security and efficient of our schemes are evaluated by analysis and proofs.2.Secondly,the scheme of Exp is extended in the practice to construct cryptographic algorithm,the OS-CSES scheme and OS-SSS scheme.By using the Exp scheme designed in this thesis,the modular exponentiation operations existing in the Cramer-Shoup encryption shceme and Schnorr signature scheme are safely outsourced.We prove that these two schemes reduce the computation load as well as ensure data security by theoretical proofs.3.Finally,a bilinear pairing outsourcing scheme based on a single untrusted server is proposed.For the complex scientific operation of biliear pairings,users need to spend a greater cost in the local computing.By adopting outsourcing computation technology,people can effectively implement.Most of existing schemes are based on two cloudservers and it is difficult to implement in real life.To solve the problems,we propose a secure and efficient outsourcing scheme NBP for bilinear pairings which supports single untrusted cloud server.The scheme improves the computational efficiency by calling the Rand subroutine,and uses the technique of splitting to ensure the privacy of the outsourcing data.Through the analysis and comparison,it proves that the scheme is safe and efficient,and has high feasibility.We apply the NBP scheme to the cryptography field and design an outsourcing computation scheme of BLS and BB04 short signatures,which can greatly improve the computational efficiency and ensure data security.