Securely Outsource Modular Exponentiations With Single Cloud Server

Modular exponentiation is one of the most fundamental operations in many encryption and signature systems.Due to the heavy computation cost of modular exponentiation,it is almost impossible for a resource-limited user to efficiently compute complex modular exponentiations.Many schemes have been proposed to outsource the complex modular exponentiations to cloud servers with the help of cloud computing technology.A lot of research works have been done on the security of outsourcing data.Nevertheless,most of the existing approaches need two non-colluded cloud servers to secure complete the modular exponentiation,which will result in private data leakage once the cloud servers collude.Besides,most existing schemes assume both base and exponent in modular exponentiation are private,which is not suitable for many real-world applications.To solve the above problems,this paper proposes two new schemes for secure outsourcing of modular exponentiations and then apply it to the process of Paillier encryption and dot product protocol respectively.The main works of this paper is as follow:(1)The existing schemes require two non-interactive cloud servers and have some shortcomings in efficiency and checkability.Combined with privacy protection techniques in secure outsourcing,we proposes two secure outsourcing schemes for fixed-base(public base and private exponent)and fixed-exponent(private base and public exponent)respectively.We securely outsource modular exponentiations to a cloud server.Meanwhile,the user can check the correctness of returned data from the cloud server.Compared with existing works,our schemes can not only securely outsource modular exponentiation with single cloud server,but also improve efficiency and checkability.The proposed schemes can also avoid collusion attack of cloud servers.Finally,theoretical analysis and experiment evaluations indicate the efficiency of our schemes.(2)Based on the secure outsourcing algorithm proposed above,we propose a Paillier encryption scheme that outsources modular exponentiations to cloud server,which make up the inefficiency of Paillier encryption caused by computing modular exponentiations.Compared with traditional Paillier encryption algorithm,our scheme can achieve higher efficiency and is provably secure.Finally,we further evaluate its efficiency through theoretical analysis and simulation experiment.Based on the former studies,we further propose a secure scalar product protocol.Our proposed secure scalar product protocol based on cloud platform is much more efficient,compared with traditional dot product protocol.We evaluate the security and checkability through theoretical analysis of secure outsourcing process.