Abstract: Cloud computing is a pristine methodology of computing in which dynamically scalable and often virtualized s are given as service over internet. Appropriation of cloud is a fascinating and yet unfamiliar province in cloud computing to imbrutes the miscellany of s for cloud purveyor becomes a challenging issue in recent years. This problem is solve by using three novel fashion for cloud purveyor with appropriation: Cloud-Dominant Strategy Incentive Compatible (C-DSIC), Cloud-Bayesian Incentive Compatible (C-BIC) and Cloud Optimal (C-OPT). In C-OPT modules where the administration is done based on host winner value, the major issue of the work is that corroboration is done for all cloud end user. To solve security issue problem in the cloud appropriation method in this effort introduce a novel Expectation Maximization (EM) algorithm for cloud optimal modules. The proposed EM methods are utilized for identifying maximum likelihood based on undiscovered dormant cloud artifice variables for virtual cost and quality of service curtailments. To corroborate the cloud end user data, cryptanalysis method is introduced in this proposed work. The proposed cryptanalysis method follows the procedure of Elliptic curve cryptography for corroborating end users and cloud purveyors. Key values between the cloud end user and cloud purveyors are exchanged. Each and every key is verified by both cloud end user and cloud purveyor. If the key value anyone becomes wrong the appropriation is not administrated to cloud end user, since these end users become uncorroborated end user, there are not allowed to perform appropriation process. A cloud negotiator with such an appropriation module enables end users to miscellany the miscellany of a cloud purveyor. Our demonstration indicates that the appropriation cost drops by calculation of the expectation maximization algorithm and more security than the existing C-OPT Methods by using the elliptic curve cryptography with multiplication in number of cloud purveyors irrespective of the fashions.