Over the recent years of research in cloud computing, different approaches are adopted for Inter-Cloud Authentication. These approaches give successful results in identifying the authentic request. Defense organization communicate with each other's through legitimate requests. For establishing a security and privacy, a PKI based authentication model is needed. This paper signifies a new approach in implementing cloud based PKI authentication inside the existing infrastructure of defense organization. As security is the prime concern for any organization and its implementation requirement varies from organization to organization, each and every organization embrace their own policies to implement it. The problem of understanding each other's security policies is a huge barrier and challenge for existing IT infrastructure for implementation purposes. Requirement to establish Inter-Cloud Authentication is made possible through this PKI based model which ensures all five security services i.e. confidentiality, integrity, authentication, digital signature and non-repudiation. This PKI model is a multi-domain atmosphere between various defense organization and their Data Centers (DC) for the facilitation and resource provisioning inside the cloud platform. This model utilizes the existing network infrastructure composed of high intercommunication traffic between various Data Centers of defense organization. In this model, a nationwide Certification Authority (CA) is implemented in the Inter-Cloud infrastructure and all other Data Centers are inter-communicated through this mechanism having different authentication approaches for legitimate access through the X.509 Certificates.