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Fog computing, being an extension to cloud computing has addressed some issues found in cloud computing by providing additional features, such as location awareness, low latency, mobility support, and so on. Its unique features have also opened a way toward security challenges, which need to be focused for making it bug-free for the users. This paper is basically focusing on overcoming the security issues encountered during the data outsourcing from fog client to fog node. We have added Shibboleth also known as security and cross domain access control protocol between fog client and fog node for improved and secure communication between the fog client and fog node. Furthermore to prove whether Shibboleth meets the security requirement needed to provide the secure outsourcing. We have also formally verified the protocol against basic security properties using high level Petri net.