Fog computing is proposed for overcoming the shortage of cloud computing in isomerism, low-latency, dense network access and service requirements. Intelligent transportation is an important application of fog computing. However, fog computing is threatened by the security of sensitive data and large data storage due to the complexity of its structure and the limited storage capability. In this paper, we will introduce a new method to solve these issues. This method combines the Information Dispersal Algorithm and Cipher-text Policy Attribute-Based Encryption to encrypt data and divides cipher-text into pieces through a random matrix generated by a trusted proxy server. The fragments of cipher-text data are then stored in storage nodes. When data is acquired, data pieces will be reconstructed into cipher-text and then be decrypted to original data. The proposed method employs double encryption to ensure security of data and takes the advantage of distributed storage to solve the problem of insufficient storage capacity in fog computing.