Digital content distribution services require that 1) only valid user devices that has a valid key can decrypt the broadcasting content, 2) the keys can no longer be used to decrypt the content, if keys in a device are revealed, and 3) invalid users who illegally use keys in a device can be identified. This paper proposes a broadcast encryption scheme with traitor tracing based on the ternary tree structure. We design a new cover-finding algorithm and label assignment algorithm in order to achieve a coalition-resistant revocation and tracing schemes. In our scheme, the number of labels stored in a client device can be reduced by about 20.4 percent and the average header length by up to 15.0 percent in the case where the total number of devices is 65,536. The efficiency of the traitor tracing is the same as the complete subtree method, and its computational cost imposed on a client device stays within O(logn). Our scheme is an improvement of the complete subtree and difference subset methods.