The new named data networking (NDN) has shifted the Internet from today's IP-based packet-delivery model to the name-based data retrieval model. The architecture shift from IP addresses to named data results in effective content delivery via in-networking cache and direct object retrieval. However, this shift has also created challenges and obstacles for securing data objects and providing appropriate access control on named data due to broad data replications and the loss of network perimeters. This paper designs, implements, and evaluates an encryption and probability based access control model for NDN with video streaming service as a case study. In particularly, we explore a combination of public-key cryptography and symmetric ciphers to encrypt video data for preventing unauthorized access. In addition, we build a bloom-filter probabilistic data structure for pre-filtering Interests from consumers without desired credentials. Our experimental results have demonstrated the capabilities of the proposed model for providing access control while incurring low system and performance overhead on producers and consumers.