This paper proposes a content-aware authentication scheme optimized to account for distortion and overhead for media streaming. When authenticated media is streamed over a lossy network, a received packet is consumed only when it is both decodable and authenticated. In most media formats, some packets are more important than others. This naturally motivates allocating more redundant authentication information for the more important packets in order to maximize their probability of authentication and thereby minimize distortion at the receiver. Toward this goal, with awareness of the media content, we formulate an optimization framework to compute an authentication graph to maximize the expected media quality at the receiver, given specific authentication overhead and knowledge of network loss rates. Experimental results with JPEG-2000 coded images demonstrate that the proposed method achieves our design goal in that the R-D curve of the authenticated image is very close to the R-D curve when no authentication is required.