We investigate the problem of securing the delivery of scalable video streams so that receivers can ensure the authenticity (originality and integrity) of the video. Our focus is on recent scalable video coding techniques, e.g., H.264/SVC, that can provide three scalability types at the same time: temporal, spatial, and quality (or PSNR). This three-dimensional scalability offers a great flexibility that enables customizing video streams for a wide range of heterogeneous receivers and network conditions. This flexibility, however, is not supported by current stream authentication schemes in the literature. We propose an efficient authentication scheme that accounts for the full scalability of video streams: it enables verification of all possible substreams that can be extracted and decoded from the original stream. Our evaluation study shows that the proposed authentication scheme is robust against packet losses, adds low communication and computation overheads, and is suitable for live streaming systems as it has short delay.