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The large prevalence of multimedia systems in recent years makes the security of multimedia communications an important and critical issue. We study the problem of securing the delivery of scalable video streams so that receivers can ensure the authenticity of the video content. Our focus is on recent scalable video coding (SVC) techniques, such as H.264/SVC, which can provide three scalability types at the same time: temporal, spatial, and visual quality. 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 and secure authentication scheme that accounts for the full scalability of video streams, and enables verification of all possible substreams that can be extracted from the original stream. In addition, we propose an algorithm for minimizing the amount of authentication information that need to be attached to streams. The proposed authentication scheme supports end-to-end authentication, in which any third-party entity involved in the content delivery process, such as stream adaptation proxies and caches, does not have to understand the authentication mechanism. Our simulation study with real video traces shows that the proposed authentication scheme is robust against packet losses, incurs low computational cost for receivers, has short delay, and adds low communication overhead. Finally, we implement the proposed authentication scheme as an open source library called svcAuth, which can be used as a transparent add-on by any multimedia streaming application.