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Onion routing and mix networks are fundamental concepts to provide users withanonymous access to the Internet. Various corresponding solutions rely on theefficient Sphinx packet format. However, flaws in Sphinx's underlying proofstrategy were found recently. It is thus currently unclear which guaranteesSphinx actually provides, and, even worse, there is no suitable proof strategyavailable. In this paper, we restore the security foundation for all theseworks by building a theoretical framework for Sphinx. We discover that thepreviously-used DDH assumption is insufficient for a security proof and showthat the Gap Diffie-Hellman (GDH) assumption is required instead. We apply itto prove that a slightly adapted version of the Sphinx packet format is secureunder the GDH assumption. Ours is the first work to provide a detailed,in-depth security proof for Sphinx in this manner. Our adaptations to Sphinxare necessary, as we demonstrate with an attack on sender privacy that would bepossible otherwise.

Provable Security for the Onion Routing and Mix Network Packet Format Sphinx