Stronger difficulty notions for client puzzles and denial-of-service-resistant protocols

Client puzzles are meant to act as a defense against denial of service (DoS) attacks by requiring a client to solve some moderately hard problem before being granted access to a resource. However, recent client puzzle difficulty definitions (Stebila and Ustaoglu, 2009; Chen et al., 2009) do not ensure that solving n puzzles is n times harder than solving one puzzle. Motivated by examples of puzzles where this is the case, we present stronger definitions of difficulty for client puzzles that are meaningful in the context of adversaries with more computational power than required to solve a single puzzle. A protocol using strong client puzzles may still not be secure against DoS attacks if the puzzles are not used in a secure manner. We describe a security model for analyzing the DoS resistance of any protocol in the context of client puzzles and give a generic technique for combining any protocol with a strong client puzzle to obtain a DoS-resistant protocol.