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In recent years, a number of puzzle-based defense mechanisms have been proposed against flooding denial-of-service (DoS) attacks in networks. Nonetheless, these mechanisms have not been designed through formal approaches and thereby some important design issues such as effectiveness and optimality have remained unresolved. This paper utilizes game theory to propose a series of optimal puzzle-based strategies for handling increasingly sophisticated flooding attack scenarios. In doing so, the solution concept of Nash equilibrium is used in a prescriptive way, where the defender takes his part in the solution as an optimum defense against rational attackers. This study culminates in a strategy for handling distributed attacks from an unknown number of sources.