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Physical Unclonable Functions (${\emph{PUF}}$) are physical objects that are unique and unclonable. ${\emph{PUF}}$s were used in the past to construct authentication protocols secure against physical attackers. However, in this paper we show that known constructions are not fully secure if attackers have raw access to the ${\emph{PUF}}$ for a short period of time. We therefore propose a new, stronger, and more realistic attacker model. Subsequently, we suggest two constructions of authentication protocols, which are secure against physical attackers in the new model and which only need symmetric primitives.