1. A method for producing a key bit for a cryptographic key, the producing comprising deriving a device-specific value from a physical unclonable function realized on a circuit unit, the method comprising: ascertaining a first response from application of a first challenge to the physical unclonable function on the circuit unit at least once; ascertaining at least one second response from application of a second challenge to the physical unclonable function at least once; deriving, by a processor, a respective categorization information item from a respective response, the deriving comprising allocating the respective response to one of at least two respective categories with regard to a statistical variation, the at least two respective categories being stipulated by at least one prescribable threshold value; deriving, by the processor, the device-specific value from at least two of the respective categorization information items, the deriving comprising ascertaining identical categorization information items from at least two responses to successive challenges, the ascertaining of the identical categorization information items comprising comparing the respective categorization information item, the deriving further comprising ascertaining a sequence property of a series of identical categorization information items; and producing, by the processor, a key bit of a cryptographic key based on the device-specific value.