Systems and methods are described based on an integrated circuit that performs a challenge-response physically unclonable function (PUF). The PUF is used for challenge-response authentication. The integrated circuit includes a PUP block configured to output an n-bit internal response corresponding to a challenge that requests a response where n is an integer greater than 1 and a response generator configured to calculate a Hamming weight of the internal response and output the response by comparing the Hamming weight with at least one reference.