Some embodiments are directed to an electronic cryptographic device arranged to determine a cryptographic key. The cryptographic device can include a physically unclonable function (PUF) arranged to produce a first noisy bit string during the enrollment phase and a second noisy bit string during the reconstruction phase, and a statistical unit arranged to execute a statistical test for verifying correct functioning of the physical unclonable function. The statistical test computes a statistical parameter for the physical unclonable function using helper data. The statistical test determines correct functioning if the statistical parameter satisfies a criterion of the statistical test.