In systems for establishing a cryptographic key depending on a physical uncloneable function (PUF) it may be a problem that internal information correlated with the cryptographic key is leaked to the outside of the system via a side-channel. To mitigate this problem a cryptographic system for reproducibly establishing a cryptographic key is presented. The system comprises a physical system comprising a physical, at least partially random, configuration of components from which an initial bit-string is derived. An error corrector corrects deviations occurring in the initial bit-string. Through the use of randomization the error corrector operates on a randomized data. Information leaking through a side channel is thereby reduced. After error correction a cryptographic key may be derived from the initial bit-string.