Using unpredictable information to minimize leakage from smartcards and other cryptosystems

A method of and cryptographic processing device for securely performing a cryptographic processing operation implementing a permutation in a manner resistant to discovery of a secret within a cryptographic processing device by external monitoring, operates by receiving a quantity to be cryptographically processed; generating unpredictable information; using the unpredictable information while processing the quantity to conceal a correlation between externally monitorable signals and the secret, this being achieved by performing a computation and incorporating the result of the computation in the cryptographic processing, and performing a computation the output of which is not incorporated in the cryptographic processing; and outputting the cryptographically processed quantity to a recipient thereof. The unpredictable information thus conceals a correlation between externally monitorable signals and the secret by randomizing the order of the permutation.