Security system based on certification

The data containing reference data is transformed into signature data by a method which depends on a variable generated by the reference data, and the identification data is certified by inverse transformation of the signature data. The signature generating rule changes in dependence on the reference data, and it is therefore extremely difficult to analyze the signature generating rule from the medium or the card reader/writer so that the forgery or modification of magnetic or other data, which is otherwise easy to duplicate, can be made extremely difficult. Therefore, even when a reader is illicitly obtained, and analyzed, it is extremely difficult to estimate the signature generating rule as it owes to the difficulty of solving a set of multivariate simultaneous equations.