The invention relates to a secure data processing system including an unscrambling module [DSC] disposed on a dedicated hardware part [HW] of an integrated circuit and intended to unscramble a stream of data [SP] scrambled according to a scrambling key, a module [CM] for calculating an unscrambling key [Kp] disposed on said dedicated hardware part [HW] and intended to manipulate data under the control of a so-called calculation program stored on said dedicated hardware part [HW], a processor [CPU] for in particular controlling the functioning of the unscrambling [DSC] and calculation [CM] modules. Said system also includes a read only memory [SME] disposed on said dedicated hardware part [HW] for storing a secret key [Kp]. Said calculation program includes instructions for prompting said calculation module [CM] to use said secret key [L] and at least one data item [AC[n,p] or Kpc)] coming from outside the secure data processing system, in order to calculate an unscrambling key [Kp]. The unscrambling is enabled only if the unscrambling key [Kp] corresponds to the scrambling key.