Algebraic attacks on clock-controlled stream ciphers

  • Authors:
  • Sultan Al-Hinai;Lynn Batten;Bernard Colbert;Kenneth Wong

  • Affiliations:
  • Information Security Institute (ISI), Queensland University of Technology (QUT), Australia;Deakin University, Australia;Deakin University, Australia;Information Security Institute (ISI), Queensland University of Technology (QUT), Australia

  • Venue:
  • ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
  • Year:
  • 2006

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Abstract

We present an algebraic attack approach to a family of irregularly clock-controlled bit-based linear feedback shift register systems. In the general set-up, we assume that the output bit of one shift register controls the clocking of other registers in the system and produces a family of equations relating the output bits to the internal state bits. We then apply this general theory to four specific stream ciphers: the (strengthened) stop-and-go generator, the alternating step generator, the self-decimated generator and the step1/step2 generator. In the case of the strengthened stop-and-go generator and of the self-decimated generator, we obtain the initial state of the registers in a significantly faster time than any other known attack. In the other two situations, we do better than or as well as all attacks but the correlation attack. In all cases, we demonstrate that the degree of a functional relationship between the registers can be bounded by two. Finally, we determine the effective key length of all four systems.