On Generating Algebraic Equations for A5-Type Key Stream Generator

Algebraic cryptanalysis is a newer and quite successful technique for the security evaluation of stream ciphers as well as a threat to the structures which are resistant to other types of attacks. Originally algebraic attacks were proved to be successful against ciphers having combining or filtering Boolean function along with the linear part. Very successful attacks have been mounted on ciphers with nonlinear components with or without memory [1–5]. So far the most successful attacks are on a particular design having two components: a nonlinear filter or combining function and a linear component of one or many LFSRs. However, algebraic attack on somewhat different structures of stream ciphers has not been much studied yet. Clock control is also one of the mechanisms employed to introduce nonlinearity into a key stream generator built from linear feedback shift registers. Algebraic attacks against clock-controlled stream ciphers have recently been studied by Sultan AH, Lynn B,Bernard C, Kenneth W [6], which to our knowledge is the first work in this direction. Although LILI 128 is also a clock-controlled cipher and successful algebraic attacks can be found against it [4], for its clock-controlled part, guessing is being used. The work in [6] basically involves stream ciphers such as the stop-and-go generator, alternating step generator, self-decimated, and step1/step2 generator in which one or more LFSRs are irregularly clocked and their clocking depends on some regularly clocked LFSR. This attack is based on the general assumption 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. This chapter aims at finding how practical can it be to mount an algebraic attack on A5/1 in which none of the LFSRs are regularly clocked. Because the feasibility of the algebraic attack has not yet been explored against it, the objective of this research is to mount an algebraic attack against an A5/1-type clock-controlled generator.