On the Statistically Optimal Divide and Conquer Correlation Attack on the Shrinking Generator.
Shahram Khazaei, Mahmoud Salmasizadeh, Javad Mohajeri · 2005
The shrinking generator is a well-known key stream generator composed of two LFSR’s, LFSRx and LFSRc, where LFSRx is clock-controlled according to the regularly clocked LFSRc. In this paper we investigate the minimum required length of the output sequence for successful reconstruction of the LFSRx initial state in an optimal probabilistic divide and conquer correlation attack. We extract an exact expression for the joint probability of the prefix oflengthmof the output sequence of LFSRx and prefix oflengthnof the output sequence of the generator. Then we use computer simulation to compare our probability measure and two other probability measures proposed in [5] and [3] in the sense of minimum required output length. Our simulation results show that our measure reduces the required output length.