Abstract
Nonlinear combination generator is a keystream generator where outputs of several Linear Feedback Shift Registers (LFSR) are combined by a binary boolean function. Correla- tion (fast) attack is an important cryptanalytic technique and is discussed against the combination generator [7], [8]. If the generator involves n-LFSRs each is of length for and the function is correlation immune of order t, in this article using fast correlation attack, it is shown that initial states of t+1 LFSRs are recovered in time where t +1≤n and the last term corresponds to the complexity of solving the linear system of L equations involving L unknowns using Gaussian elimination. If l(< n) denotes the number of LFSRs whose initial states are known and L′ is the length of a constituent LFSR whose state is to be recovered then exploiting the known initial states of l LFSRs, a simple constraint is derived from Walsh transform to decide whether a state of the LFSR, using fast correlation attack, can be recovered in time .
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