Many of the keystream generators which are used in practice are LFSR-based in the sense that they produce the keystream according to a rule y = C(L(x)), where L(x) denotes an internal linear bitstream, produced by a small number of parallel linear feedback shift registers (LPSRs), and C denotes some nonlinear compression function. We present an n~(O(1))2~((1-α)/(1+α)n) time bounded attack, the FBDD-attack, against LFSR-based generators, which computes the secret initial state x ∈ {0, l}~n from cn consecutive keystream bits, where a denotes the rate of information, which C reveals about the internal bitstream, and c denotes some small constant. The algorithm uses Free Binary Decision Diagrams (FBDDs), a data structure for minimizing and manipulating Boolean functions. The FBDD-attack yields better bounds on the effective key length for several keystream generators of practical use, so a 0.656n bound for the self-shrinking generator, a 0.6403n bound for the A5/1 generator, used in the GSM standard, a 0.6n bound for the E_0 encryption standard in the one level mode, and a 0.8823n bound for the two-level E_0 generator used in the Bluetooth wireless LAN system.
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