Attack on stream cipher that XOR's the output of two LFSRs There are two LFSRs of different lengths: LFSR-17 and LFSR-25. LFSR-17 Initially contains a two byte seed, with a 1 injected into the fourth bit, for a total of 17 bits. LFSR-25 operates in the same way.

Of the 40-bit key, 2 bytes is seeded into the first LFSR and 3 bytes into the other. If the outputs of each LFSR were simply XORd to produce the keystream, how could we launch a known plaintext to retrieve the key?
There is another method named algebraic attack.


Name each of the keys initial keys by $l_{1i}$ and $l_{2i}$.
Since the LFSRs are linear and the combining function, x-or, is also linear compute algebraic equations
Solve them. They construct a linear system of solutions.


Since only 38 bits are keys, you will only need 38-bit output if the if the equations are linearly independent. 

if you use the Gaussian elimination method it will have $40^3$ operations.