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Unformatted text preview: e key sequence. 3. If not, try m =3 and so on… Setting up the Equations to Attack LFSR
Setting
This is best shown with an example.
Example: Suppose we have the key sequence (011010111100)
m=2: Recurrence is x n + 2 = c 0 x n + c1x n +1 Which yields the system of equations: 1 = c 0 ⋅ 0 + c1 ⋅1
0 = c 0 ⋅1 + c1 ⋅1
⇒ Solve to get : c 0 = 1, c1 = 1. Try this out. Note that
We must try m=3! x n +6 ≠ x 4 + x 5 Setting up the Equations to Attack LFSR, pg 2
Setting
m=3: The recurrence is: x n +3 = c 0 x n + c1x n +1 + c 2 x n + 2 The system of equations we get is: ⎛ 0 1 1 ⎞⎛ c 0 ⎞ ⎛ 0 ⎞
⎟⎜ ⎟ ⎜ ⎟
⎜
⎜ 1 1 0 ⎟⎜ c1 ⎟ = ⎜ 1 ⎟
⎜ 1 0 1 ⎟⎜ c ⎟ ⎜ 0 ⎟
⎠...
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This note was uploaded on 01/07/2013 for the course 332 519 taught by Professor Wadetrappe during the Fall '12 term at Rutgers.
 Fall '12
 WadeTrappe

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