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Unformatted text preview: r feedback shift registers (LFSRs) are a fast method for
generating pseudo-random bits.
Output bits depend on previous output bits using a linear
The general linear recurrence is:
x n + m = c 0 x n + c1x n +1 + L + c m −1x n + m −1 (mod 2 ) where the initial values are x1 , x 2 , L , x m
Why would we want to do this?
– Its fast!
– A small key (coefficients and/or initial values) can generate
a key sequence with a large periodicity. LFSR, the BAD!!!
Why shouldn’t we use LFSR? Answer: WEAK security
LFSR succumbs easily to a known plaintext attack:
– A few bits of plaintext and the corresponding ciphertext and we
can solve for the recurrence relationship and generate all future
bits in the key sequence. How to do this evil deed?
1. First, get the corresponding key sequence. (How?) 2. We don’t know the length of the coefficient vector, so start
with m=2. Set up system of linear equations.
Solve linear equations for c-vector and then test to see if this
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- Fall '12