Otherwise the LFSR will never leave this state, since the feedback function is linear. And yes, I said 2^16-1 instead of 2^16 because the zero state should never appear. So, if we have 16 bit registers, we'd want to have the LFSR pass through the 2^16-1 states before cycling back to the first one. For its study, the connections in an LFSR are usually represented as a polynomial and the properties such a polynomial needs to meet to achieve maximal period are analyzed.īasically, we need to get the LFSR to run through all its possible states before going back into the first one. The idea is to generate a stream of bits with the minimum repetition possible, i.e. So far, you probably have guessed that the main use of an LFSR in encryption systems is generating a series of pseudo-random bits to be used as a key stream in a stream cipher.
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