# How to find output sequence for LFSR from its polynomial? [duplicate]

LFSR characterized by $p_2 = 1$, $p_1 = 0$, $p_0 = 1$.

I've computed that, the corresponding polynomial is $P(x) = x^3 + x^2 + 1$

What is the sequence generated from the initialization vector $s_2 = 1$, $s_1 = 0$, $s_0 = 0$?

• Just to clarify: How is this LFSR question related to cryptography as defined in our help center? – e-sushi Mar 31 '17 at 22:22
• And of course, the notation about LFSRs is so well standardized that everyone is supposed to understand what $p_2 = 1$, $p_1 = 0$, $p_0 = 1$, and initialization vector $s_2 = 1$, $s_1 = 0$, $s_0 = 0$ means. There's no such dichotomy as Galois and Fibonacci structure. No ambiguity about where the output is taken, and if the first output is an initial state bit or not. So there must be a single possible answer. – fgrieu Mar 31 '17 at 22:38

# Hint

I don't know what you mean by $p_2, p_1$ and $p_0$ but if your polynomial is $P(x) = x^3 + x^2 + 1$ then the associated Galois representation of the LFSR is as follow:

+---------------------------+-------------+
|                           |             |
|    +------+     +------+  |  +------+   |
|    |      |     |      |  v  |      |   |
+---->  S0  +----->  S1  +--+-->  S2  +-------> output
|      |     |      |     |      |
+------+     +------+     +------+


From this you should be able to determine the sequence as demanded.