Understanding Cryptography by Christof Paar and Jan Pelzl - Chapter 2 Solutions - Ex2.5

- 2 mins

Exercise 2.5

We will now analyze a pseudorandom number sequence generated by a LFSR characterized by .

  1. What is the sequence generated from the initialization vector ?
  2. What is the sequence generated from the initialization vector ?
  3. How are the two sequences related?

Solution

This solution is verified as correct by the official Solutions for Odd-Numbered Questions manual.

This LFSR can be visualised as such:

LFSR

1. The sequence generated by is as follows:

Note: the final row is the same as the first, meaning it will loop infinitely.

2. The sequence generated by is as follows:

Note: the final row is the same as the first, meaning it will loop infinitely.

3. Since is part of the sequence for , its loop is exactly the same, but rotated back by three positions. Both of them give the same loop of states (which contains of all non-zero 3-bit binary numbers), but starting from whatever was chosen to initialise it.


Thomas Busby

Thomas Busby

I write about computing stuff

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