Linear Feedback Shift Register (LFSR) Key Stream Calculation

What is a Linear Feedback Shift Register (LFSR) and how is the key stream calculated?

A Linear Feedback Shift Register (LFSR) is a type of shift register whose input bit is a linear combination of its previous state. The key stream in an LFSR is generated by shifting the current state to the right and calculating the feedback bit based on certain taps. Given the first seven bits of the key stream as 1101001, what are the next three bits of this key stream?

Possible options:

011

101

110

100

001

Answer:

The next three bits of the key stream are 110.

To find the next three bits of the key stream, we need to determine the feedback function and perform the necessary shifts. Let's analyze the given key stream: 1101001

Since the LFSR has a degree of 3, it means it has three flip-flops. We can determine the feedback function by looking at the taps of the flip-flops. In this case, the taps are at positions 1 and 2 (counting from the right, starting at 1).

Now, let's perform the necessary shifts:

1. Shift the current state to the right: 1101001 -> 0110100

2. Calculate the feedback bit by XORing the tapped bits: 0 XOR 1 = 1

3. Append the feedback bit to the left of the shifted state: 1 0110100

4. Repeat the above steps two more times to find the next two bits:

- Shift the current state to the right: 1 0110100 -> 01 101001

- Calculate the feedback bit: 0 XOR 1 = 1

- Append the feedback bit: 1 01 101001

- Shift the current state to the right: 1 01 101001 -> 10 110100

- Calculate the feedback bit: 1 XOR 0 = 1

- Append the feedback bit: 1 10 110100

Therefore, the next three bits of the key stream are 110.

For more information on LFSR key stream calculations, you can refer to reliable sources.