galois.FLFSR.to_galois_lfsr

galois.FLFSR.to_galois_lfsr() → GLFSR

Converts the Fibonacci LFSR to a Galois LFSR that produces the same output.

Returns¶: An equivalent Galois LFSR.

Examples¶

Create a Fibonacci LFSR with a given initial state.

In [1]: c = galois.primitive_poly(7, 4); c
Out[1]: Poly(x^4 + x^2 + 3x + 5, GF(7))

In [2]: fibonacci_lfsr = galois.FLFSR(c.reverse(), state=[1, 2, 3, 4])

In [3]: print(fibonacci_lfsr)
Fibonacci LFSR:
  field: GF(7)
  feedback_poly: 5x^4 + 3x^3 + x^2 + 1
  characteristic_poly: x^4 + x^2 + 3x + 5
  taps: [0 6 4 2]
  order: 4
  state: [1 2 3 4]
  initial_state: [1 2 3 4]

Convert the Fibonacci LFSR to an equivalent Galois LFSR. Notice the initial state is different.

In [4]: galois_lfsr = fibonacci_lfsr.to_galois_lfsr()

In [5]: print(galois_lfsr)
Galois LFSR:
  field: GF(7)
  feedback_poly: 5x^4 + 3x^3 + x^2 + 1
  characteristic_poly: x^4 + x^2 + 3x + 5
  taps: [2 4 6 0]
  order: 4
  state: [2 6 3 4]
  initial_state: [2 6 3 4]

Step both LFSRs and see that their output sequences are identical.

In [6]: fibonacci_lfsr.step(10)
Out[6]: GF([4, 3, 2, 1, 4, 6, 4, 5, 0, 2], order=7)

In [7]: galois_lfsr.step(10)
Out[7]: GF([4, 3, 2, 1, 4, 6, 4, 5, 0, 2], order=7)