galois.GLFSR.to_fibonacci_lfsr

galois.GLFSR.to_fibonacci_lfsr() → FLFSR

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

Returns:¶: An equivalent Fibonacci LFSR.

Examples¶

Create a Galois 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]: galois_lfsr = galois.GLFSR(c.reverse(), state=[1, 2, 3, 4])

In [3]: 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: [1 2 3 4]
  initial_state: [1 2 3 4]

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

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

In [5]: 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: [0 5 3 4]
  initial_state: [0 5 3 4]

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

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

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